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AuthorTitleYearJournal/ProceedingsReftypeDOI/URL
Bittner, B., Hatton, R. and Revzen, S. A Data-Driven Approach to Connection Modeling 2018 arXiv preprint  article URL 
BibTeX:
@article{bittner-2018-arxiv,
  author = {B Bittner, R Hatton, S Revzen},
  title = {A Data-Driven Approach to Connection Modeling},
  journal = {arXiv preprint},
  year = {2018},
  url = {http://arxiv.org/abs/1801.08190}
}
Bittner, B.A., Hatton, R.A. and Revzen, S. Geometrically Optimal Gaits: a Data-Driven Approach 2018 Nonlinear Dynamics
Vol. 94(3), pp. 1933-1948 
article DOI  
BibTeX:
@article{bittner-2018-gog,
  author = {Bittner, B A and Hatton, R A and Revzen, S},
  title = {Geometrically Optimal Gaits: a Data-Driven Approach},
  journal = {Nonlinear Dynamics},
  year = {2018},
  volume = {94},
  number = {3},
  pages = {1933--1948},
  doi = {https://doi.org/10.1007/s11071-018-4466-9}
}
Bittner, B., Hatton, R.L. and Revzen, S. Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems 2020 arxiv  article URL 
Abstract: The study of systems whose movement is both geometric and dissipative offers an opportunity to quickly both identify models and optimize motion. Here, the geometry indicates reduction of the dynamics by environmental homogeneity while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. In this work, we extend the tools of geometric system identification to "Shape-Underactuated Dissipative Systems (SUDS)" -- systems whose motions are kinematic, but whose actuation is restricted to a subset of the body shape coordinates. A large class of SUDS includes highly damped robots with series elastic actuators, and many soft robots. We validate the predictive quality of the models using simulations of a variety of viscous swimming systems. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs suggesting that, e.g., systems with soft pneumatic actuators or dielectric elastomers, could be controlled in this way. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.
BibTeX:
@article{bittner-2020-SUDS-arxiv,
  author = {B Bittner and R L Hatton and S Revzen},
  title = {Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems},
  journal = {arxiv},
  year = {2020},
  url = {https://arxiv.org/abs/2012.11064}
}
Burden, S., Revzen, S. and Sastry, S.S. Dimension reduction near periodic orbits of hybrid systems 2011 IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 6116 - 6121  article DOI  
Abstract: When the Poincare map associated with a periodic orbit of a hybrid
dynamical system has constant-rank iterates, there exists a constant-dimensional
invariant subsystem near the orbit which attracts all nearby trajectories
in finite time. This result shows that the long-term behavior of
a hybrid model with a large number of degrees-of-freedom may be governed
by a low-dimensional smooth dynamical system. The appearance of such
simplified models enables the translation of analytical tools from
smooth systems to the hybrid setting and provides a bridge between
the efforts of biologists and engineers studying legged locomotion.
BibTeX:
@article{burden-2011-drn,
  author = {S Burden and S Revzen and S S Sastry},
  title = {Dimension reduction near periodic orbits of hybrid systems},
  journal = {IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)},
  year = {2011},
  pages = {6116 -- 6121},
  doi = {https://doi.org/10.1109/CDC.2011.6160405}
}
Burden, S.A., Revzen, S. and Sastry, S.S. Model reduction near periodic orbits of hybrid dynamical systems 2013 arXiv preprint  article URL 
BibTeX:
@article{burden-2013-mrn-arxiv,
  author = {Burden, S A and Revzen, S and Sastry, S S},
  title = {Model reduction near periodic orbits of hybrid dynamical systems},
  journal = {arXiv preprint},
  year = {2013},
  url = {http://arxiv.org/abs/1308.4158}
}
Burden, S.A., Sastry, S.S., Koditschek, D.E. and Revzen, S. Event-selected vector field discontinuities yield piecewise-differentiable flows 2014 arXiv preprint  article URL 
BibTeX:
@article{burden-2014-event,
  author = {Burden, S A and Sastry, S S and Koditschek, D E and Revzen, S},
  title = {Event-selected vector field discontinuities yield piecewise-differentiable flows},
  journal = {arXiv preprint},
  year = {2014},
  url = {http://arxiv.org/abs/1407.1775}
}
Burden, S.A., Revzen, S. and Sastry, S.S. Model reduction near periodic orbits of hybrid dynamical systems 2015 IEEE Transactions on Automatic Control
Vol. 60(10), pp. 2626-2639 
article DOI  
Abstract: We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical system, nearby executions generically contract super exponentially to a constant-dimensional subsystem. Under a non-degeneracy condition on the rank deficiency of the associated Poincaré map, the contraction occurs in finite time regardless of the stability properties of the orbit. Hybrid transitions may be removed from the resulting subsystem via a topological quotient that admits a smooth structure to yield an equivalent smooth dynamical system. We demonstrate reduction of a high-dimensional underactuated mechanical model for terrestrial locomotion, assess structural stability of deadbeat controllers for rhythmic locomotion and manipulation, and derive a normal form for the stability basin of a hybrid oscillator. These applications illustrate the utility of our theoretical results for synthesis and analysis of feedback control laws for rhythmic hybrid behavior.
BibTeX:
@article{burden-2015-mrd,
  author = {Burden, S A and Revzen, S and Sastry, S S},
  title = {Model reduction near periodic orbits of hybrid dynamical systems},
  journal = {IEEE Transactions on Automatic Control},
  publisher = {IEEE},
  year = {2015},
  volume = {60},
  number = {10},
  pages = {2626--2639},
  doi = {https://doi.org/10.1109/TAC.2015.2411971}
}
Burden, S.A., Sastry, S.S., Koditschek, D.E. and Revzen, S. Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows 2016 SIAM Journal of Applied Dynamical Systems
Vol. 15(2), pp. 1227-1267 
article DOI  
Abstract: We study a class of discontinuous vector fields that arise in biomechanics
and neuroscience. Under the conditions that (i) the vector field's
discontinuities are locally confined to a finite number of smooth
submanifolds and (ii) the vector field is transverse to these surfaces
in an appropriate sense, we show that the vector field yields a well-defined
flow that is Lipschitz continuous and piecewise-differentiable. This
implies that although the flow is not classically differentiable,
nevertheless it admits a first--order approximation (known as a Bouligand
derivative). We exploit this first-order approximation to infer existence
of piecewise-differentiable impact maps and assess structural stability
of the flow
BibTeX:
@article{Burden-2015-multi,
  author = {Burden, S A and Sastry, S S and Koditschek, D E and Revzen, S},
  title = {Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows},
  journal = {SIAM Journal of Applied Dynamical Systems},
  year = {2016},
  volume = {15},
  number = {2},
  pages = {1227--1267},
  doi = {https://doi.org/10.1137/15M1016588}
}
Council, G. and Revzen, S. Fast Recovery of Robot Behaviors 2020 arxivarxiv:2005.00506  article URL 
Abstract: If robots are ever to achieve autonomous motion comparable to that exhibited by animals, they must acquire the ability to quickly recover motor behaviors when damage, malfunction, or environmental conditions compromise their ability to move effectively. We present an approach which allowed our robots and simulated robots to recover high-degree of freedom motor behaviors within a few dozen attempts. Our approach employs a behavior specification expressing the desired behaviors in terms as rank ordered differential constraints. We show how factoring these constraints through an encoding templates produces a recipe for generalizing a previously optimized behavior to new circumstances in a form amenable to rapid learning. We further illustrate that adequate constraints are generically easy to determine in data-driven contexts. As illustration, we demonstrate our recovery approach on a physical 7 DOF hexapod robot, as well as a simulation of a 6 DOF 2D kinematic mechanism. In both cases we recovered a behavior functionally indistinguishable from the previously optimized motion.
BibTeX:
@article{council-2020-FRRB-arxiv,
  author = {G Council and S Revzen},
  title = {Fast Recovery of Robot Behaviors},
  journal = {arxiv},
  year = {2020},
  url = {https://arxiv.org/abs/2005.00506}
}
Council, G., Revzen, S. and Burden, S.A. Representing and computing the B-derivative of an EC^r vector field's PC^r flow 2021 arxiv  article URL 
Abstract: This paper concerns the first-order approximation of the piecewise-differentiable flow generated by a class of nonsmooth vector fields.
Specifically, we represent and compute the Bouligand (or B-)derivative of the piecewise-C^r flow generated by an event-selected C^r vector field.
Our results are remarkably efficient: although there are factorially many "pieces" of the desired derivative, we provide an algorithm that evaluates its
action on a given tangent vector using polynomial time and space, and verify the algorithm's correctness by deriving a representation for the
B-derivative that requires "only" exponential time and space to construct. We apply our methods in two classes of illustrative examples:
piecewise-constant vector fields and mechanical systems subject to unilateral constraints.
BibTeX:
@article{council2021representing,
  author = {G Council and S Revzen and S A Burden},
  title = {Representing and computing the B-derivative of an EC^r vector field's PC^r flow},
  journal = {arxiv},
  year = {2021},
  url = {https://arxiv.org/abs/2102.10702}
}
Eldering, J., Kvalheim, M. and Revzen, S. Global linearization and fiber bundle structure of invariant manifolds 2018 Nonlinearity
Vol. 31(9), pp. 4202 
article DOI  
BibTeX:
@article{eldering-2018-glfb,
  author = {Eldering, J and Kvalheim, M and Revzen, S},
  title = {Global linearization and fiber bundle structure of invariant manifolds},
  journal = {Nonlinearity},
  year = {2018},
  volume = {31},
  number = {9},
  pages = {4202},
  doi = {https://doi.org/10.1088/1361-6544/aaca8d}
}
Fitzner, I., Sun, Y., Sachdeva, V. and Revzen, S. Rapidly Prototyping Robots: Using Plates and Reinforced Flexures 2017 IEEE Robotics Automation Magazine
Vol. 24(1), pp. 41-47 
article DOI  
Abstract: In this article, we present plate and reinforced flexure (PARF) fabrication, an inexpensive, rapid fabrication technique for robot mechanisms inspired by the smart composite manufacturing (SCM) used in VelociRoACH and RoboBee designs. PARF extends SCM to larger sizes at low costs. We used PARF to develop a meter-scale hexapedal robot, BigANT, a design we made publicly available. Manufacture of BigANT requires minimal tooling-foam board, tape, a saw blade, and a knife; the chassis costs <; US$20 in materials, encouraging its use in research, education, and recreation. We present a study of PARF joints, showing several variations spanning a range of fabrication effort and mechanical properties. PARF promises the possibility of quickly and inexpensively building robot mechanisms for tasks as the requirements arise, rather than relying on prefabricated robot bodies.
BibTeX:
@article{Fitzner-2017-PARF,
  author = {I Fitzner and Y Sun and V Sachdeva and S Revzen},
  title = {Rapidly Prototyping Robots: Using Plates and Reinforced Flexures},
  journal = {IEEE Robotics Automation Magazine},
  year = {2017},
  volume = {24},
  number = {1},
  pages = {41-47},
  doi = {https://doi.org/10.1109/MRA.2016.2639058}
}
Jusufi, A., Goldman, D.I., Revzen, S. and Full, R.J. Active tails enhance arboreal acrobatics in geckos 2008 PNAS
Vol. 105(11), pp. 4215-4219 
article DOI  
Abstract: Geckos are nature's elite climbers. Their remarkable climbing feats
have been attributed to specialized feet with hairy toes that uncurl
and peel in milliseconds. Here, we report that the secret to the
gecko's arboreal acrobatics includes an active tail. We examine the
tail's role during rapid climbing, aerial descent, and gliding. We
show that a gecko's tail functions as an emergency fifth leg to prevent
falling during rapid climbing. A response initiated by slipping causes
the tail tip to push against the vertical surface, thereby preventing
pitch-back of the head and upper body. When pitch-back cannot be
prevented, geckos avoid falling by placing their tail in a posture
similar to a bicycle's kickstand. Should a gecko fall with its back
to the ground, a swing of its tail induces the most rapid, zero-angular
momentum air-righting response yet measured. Once righted to a sprawled
gliding posture, circular tail movements control yaw and pitch as
the gecko descends. Our results suggest that large, active tails
can function as effective control appendages. These results have
provided biological inspiration for the design of an active tail
on a climbing robot, and we anticipate their use in small, unmanned
gliding vehicles and multisegment spacecraft.
BibTeX:
@article{jusufi-2008-PNAS,
  author = {Jusufi, A and Goldman, D I and Revzen, S and Full, R J},
  title = {Active tails enhance arboreal acrobatics in geckos},
  journal = {PNAS},
  year = {2008},
  volume = {105},
  number = {11},
  pages = {4215-4219},
  doi = {https://doi.org/10.1073/pnas.0711944105}
}
Kaspari, M., Clay, N.A., Lucas, J.A., Revzen, S., Kay, A.D. and Yanoviak, S.P. Thermal adaptation and phosphorus shape thermal performance in an assemblage of rainforest ants 2015 Ecology
Vol. 97(4), pp. 1038-1047 
article DOI  
Abstract: We studied the Thermal Performance Curves (TPCs) of 87 species of rainforest ants and found support for both the Thermal Adaptation and Phosphorus-Tolerance hypotheses. TPCs relate a fitness proxy (here, worker speed) to environmental temperature. Thermal Adaptation posits that thermal generalists (ants with flatter, broader TPCs) are favored in the hotter, more variable tropical canopy compared to the cooler, less variable litter below. As predicted, species nesting in the forest canopy 1) had running speeds less sensitive to temperature; 2) ran over a greater range of temperatures; and 3) ran at lower maximum speeds. Tradeoffs between tolerance and maximum performance are often invoked for constraining the evolution of thermal generalists. There was no evidence that ant species traded off thermal tolerance for maximum speed, however. Phosphorus-Tolerance is a second mechanism for generating ectotherms able to tolerate thermal extremes. It posits that ants active at high temperatures invest in P-rich machinery to buffer their metabolism against thermal extremes. Phosphorus content in ant tissue varied three-fold, and as predicted, temperature sensitivity was lower and thermal range was higher in P-rich species. Combined, we show how the vertical distribution of hot and variable vs. cooler and stable microclimates in a single forest contribute to a diversity of TPCs and suggest that a widely varying P stoichiometry among these ants may drive some of these differences.
BibTeX:
@article{kaspari-2015-thermal,
  author = {Kaspari, M and Clay, N A and Lucas, J A and Revzen, S and Kay, A D and Yanoviak, S P},
  title = {Thermal adaptation and phosphorus shape thermal performance in an assemblage of rainforest ants},
  journal = {Ecology},
  publisher = {Eco Soc America},
  year = {2015},
  volume = {97},
  number = {4},
  pages = {1038-1047},
  doi = {https://doi.org/10.1890/15-1225.1}
}
Kvalheim, M. and Revzen, S. Reverse-engineering invariant manifolds with asymptotic phase 2016 arXiv preprint  article URL 
Abstract: We present a recipe for rendering a submanifold normally hyperbolic and invariant within a stability basin. The construction includes the ability to choose the asymptotic phase map. We are motivated by the notion of "templates and anchors" -- the biomechanical observation that animal motions are often governed by low dimensional dynamics -- and the growing applications in robotics which desire means for making such biologically derived templates govern the dynamics of robots. Our approach is fairly universal, in the sense that a broad range of model reduction constructions must be normally hyperbolic if they are robust, and a broad range of such normally hyperbolic systems can be produces from our construction.
BibTeX:
@article{kvalheim-2016-reverse,
  author = {Kvalheim, Matthew and Revzen, Shai},
  title = {Reverse-engineering invariant manifolds with asymptotic phase},
  journal = {arXiv preprint},
  year = {2016},
  url = {https://arxiv.org/abs/1608.08442}
}
Kvalheim, M.D. and Revzen, S. Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits 2019 arXiv preprint arXiv:1911.11996  article URL 
Abstract: We consider C^1 dynamical systems having a globally attracting hyperbolic fixed point or periodic orbit and prove existence and uniqueness results for C^k,α_loc globally defined linearizing semiconjugacies, of
which Koopman eigenfunctions are a special case. Our main results both generalize and sharpen Sternberg’s
C^k linearization theorem for hyperbolic sinks, and in particular our corollaries include uniqueness statements for Sternberg linearizations and Floquet normal forms. Additional corollaries include existence and uniqueness results for C^k,α_loc Koopman eigenfunctions, including a complete classification of C^∞ eigenfunctions assuming a C^∞ dynamical system with semisimple and nonresonant linearization. We give an intrinsic definition of “principal Koopman eigenfunctions” which generalizes the definition of Mohr and Mezić for linear systems, and which includes the notions of “isostables” and “isostable coordinates” appearing in work by Ermentrout, Mauroy, Mezić, Moehlis, Wilson, and others. Our main results yield existence and uniqueness theorems for the principal eigenfunctions and isostable coordinates and also show, e.g., that the (a priori non-unique) “pullback algebra” defined in [MM16b] is unique under certain conditions. We also discuss the limit used to define the “faster” isostable coordinates in [WE18, MWMM19] in light of our main results.
BibTeX:
@article{kvalheim2019existence,
  author = {Kvalheim, Matthew D and Revzen, Shai},
  title = {Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits},
  journal = {arXiv preprint arXiv:1911.11996},
  year = {2019},
  url = {https://arxiv.org/abs/1911.11996}
}
Kvalheim, M., Bittner, B. and Revzen, S Gait modeling and optimization for the perturbed Stokes regime 2019 J Nonlinear Dynamics  article DOI  
Abstract: Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the “Stokesian” (viscous; zero Reynolds number) limit, the motion is governed by a reduced-order “connection” model that describes how body shape change produces motion for the body frame with respect to the world. In the “perturbed Stokes regime” where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer linear in shape change rate. We derive this model using results from singular perturbation theory and the theory of noncompact normally hyperbolic invariant manifolds. Using the theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a “gait”) directly from observational data of shape and body motion. This extends our previous work which assumed kinematic “connection” models. To compare the old and new algorithms, we analyze simulated swimmers over a range of inertia-to-damping ratios. Our new class of models performs well on the Stokesian regime and over several orders of magnitude outside it into the perturbed Stokes regime, where it gives significantly improved prediction accuracy compared to previous work. In addition to algorithmic improvements, we thereby present a new class of models that is of independent interest. Their application to data-driven modeling improves our ability to study the optimality of animal gaits and our ability to use hardware-in-the-loop optimization to produce gaits for robots.
BibTeX:
@article{Kvalheim2019gmpsr,
  author = {Kvalheim, M and Bittner, B and Revzen S},
  title = {Gait modeling and optimization for the perturbed Stokes regime},
  journal = {J Nonlinear Dynamics},
  year = {2019},
  doi = {https://doi.org/10.1007/s11071-019-05121-3}
}
Kvalheim, M.D., Hong, D. and revzen , S. Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits 2020 arxiv  article URL 
Abstract: Our recent work established existence and uniqueness results for C^k,α_loc globally defined linearizing semiconjugacies for C^1 flows having a globally attracting hyperbolic fixed point or periodic orbit (Kvalheim and Revzen, 2019). Applications include (i) improvements, such as uniqueness statements, for the Sternberg linearization and Floquet normal form theorems; (ii) results concerning the existence, uniqueness, classification, and convergence of various quantities appearing in the "applied Koopmanism" literature, such as principal eigenfunctions, isostables, and Laplace averages.
In this work we give an exposition of some of these results, with an emphasis on the Koopmanism applications, and consider their broadness of applicability. In particular we show that, for "almost all" C^∞ flows having a globally attracting hyperbolic fixed point or periodic orbit, the C^∞ Koopman eigenfunctions can be completely classified, generalizing a result known for analytic systems. For such systems, every C^∞ eigenfunction is uniquely determined by its eigenvalue modulo scalar multiplication.
BibTeX:
@article{kvalheim-2020-genericKoop-arxiv,
  author = {M D Kvalheim and D Hong and S revzen},
  title = {Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits},
  journal = {arxiv},
  year = {2020},
  url = {https://arxiv.org/abs/2010.04008}
}
Maus, H.-M., Revzen, S., Guckenheimer, J.M., Ludwig, C., Reger, J. and Seyfarth, A. Constructing predictive models of human running 2015 Journal of The Royal Society Interface
Vol. 12(103), pp. 2014.0899 
article DOI  
BibTeX:
@article{maus-2015-constructing,
  author = {Maus, H-M and Revzen, S and Guckenheimer, J M and Ludwig, C and Reger, J and Seyfarth, A},
  title = {Constructing predictive models of human running},
  journal = {Journal of The Royal Society Interface},
  publisher = {The Royal Society},
  year = {2015},
  volume = {12},
  number = {103},
  pages = {2014.0899},
  doi = {https://doi.org/10.1098/rsif.2014.0899}
}
Revzen, S. and Guckenheimer, J.M. Estimating the phase of synchronized oscillators 2008 Physical Review E
Vol. 78(5), pp. 051907 
article DOI  
Abstract: The state of a collection of phase-locked oscillators is determined
by a single phase variable or cyclic coordinate. This paper presents
a computational method, Phaser, for estimating the phase of phase-locked
oscillators from limited amounts of multivariate data in the presence
of noise and measurement errors. Measurements are assumed to be a
collection of multidimensional time series. Each series consists
of several cycles of the same or similar systems. The oscillators
within each system are not assumed to be identical. Using measurements
of the noise covariance for the multivariate input, data from the
individual oscillators in the system are combined to reduce the variance
of phase estimates for the whole system. The efficacy of the algorithm
is demonstrated on experimental and model data from biomechanics
of cockroach running and on simulated oscillators with varying levels
of noise.
BibTeX:
@article{revzen-2008-phaser,
  author = {S Revzen and J M Guckenheimer},
  title = {Estimating the phase of synchronized oscillators},
  journal = {Physical Review E},
  year = {2008},
  volume = {78},
  number = {5},
  pages = {051907},
  doi = {https://doi.org/10.1103/PhysRevE.78.051907}
}
Revzen, S. and Guckenheimer, J.M. Finding the dimension of slow dynamics in a rhythmic system 2012 Journal of The Royal Society Interface
Vol. 9(70), pp. 957-971 
article DOI  
BibTeX:
@article{revzen-2010-fdsd,
  author = {Revzen, S and Guckenheimer, J M},
  title = {Finding the dimension of slow dynamics in a rhythmic system},
  journal = {Journal of The Royal Society Interface},
  year = {2012},
  volume = {9},
  number = {70},
  pages = {957-971},
  doi = {https://doi.org/10.1098/rsif.2011.0431}
}
Revzen, S., Burden, S.A., Moore, T.Y., Mongeau, J.-M. and Full, R.J. Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches 2013 Biological Cybernetics
Vol. 107(2), pp. 179-200 
article DOI  
Abstract: Instantaneous kinematic phase calculation allows the development of
reduced-order oscillator models useful in generating hypotheses of
neuromechanical control. When perturbed, changes in instantaneous
kinematic phase and frequency of rhythmic movements can provide details
of movement and evidence for neural feedback to a system-level neural
oscillator with a time resolution not possible with traditional approaches.
We elicited an escape response in cockroaches (Blaberus discoidalis)
that ran onto a movable cart accelerated laterally with respect to
the animals’ motion causing a perturbation. The specific impulse
imposed on animals (0.50+/-0.04 m/s; mean, SD) was nearly twice their
forward speed (0.25+/- 0.06 m/s) . Instantaneous residual phase computed
from kinematic phase remained constant for 110 ms after the onset
of perturbation, but then decreased representing a decrease in stride
frequency. Results from direct muscle action potential recordings
supported kinematic phase results in showing that recovery begins
with self-stabilizing mechanical feedback followed by neural feedback
to an abstracted neural oscillator or central pattern generator.
Trials fell into two classes of forward velocity changes, while exhibiting
statistically indistinguishable frequency changes. Animals pulled
away from the side with front and hind legs of the tripod in stance
recovered heading within 300 ms, whereas animals that only had a
middle leg of the tripod resisting the pull did not recover within
this period. Animals with eight or more legs might be more robust
to lateral perturbations than hexapods.
BibTeX:
@article{revzen-2013-ikp,
  author = {Revzen, S and Burden, S A and Moore, T Y and Mongeau, J-M and Full, R J},
  title = {Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches},
  journal = {Biological Cybernetics},
  publisher = {Springer-Verlag},
  year = {2013},
  volume = {107},
  number = {2},
  pages = {179-200},
  doi = {https://doi.org/10.1007/s00422-012-0545-z}
}
Revzen, S. and Burden, S.A. Computing the Bouligand derivative of a class of piecewise-differentiable flows 2016 arXiv preprint  article URL 
BibTeX:
@article{revzen-2016-computing,
  author = {Revzen, S and Burden, S A},
  title = {Computing the Bouligand derivative of a class of piecewise-differentiable flows},
  journal = {arXiv preprint},
  year = {2016},
  url = {http://arxiv.org/abs/1612.02763}
}
Revzen, S. and Koditschek, D.E. Why we need more degrees of freedom 2017 Procedia IUTAM
Vol. 20, pp. 89 - 93 
article DOI  
Abstract: Mechanical systems encountered in biology typically have many more degrees of freedom (DOF) than the 6 DOF required to manipulate a body in space. Even the relatively rigid arthropods and crustaceans have at least 5 DOF in each limb; tentacles and human hands have many more. Robotics engineers are routinely required to choose the number of DOF in a robot in the early design stages, potentially limiting the robot's future uses. We theoretically motivate the definition of “mechanical versatility” as the ability of a mechanical system to express distinct static configurations and switch among them rapidly. Requiring versatility and assuming that the systems are power and force limited, and must furthermore resist finite energy environmental disturbances to their state, we show that such multiuse 1 mechanical systems have a lower bound on the number of DOF they require. For bio-mechanics, this suggests which organs and organisms will be driven to become more complex mechanically by indicating domains where higher DOF systems would intrinsically out-compete lower DOF systems.
BibTeX:
@article{revzen-2017-dof,
  author = {S Revzen and D E Koditschek},
  title = {Why we need more degrees of freedom},
  journal = {Procedia IUTAM},
  year = {2017},
  volume = {20},
  pages = {89 - 93},
  note = {24th International Congress of Theoretical and Applied Mechanics},
  doi = {https://doi.org/10.1016/j.piutam.2017.03.012}
}
Spence, A.J., Revzen, S., Seipel, J., Mullens, C. and Full, R.J. Insects running on elastic surfaces 2010 Journal of Experimental Biology
Vol. 213(11), pp. 1907-1920 
article DOI  
Abstract: In nature, cockroaches run rapidly over complex terrain such as leaf litter.
These substrates are rarely rigid, and are frequently very compliant. Whether and how compliant surfaces change the dynamics of rapid insect locomotion has not been investigated to date; largely due to experimental limitations.
Here we test the hypothesis that a running insect can maintain average forward speed over an extremely soft elastic surface (10 N/m) equal to 2/3 of its virtual leg stiffness (15 N/m).
Cockroaches (Blaberus discoidalis) running from a rigid surface onto an elastic surface were able to maintain forward speed (39.6 +/- 0.7 cm/s, rigid substrate, versus 43.3 +/- 1.1 cm/s, elastic substrate; p = 0.0064).
Step frequency was unchanged (25.5 +/- 0.3 steps/sec, rigid surface, versus 26.1 +/- 0.5 steps/sec, elastic surface; p = 0.28).
To uncover the mechanism we measured the animal's COM dynamics using
a novel miniature backpack, consisting chiefly of a 3-axis MEMs accelerometer attached very near the COM.
Vertical acceleration of the COM on the elastic surface had smaller peak-to-peak amplitudes (13.95 +/- 0.41 m/s2, rigid, vs. 10.07 +/- 0.50 m/s2 on the elastic surface; p < 0.0001).
The observed change in COM acceleration over an elastic surface requires no change in effective stiffness when duty factor and ground stiffness are taken into account.
Due to the lowering of the COM towards the elastic surface the swing leg lands earlier and increases the period of double support.
A simple feedforward control model explains the experimental result and provides one plausible model mechanism.
We find no evidence for active neural control of effective leg stiffness.
BibTeX:
@article{spence-2009-JEB,
  author = {A J Spence and S Revzen and J Seipel and C Mullens and R J Full},
  title = {Insects running on elastic surfaces},
  journal = {Journal of Experimental Biology},
  year = {2010},
  volume = {213},
  number = {11},
  pages = {1907--1920},
  doi = {https://doi.org/10.1242/jeb.042515}
}
Sundaram, S., Revzen, S. and Pappas, G. Linear iterative strategies to identify and overcome malicious links in wireless networks 2012 Automatica
Vol. 48(11), pp. 2894-2901 
article DOI  
Abstract: We consider a network where every node has a value that we wish to
disseminate to all other nodes. A certain number of communication
links between nodes are allowed to be under the control of an attacker
who maliciously chooses the messages carried by these links. We study
linear iterative strategies that disseminate information despite
such attacks. In such strategies, at each time-step each node in
the network broadcasts a value to its neighbors that is a linear
combination of its previous value and the values received from its
neighbors. As long the number of incoming links to any node and the
total number of other nodes with incoming malicious links is no greater
than f , we show that linear strategies are almost always resilient
to malicious behavior provided that vertex-connectivity of the network
is at least 2f + 1. Furthermore, we show that each node can identify
the exact set of malicious links that directly enter that node, and
can communicate this information to the other nodes via the linear
strategy.
BibTeX:
@article{sundaram-2011-lis,
  author = {S Sundaram and S Revzen and G Pappas},
  title = {Linear iterative strategies to identify and overcome malicious links in wireless networks},
  journal = {Automatica},
  year = {2012},
  volume = {48},
  number = {11},
  pages = {2894-2901},
  doi = {https://doi.org/10.1016/j.automatica.2012.06.072}
}
White, P.J., Revzen, S., Thorne, C.E. and Yim, M. A general stiffness model for programmable matter and modular robotic structures 2011 Robotica
Vol. 29(01), pp. 103-121 
article DOI  
Abstract: The fields of modular reconfigurable robotics and programmable matter
study how to compose functionally useful systems from configurations
of modules. In addition to the external shape of a module configuration,
the internal arrangement of modules and bonds between them can greatly
impact functionally relevant mechanical properties such as load bearing
ability. A fast method to evaluate the mechanical property aids the
search for an arrangement of modules achieving a desired mechanical
property as the space of possible configurations grows combinatorially.
We present a fast approximate method where the bonds between modules
are represented with stiffness matrices that are general enough to
represent a wide variety of systems and follows the natural modular
decomposition of the system. The method includes nonlinear modeling
such as anisotropic bonds and properties that vary as components
flex. We show that the arrangement of two types of bonds within a
programmable matter systems enables programming the apparent elasticity
of the structure. We also present a method to experimentally determine
the stiffness matrix for chain style reconfigurable robots. The efficacy
of applying the method is demonstrated on the CKBot modular robot
and two programmable matter systems: the Rubik's snake folding chain
toy and a right angle tetrahedron chain called RATChET7mm. By allowing
the design space to be rapidly explored we open the door to optimizing
modular structures for desired mechanical properties such as enhanced
load bearing and robustness.
BibTeX:
@article{white-2010-stiffness,
  author = {P J White and S Revzen and C E Thorne and M Yim},
  title = {A general stiffness model for programmable matter and modular robotic structures},
  journal = {Robotica},
  publisher = {Cambridge Univ Press},
  year = {2011},
  volume = {29},
  number = {01},
  pages = {103--121},
  doi = {https://doi.org/10.1017/S0263574710000743}
}
Wilshin, S., Reeve, M.A., Haynes, G.C., Revzen, S., Koditschek, D.E. and Spence, A.J. Longitudinal quasi-static stability predicts changes in dog gait on rough terrain 2017 Journal of Experimental Biology
Vol. 220(10), pp. 1864-1874 
article DOI  
Abstract: Legged animals utilize gait selection to move effectively and must recover from environmental perturbations. We show that on rough terrain, domestic dogs, Canis lupus familiaris, spend more time in longitudinal quasi-statically stable patterns of movement. Here, longitudinal refers to the rostro-caudal axis. We used an existing model in the literature to quantify the longitudinal quasi-static stability of gaits neighbouring the walk, and found that trot-like gaits are more stable. We thus hypothesized that when perturbed, the rate of return to a stable gait would depend on the direction of perturbation, such that perturbations towards less quasi-statically stable patterns of movement would be more rapid than those towards more stable patterns of movement. The net result of this would be greater time spent in longitudinally quasi-statically stable patterns of movement. Limb movement patterns in which diagonal limbs were more synchronized (those more like a trot) have higher longitudinal quasi-static stability. We therefore predicted that as dogs explored possible limb configurations on rough terrain at walking speeds, the walk would shift towards trot. We gathered experimental data quantifying dog gait when perturbed by rough terrain and confirmed this prediction using GPS and inertial sensors (n=6, P&lt;0.05). By formulating gaits as trajectories on the n-torus we are able to make tractable the analysis of gait similarity. These methods can be applied in a comparative study of gait control which will inform the ultimate role of the constraints and costs impacting locomotion, and have applications in diagnostic procedures for gait abnormalities, and in the development of agile legged robots.
BibTeX:
@article{Wilshin-2017-lqss,
  author = {Wilshin, S and Reeve, M A and Haynes, G C and Revzen, S and Koditschek, D E and Spence, A J},
  title = {Longitudinal quasi-static stability predicts changes in dog gait on rough terrain},
  journal = {Journal of Experimental Biology},
  publisher = {The Company of Biologists Ltd},
  year = {2017},
  volume = {220},
  number = {10},
  pages = {1864--1874},
  doi = {https://doi.org/10.1242/jeb.149112}
}
Wilshin, S., Haynes, G.C., Porteous, J., Koditschek, D.E., Revzen, S. and Spence, A.J. Morphology and the gradient of a symmetric potential predict gait transitions of dogs 2017 Biological Cybernetics
Vol. 111(3), pp. 269-277 
article DOI  
Abstract: Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a 22% increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was 1700% larger. This shift is related to (linear regression, n=5, p=0.0328) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models.
BibTeX:
@article{Wilshin-2017-mgsp,
  author = {Wilshin, S and Haynes, G C and Porteous, J and Koditschek, D E and Revzen, S and Spence, A J},
  title = {Morphology and the gradient of a symmetric potential predict gait transitions of dogs},
  journal = {Biological Cybernetics},
  year = {2017},
  volume = {111},
  number = {3},
  pages = {269--277},
  doi = {https://doi.org/10.1007/s00422-017-0721-2}
}
Wu, Z., Zhao, D. and Revzen, S. Coulomb Friction Crawling Model Yields Linear Force--Velocity Profile 2019 J Applied Mechanics
Vol. 86(5) 
article DOI  
Abstract: Conventional wisdom would have it that moving mechanical systems that dissipate energy by Coulomb friction have no relationship between force and average speed. One could argue that the work done by friction is constant per unit of distance travelled, and if propulsion forces exceed friction, the net work is positive, and the system accumulates kinetic energy without bound. We present a minimalistic model for legged propulsion with slipping under Coulomb friction, scaled to parameters representative of single kilogram robots and animals. Our model, amenable to exact solutions, exhibits nearly linear (R2 > 0.96) relationships between actuator force and average speed over its entire range of parameters, and in both motion regimes, it supports. This suggests that the interactions inherent in multilegged locomotion may lead to governing equations more reminiscent of viscous friction than would be immediately obvious.
BibTeX:
@article{wu2019coulomb,
  author = {Wu, Ziyou and Zhao, Dan and Revzen, Shai},
  title = {Coulomb Friction Crawling Model Yields Linear Force--Velocity Profile},
  journal = {J Applied Mechanics},
  publisher = {American Society of Mechanical Engineers Digital Collection},
  year = {2019},
  volume = {86},
  number = {5},
  doi = {https://doi.org/10.1115/1.4042696}
}
Zhao, D. and Revzen, S. Multi-legged steering and slipping with low DoF hexapod robots 2020 Bioinspiration & biomimetics
Vol. 15(4), pp. 045001 
article DOI  
Abstract: Thanks to their sprawled posture and multi-legged support, stability is not as hard to achieve for hexapedal robots as it is for bipeds and quadrupeds. A key engineering challenge with hexapods has been to produce insect-like agility and maneuverability, of which steering is an essential part. However, the mechanisms of multi-legged steering are not always clear, especially for robots with underactuated legs. Here we propose a formal definition of steering, and show why steering is difficult for robots with 6 or more underactuated legs. We show that for many of these robots, steering is impossible without slipping, and present experimental results which demonstrate the importance of allowing for slipping to occur intentionally when optimizing steering ability. Our results suggest that a non-holonomic multi-legged slipping model might be more appropriate than dynamic models for representing such robots, and that conventional non-slip contact models might miss significant parts of the performance envelope.
BibTeX:
@article{zhao-2020-steeringSlipping,
  author = {D Zhao and S Revzen},
  title = {Multi-legged steering and slipping with low DoF hexapod robots},
  journal = {Bioinspiration & biomimetics},
  year = {2020},
  volume = {15},
  number = {4},
  pages = {045001},
  doi = {https://doi.org/10.1088/1748-3190/ab84c0}
}
Anderson, M., McLaughlin, T. and Revzen, S. Serial Elastic versus Parallel Elastic Actuators in Hopping 2020 (513)Dynamic Walking  conference URL 
Abstract: https://www.seas.upenn.edu/ posa/DynamicWalking2020/750-1140-1-RV.pdf
BibTeX:
@conference{anderson-2020-dw,
  author = {M Anderson, T McLaughlin, S Revzen},
  title = {Serial Elastic versus Parallel Elastic Actuators in Hopping},
  booktitle = {Dynamic Walking},
  year = {2020},
  number = {513},
  url = {https://www.seas.upenn.edu/ posa/DynamicWalking2020/750-1140-1-RVp.pdf}
}
Bittner, B. and Revzen, S. Geometric Insights for Data-Driven Gait Analysis 2017 IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology  conference URL 
BibTeX:
@conference{bittner-2017-iros,
  author = {Bittner, B and Revzen, S},
  title = {Geometric Insights for Data-Driven Gait Analysis},
  booktitle = {IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology},
  year = {2017},
  url = {http://gravishlab.ucsd.edu/iros2017/posters/bittner_revzen_iros_2017.pdf}
}
Bittner, B. and Revzen, S. The Locality of Data-Driven Models 2018 Dynamic Walking  conference  
Abstract: Data-driven modeling of gaits allows for the fast generation of predictive motion models from experimental data. An important consideration is the locality of these models. In what state space of the robot do data-driven models maintain predictive quality? We present our approach to measuring this notion of locality.
BibTeX:
@conference{bittner-2018-dw-lddm,
  author = {B Bittner and S Revzen},
  title = {The Locality of Data-Driven Models},
  booktitle = {Dynamic Walking},
  year = {2018}
}
Bittner, B. and Revzen, S. What do nematode swimming gaits optimize? 2018 Yearly Meeting of the Society for Integrative and Comparative Biology  conference  
Abstract: Work on a variety of organisms suggests that at moderate to high speeds animals can select their gaits for many goals, optimizing the cost of transport, speed, or chances of avoiding injury. Here we examine the motion of the nematode Caenorhabditis elegans using a newly developed geometric gait optimization tool. For animals operating in friction dominated regimes, such as viscous swimming, the locomotion is governed by a "connection" as used in the theory of geometric mechanics. By combining tools of kinematic phase analysis with those of geometric mechanics, our gait optimization tool models the connection governing a gait, allowing the computer to climb the gradient of goal functions such as the cost of transport. Using swimming data kindly provided by the Penn Complex Fluids Lab, we validated a Purcell swimming model and discovered that its moment equation contributed little (< 1 per cent) to the motion per cycle. Using a simplified model absent the moment equation, we optimized gaits for extremal motion (maximum displacement per cycle) and for cost of transport, using the animals' observed motion as the initial condition. We classified the resulting gaits by the mean time derivative of absolute curvature, and by the mean power. This gave 4.2+/-.27 [rad/mms] and 74.+/-12. [fW] for the animals, falling close to the 5.6 [rad/mms] and 15. [fW] of the optimal cost of transport gait, and further away from the 11. [rad/mms] and 270. [fW] of the extremal gait. We conclude that these nematodes motions are consistent with cost of transport having a significant weight in their choice of gait. Although unused here, our tool is model free, and can model the connection from motion captured gait data. This work may further illuminate how animals select their locomotor patterns and allow hypotheses of optimality to be rapidly tested.
BibTeX:
@conference{bittner-2018-sicb-wns,
  author = {B Bittner and S Revzen},
  title = {What do nematode swimming gaits optimize?},
  booktitle = {Yearly Meeting of the Society for Integrative and Comparative Biology},
  year = {2018}
}
Bittner, B. and Revzen, S. Optimizing Gaits for Coverage on Lie Groups 2019 (513)Dynamic Walking  conference URL 
Abstract: Individual performance criteria, such as robustness and efficiency, often drive behavior selection in mobile robotic platforms. However, navigational capabilities can rely heavily on the coordination of all behaviors available to the robot, rather than the performance of one behavior. Here, we studied how a collection of availabile gaits (cyclic internal motions) can be related to the variability and density of external motions that a system can achieve. We attempted to capture this capability, termed ''coverage'', with an associative fast-to-compute cost function that can be used to simultaneously optimize a collection of gaits. The cost function can be weighted such that users may specify the importance of various classes of external motions. A resulting optimization framework produced three gaits for a 3-link Purcell swimmer, locally maximizing coverage on the space of planar rigid body motions.
BibTeX:
@conference{Bittner2019,
  author = {B Bittner and S Revzen},
  title = {Optimizing Gaits for Coverage on Lie Groups},
  booktitle = {Dynamic Walking},
  year = {2019},
  number = {513},
  url = {https://docs.google.com/document/d/155IGklc5VWjCga3UaZyJ66UeFiV2_94IlAl5AmnqK7Y/view}
}
Bittner, B. and Revzen, S. Optimizing Gaits for Coverage on Lie Groups 2019 Dynamic Walking  conference URL 
Abstract: Individual performance criteria, such as robustness and efficiency, often drive behavior selection in mobile robotic platforms. However, navigational capabilities can rely heavily on the coordination of all behaviors available to the robot, rather than the performance of one behavior. Here, we studied how a collection of availabile gaits (cyclic internal motions) can be related to the variability and density of external motions that a system can achieve. We attempted to capture this capability, termed ''coverage'', with an associative fast-to-compute cost function that can be used to simultaneously optimize a collection of gaits. The cost function can be weighted such that users may specify the importance of various classes of external motions. A resulting optimization framework produced three gaits for a 3-link Purcell swimmer, locally maximizing coverage on the space of planar rigid body motions.
BibTeX:
@conference{bittner-2019-dw,
  author = {B Bittner and S Revzen},
  title = {Optimizing Gaits for Coverage on Lie Groups},
  booktitle = {Dynamic Walking},
  year = {2019},
  url = {https://docs.google.com/document/d/155IGklc5VWjCga3UaZyJ66UeFiV2_94IlAl5AmnqK7Y/view}
}
Bittner, B. and Revzen, S. Geometric Gait Optimization with a five-link wheeled snake 2020 Bulletin of the American Physical Society  conference URL 
BibTeX:
@conference{bittner2020geometric,
  author = {Bittner, B and Revzen, S},
  title = {Geometric Gait Optimization with a five-link wheeled snake},
  journal = {Bulletin of the American Physical Society},
  publisher = {American Physical Society},
  year = {2020},
  url = {http://meetings.aps.org/Meeting/MAR20/Session/U22.4}
}
Bittner, B., Hatton, R. and Revzen, S. Step Selection in Data-Driven Geometric Gait Optimization 2018 American Physical Society March Meeting  conference  
Abstract: Geometric mechanics offers a powerful set of tools for understanding locomotion. In past work we used data-driven oscillator theory to design a sample efficient method for modeling geometric systems such as the Purcell swimmer. We extended this method to include the modeling of highly damped systems inhabiting the perturbed Stokes dynamical regime. Here, we present a case study on a physical five-link wheeled snake robot. Under each link, a pair of wheels were co-aligned to decrease friction in the direction along the link. We seeded the geometric gait optimizer with a zero displacement gait. After 9 iterations of 80 cycles, we produced a motion that achieved 45% body length per cycle translation motion, while optimizing over 84 parameters. Running the system at 0.5 Hz, this took 24 minutes. We noticed the final gait changes combinations of wheels that are contacting and not contacting the ground, a feature not observed in the first gait, suggesting that the optimizer successfully exploited hybrid features of the dynamics.
*NSF CMMI 1825918
BibTeX:
@conference{bittner-aps-2018-ssddg,
  author = {B Bittner, R Hatton, S Revzen},
  title = {Step Selection in Data-Driven Geometric Gait Optimization},
  booktitle = {American Physical Society March Meeting},
  year = {2018}
}
Burden, S.A., Revzen, S. and Sastry, S.S. From anchors to templates: Exact and approximate reduction in models of legged locomotion 2013 Dynamic Walking  conference URL 
BibTeX:
@conference{burden-2013-fatt,
  author = {Burden, S A and Revzen, S and Sastry, S S},
  title = {From anchors to templates: Exact and approximate reduction in models of legged locomotion},
  booktitle = {Dynamic Walking},
  year = {2013},
  url = {http://www.cmu.edu/dynamic-walking/files/abstracts/Burden_2013_DW.pdf}
}
Burden, S.A., Revzen, S., Moore, T.Y., Sastry, S.S. and Full, R.J. Using reduced-order models to study dynamic legged locomotion: Parameter identification and model validation 2013 Integrative and comparative biology  conference  
BibTeX:
@conference{burden-sicb13,
  author = {Burden, S A and Revzen, S and Moore, T Y and Sastry, S S and Full, R J},
  title = {Using reduced-order models to study dynamic legged locomotion: Parameter identification and model validation},
  booktitle = {Integrative and comparative biology},
  year = {2013}
}
Council, G. and Revzen, S. Running with certainty on uncertain terrain requires little to no neural feedback 2015 Integrative and comparative biology  conference URL 
Abstract: Rapid legged locomotion is of critical importance for many animal
species. In most natural environments, animals cannot rely on the
ground being predictably flat. We present a result from nonlinear
control showing that under most circumstances animals should be able
to select a feed-forward strategy that would eliminate the uncertainty
in movement generated by non-flat terrain. Since this strategy requires
no sensory feedback, it may be implemented morphologically in the
shape of the body and the mechanical structure of the limbs. We demonstrate
such a strategy for the Spring Loaded Inverted Pendulum model of
running. We hypothesize that such controllers appear in some rapidly
running organisms. In such systems, no investigation of neural feedback
could reveal the dominant mechanism of control, and analysis of neuronal
responses would at best be misleading.
BibTeX:
@conference{council-2015-sicb,
  author = {Council, G and Revzen, S},
  title = {Running with certainty on uncertain terrain requires little to no neural feedback},
  booktitle = {Integrative and comparative biology},
  year = {2015},
  url = {http://www.sicb.org/meetings/2015/schedule/abstractdetails.php?id=1409}
}
Council, G. and Revzen, S. Recovering a gait using energy and phase 2016 Dynamic Walking  conference  
BibTeX:
@conference{council-2016-dw,
  author = {Council, G and Revzen,S},
  title = {Recovering a gait using energy and phase},
  booktitle = {Dynamic Walking},
  year = {2016}
}
Council, G. and Revzen, S. Gait Synthesis with Reduced Proprioceptive Requirements 2017 IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology  conference URL 
BibTeX:
@conference{council-2017-iros,
  author = {Council, G and Revzen, S},
  title = {Gait Synthesis with Reduced Proprioceptive Requirements},
  booktitle = {IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology},
  year = {2017},
  url = {http://gravishlab.ucsd.edu/iros2017/posters/Gait_Synthesis_Reduced_Sensing_Abstract.pdf}
}
Council, G. and Revzen, S. Limb Coordination with Reduced Prioprioceptive Requirements via Event-Selected Dynamics 2017 MBI workshop 4: Sensori-Motor Control of Animals and Robots  conference URL 
BibTeX:
@conference{council-2017-mbi,
  author = {Council, G and Revzen, S},
  title = {Limb Coordination with Reduced Prioprioceptive Requirements via Event-Selected Dynamics},
  booktitle = {MBI workshop 4: Sensori-Motor Control of Animals and Robots},
  year = {2017},
  url = {https://mbi.osu.edu/event/?id=11043schedule}
}
Council, G. and Revzen, S. Recovery of Behaviors of Robots without Dynamics 2020 Bulletin of the American Physical Society  conference URL 
Abstract: The conventional choice would be to model the damaged robot, either by anticipating damage types and their effects on a known model, or by performing system identification on the damaged device. However, anticipating failure is fragile, and data-driven system ID of dynamics is expensive in time and robot wear-and-tear.
BibTeX:
@conference{council2020recovery,
  author = {Council, George and Revzen, Shai},
  title = {Recovery of Behaviors of Robots without Dynamics},
  journal = {Bulletin of the American Physical Society},
  publisher = {American Physical Society},
  year = {2020},
  url = {http://meetings.aps.org/Meeting/MAR20/Session/S22.12}
}
Daley, M., Revzen, S. and Wilshin, S.D. Towards a unified notion of gaits 2012 Animal Abstracts  conference  
Abstract: While a variety of definitions of "gait" have proved useful in experimental
biology, there exist many superficially disparate definitions of
"gait", both in the literature and among practicing biologists. At
times these definitions are contradictory, for example a definition
of gait which required a discrete jump in some quantity (as occurs
for the walk-trot transition in dogs) could imply that walking and
running are indistinct in some birds; yet, these are intuitively
different modes of locomotion. Here we propose a unified conception
of gait and show how the hierarchical nature of our definition solves
this difficulty and highlights important questions in control and
in the determinants of locomotion. We propose to define "gait" as
"a parametrically related family of non-dimensional kinematic observations
of a locomotor behavior which can persist indefinitely". We arrived
at this definition by identifying the commonalities between existing
definitions, highlighting the utility of distinctions such as the
scale free nature of gait metrics, the cyclic nature of most familiar
"gaits", and the natural hierarchies of gaits. We show how existing
definitions are embedded in ours. Additionally, we highlight the
practical utility of our definition in terms of both pedagogy and
research. Our definition conceptually clarifies theories of gait
by highlighting the relations between gait hierarchies and locomotion
model hierarchies. Our approach sharpens the ability to formulate
biomechanical research hypotheses about all forms of locomotion in
both species-specific and comparative studies. The resulting language
can also be used to describe gaits in non-cyclic locomotion.
BibTeX:
@conference{daley-2012-SEB,
  author = {Daley, M and Revzen, S and Wilshin, S D},
  title = {Towards a unified notion of gaits},
  booktitle = {Animal Abstracts},
  year = {2012}
}
Frimerman, A., Revzen, S and Shani, B Spatial Relation of QRS-T Vectorcardiogram is a Good Predictor of Coronary Disease in Patients with Normal Rest 12-Leads ECG (poster) 2008 55th Annual Conference of the Israel Heart Society and the Israel Society of Cardiothoracic Surgery  conference  
BibTeX:
@conference{frimerman-2008,
  author = {Frimerman, A and Revzen S and Shani B},
  title = {Spatial Relation of QRS-T Vectorcardiogram is a Good Predictor of Coronary Disease in Patients with Normal Rest 12-Leads ECG (poster)},
  booktitle = {55th Annual Conference of the Israel Heart Society and the Israel Society of Cardiothoracic Surgery},
  year = {2008}
}
R Hatton B Bittner, S.R. and Revzen, S. Data-driven geometric gait analysis 2017 Dynamic Walking  conference URL 
BibTeX:
@conference{hatton-2017-dw-gga,
  author = {R Hatton, B Bittner, S Ramasamy and S Revzen},
  title = {Data-driven geometric gait analysis},
  booktitle = {Dynamic Walking},
  year = {2017},
  url = {http://ruina.tam.cornell.edu/dynwalk17abstracts/215-Ross0Hatton0-0HattonRevzenDynamicWalkingAbstract.pdf}
}
Kaspari, M., Clay, N.A., Yanoviak, S.P., Revzen, S., Kay, A. and Lucas, J. On the evolution of ant thermal performance: clues from a Neotropical forest 2013 Association for Tropical Biology and Conservation  conference  
BibTeX:
@conference{kaspari-2013-atbc,
  author = {Kaspari, M and Clay, N A and Yanoviak, S P and Revzen, S and Kay, A and Lucas, J},
  title = {On the evolution of ant thermal performance: clues from a Neotropical forest},
  booktitle = {Association for Tropical Biology and Conservation},
  year = {2013}
}
Kaspari, M., Clay, N.A., Yanoviak, S., Revzen, S., Czekanski-Moir, J., Lucas, J. and Kay, A. On the evolution of ant thermal performance: clues from a Neotropical forest 2013 Yearly Meeting of the Society for Integrative and Comparative Biology  conference  
BibTeX:
@conference{kaspari-2013-sicb,
  author = {Kaspari, M and Clay, N A and Yanoviak, SP and Revzen, S and Czekanski-Moir, J and Lucas, J and Kay, A},
  title = {On the evolution of ant thermal performance: clues from a Neotropical forest},
  booktitle = {Yearly Meeting of the Society for Integrative and Comparative Biology},
  year = {2013}
}
Kvalheim, M. and Revzen, S. Better models of rhythmic systems: predicting locomotion from phase alone 2015 Integrative and comparative biology  conference URL 
Abstract: Many animal locomotion behaviors consist of repeating stereotyped
body motions in a rhythmic fashion. When these rhythmic motions are
recovered after the body encounters a disturbance, one may consider
the characteristic motion to be a limit cycle of a stable nonlinear
oscillator. We show, under the assumption that our data set consists
of a collection of N trials each containing M cycles, that partitioning
the data into cycles based on a distinguished event such as heel-strike
(often used for human motion studies) and averaging the cycles produces
statistically inferior model of typical motions to averaging based
on an estimate of dynamical phase. The improved accuracy of the phase
based model can enable effects to be detected that would otherwise
require many more trials. Examples from several locomotion experimental
datasets will be provided
BibTeX:
@conference{kvalheim-2015-sicb,
  author = {Kvalheim, M and Revzen, S},
  title = {Better models of rhythmic systems: predicting locomotion from phase alone},
  booktitle = {Integrative and comparative biology},
  year = {2015},
  url = {http://www.sicb.org/meetings/2015/schedule/abstractdetails.php?id=1426}
}
Kvalheim, M. and Revzen, S. A dynamical systems perspective on Templates & Anchors: some general methods for anchoring templates 2017 IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology  conference URL 
Abstract: A template and anchor are a pair of models such that the template describes the essential features of a
biomechanical behavior, whereas the anchor is a more detailed model that often contains specifics of the individual
animal morphology [FK99]. Many biomechanical behaviors are well-approximated by template models, which
is to say that animals have many degrees of freedom, but move “as if” they have only a few.

Control theory as used in robotics and the related dynamical systems theory provide a mathematical frame-
work wherein smooth templates can be described as attracting normally hyperbolic invariant manifolds (NHIMs)

[HPS77], [Eld13]. NHIMs (i) persist under perturbations, so are physically relevant, and (ii) come equipped
with a natural “asymptotic phase” reduction map which faithfully relates (semi-conjugates) anchor states to their
template representation [BK94]. This map generalizes the classical notions of asymptotic phase and isochrons
for a nonlinear oscillator [Guc75].
We present a systematic procedure for anchoring such smooth templates M within an anchor B. Our recipe
includes the ability to choose the asymptotic phase map P: B → M, as well as arbitrary smooth template dynamics
g: M → TM. See Figure 1. Our result is universal: every attracting NHIM possessing smooth asymptotic
phase arises from our construction. For some biological systems satisfying a “posture principle” (as defined
in [HFKG06]), our results construct a force law that anchors such a postural template.

BibTeX:
@conference{kvalheim-2017-iros,
  author = {Kvalheim, M and Revzen, S},
  title = {A dynamical systems perspective on Templates & Anchors: some general methods for anchoring templates},
  booktitle = {IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology},
  year = {2017},
  url = {http://gravishlab.ucsd.edu/iros2017/posters/Kvalheim_abstract.pdf}
}
Kvalheim, M. and Revzen, S. Asymptotic phase, model reduction, and control of Templates Anchors 2017 MBI workshop 4: Sensori-Motor Control of Animals and Robots  conference URL 
BibTeX:
@conference{kvalheim-2017-mbi,
  author = {Kvalheim, M and Revzen, S},
  title = {Asymptotic phase, model reduction, and control of Templates Anchors},
  booktitle = {MBI workshop 4: Sensori-Motor Control of Animals and Robots},
  year = {2017},
  url = {https://mbi.osu.edu/event/?id=11043schedule}
}
Kvalheim, M., Eldering, J. and Revzen, S. Global linearization and fiber bundle structure of invariant manifolds 2018 AIMS  conference URL 
Abstract: We study properties of the global (center-)stable manifold of a compact normally attracting invariant manifold (NAIM) for a flow, the special case of a normally hyperbolic invariant manifold (NHIM) with empty unstable bundle. As a slight generalization, we allow the NAIM to be inflowing invariant, which means that the boundary of the NAIM might be nonempty, but the vector field points inwards there. We extend a classical result of Pugh and Shub for the boundaryless case, showing that the flow near an inflowing NAIM is "linearizable" or topologically conjugate to its linearization at the NAIM. Moreover, we give conditions ensuring the existence of a Ck conjugacy. We also show that a Ck locally linearizable inflowing NAIM is automatically globally Ck linearizable, with the conjugacy defined on the entire global (center)-stable manifold. We finally show that under weaker k-center bunching conditions, the global stable foliation has a Ck disk bundle structure, which can be interpreted as a weak form of our global linearization results. We apply our results to geometric singular perturbation theory by extending the domain of the Fenichel Normal Form to the entire global stable manifold, and under additional nonresonance assumptions we derive a smooth global linear normal form.
BibTeX:
@conference{kvalheim-2018-aims,
  author = {Kvalheim, M and Eldering, J and Revzen, S},
  title = {Global linearization and fiber bundle structure of invariant manifolds},
  booktitle = {AIMS},
  year = {2018},
  url = {http://aimsciences.org/conferences/2018/2018_posterSessions.html}
}
Kvalheim, M. and Revzen, S. Templates and Anchors: a review of notions of model reduction 2018 Dynamic Walking  conference URL 
Abstract: N/A (video abstract only submitted). This poster was a summary of the templates and anchors chapter in the
Bioinspired Legged Locomotion book (reference kvalheim-2017-tempanch).
BibTeX:
@conference{kvalheim-2018-dw,
  author = {Kvalheim, M and Revzen, S},
  title = {Templates and Anchors: a review of notions of model reduction},
  booktitle = {Dynamic Walking},
  year = {2018},
  url = {http://robots.ihmc.us/dynamicwalking2018/}
}
Kvalheim, M. and Revzen, S. Principal Koopman Eigenfunctions for Nonlinear and Nonsmooth Systems 2019 IPAM workshop: Operator Theoretic Methods in Dynamic Data Analysis and Control  conference  
BibTeX:
@conference{kvalheim-2019-IPAM,
  author = {M Kvalheim and S Revzen},
  title = {Principal Koopman Eigenfunctions for Nonlinear and Nonsmooth Systems},
  booktitle = {IPAM workshop: Operator Theoretic Methods in Dynamic Data Analysis and Control},
  year = {2019},
  note = {(poster)}
}
Maus, M. and Revzen, S. Linear structure in human treadmill running? 2011 Dynamic Walking  conference  
BibTeX:
@conference{maus-2011-dw,
  author = {Maus, M and Revzen, S},
  title = {Linear structure in human treadmill running?},
  booktitle = {Dynamic Walking},
  year = {2011}
}
Maus, M., Revzen, S. and Guckenheimer, J.M. Drift and deadbeat control in the Floquet structure of human running 2012 Dynamic Walking  conference URL 
BibTeX:
@conference{maus-2012-DW,
  author = {Maus, M and Revzen, S and Guckenheimer, J M},
  title = {Drift and deadbeat control in the Floquet structure of human running},
  booktitle = {Dynamic Walking},
  year = {2012},
  note = {video https://youtu.be/tG_cfN0yufA},
  url = {http://www.ihmc.us/dwc2012files/Revzen.pdf}
}
McLaughlin, T., Anderson, M. and Revzen, S. Hopping with Elastic Restitution Is More Difficult Than It Seems 2020 Bulletin of the American Physical Society  conference URL 
Abstract: Bouncing rubber balls and hopping on pogo sticks might suggest that building a robot that hops with a significant fraction of elastic energy restitution would be straightforward. Using spring steel legs with 99% restitution individually, we built a three-legged hopper. The hopper achieved a minute 11.2% restitution when using the springs in series with the actuators. We present five generations of three-legged hoppers: four have actuators in series with springs. Three different types of ground contact were tested. Our best design so far uses actuators in parallel with the springs, and achieves 49+/-5% restitution. This work will be of use to those interested in using elastic energy storage in legged locomotion.
BibTeX:
@conference{mclaughlin2020hopping,
  author = {McLaughlin, Taylor and Anderson, Marion and Revzen, Shai},
  title = {Hopping with Elastic Restitution Is More Difficult Than It Seems},
  journal = {Bulletin of the American Physical Society},
  publisher = {American Physical Society},
  year = {2020},
  url = {http://meetings.aps.org/Meeting/MAR20/Session/S22.11}
}
Moore, T.Y., Revzen, S., Burden, S. and Full, R.J. Adding Inertia and Mass to Test Stability Predictions in Rapid Running Insects (abstract only) 2010 Yearly Meeting of the Society for Integrative and Comparative Biology  conference  
Abstract: A spring-mass model for the horizontal plane dynamics of sprawled
running animals (Lateral Leg Spring Model) predicts that added inertia
reduces stability and increases the time required to recover from
a perturbation. To empirically test this model, we perturbed cockroaches
while running across a platform inserted into a track. Cockroaches
(Blaberus discoidalis; N=9, 2.17 g mass, 2.18 g cm^2 moment of inertia)
ran along the surface of the platform at 31+/-6 cm/sec with a stride
frequency of 12.5+/-1.7 Hz. We accelerated the platform (10 cm x
25 cm) laterally at 0.6+/-0.1 g in a 0.1 sec interval providing a
50+/-3 cm/sec velocity change from the impulse. We affixed one of
three backpacks on the cockroach to change its inertia distribution
and mass. We used a computer vision-based tracking of body roll,
pitch, yaw, leg position, and velocity on the translating platform.
The control backpack increased the animal's mass by 36% and moment
of inertia by 25 the mass backpack increased mass by 84% and moment
of inertia by 26 the inertia backpack increased mass by 93% and
moment of inertia by 865%. Animals equipped with the inertia backpack
were not less stable than controls, thereby rejecting the prediction
of the horizontal plane Lateral Leg Spring Model. Animals running
with the mass backpack were least stable, showing greater body angular
changes than other conditions. Larger angular body exercisions of
the animals with mass backpacks were delayed by approximately one
to two steps. Consistent with this delay was a lag in the change
of lateral foot placement relative to the body axis along with its
recovery to the pre-perturbation values. Results suggest that a three
dimensional model is necessary even in sprawled- posture animals
to test hypotheses of self-stabilization, and the role of both mechanical
and neural feedback.
BibTeX:
@conference{moore-2012-SICB,
  author = {T Y Moore and S Revzen and S Burden and R J Full},
  title = {Adding Inertia and Mass to Test Stability Predictions in Rapid Running Insects (abstract only)},
  booktitle = {Yearly Meeting of the Society for Integrative and Comparative Biology},
  year = {2010}
}
Reeve, M.A., Wilshin, S., Haynes, G.C., Revzen, S. and Spence, A.J. Dog gait on rough terrain confirms the prediction of a stability inspired dynamical systems model of quadrupedal leg control 2012 Animal Abstracts, pp. A1.31  conference  
Abstract: In nature, quadrupeds must maintain stability when moving over uneven terrain in order to survive and reproduce. Gait choice and the maintenance of idealized gaits are likely to be critical for stability, particularly over rough ground. In recent work we have formulated a dynamical systems model of quadrupedal gait that accurately reproduces the relative leg phases over time during the walk, trot and transitions between the two. In this study, we sought independent testing of this model. We therefore tested predictions of the model when experiencing injected noise, by comparing output from simulations of the model with data from freely-running dogs on rough terrain. Model simulations in which random noise was injected at walking speed showed a gait that moved from the idealized walk towards a trot. To test this prediction, we utilized a wirelessly synchronized sensor suite fitted to five male dogs, of shoulder height 522.0+/-2.6 mm (mean +/- standard deviation) and body mass 20.0 +/- 2.5 kg (mean +/- standard deviation). Devices were attached to the proximal-most segment of each leg, and on the midline of the back at the front legs. Sensor data were
used to compute animal speed, position and a continuous estimate of leg phase. The centroids of relative leg phase (averaged across time within each stride) describing the gait used moved
significantly towards trot on rough terrain (linear mixed model; n=5 dogs, p<0.05). To explain why we observe these changes, we propose experiments using a physical model, the XRL robot.
BibTeX:
@conference{reeve-2012-seb,
  author = {M A Reeve and S Wilshin and G C Haynes and S Revzen and A J Spence},
  title = {Dog gait on rough terrain confirms the prediction of a stability inspired dynamical systems model of quadrupedal leg control},
  booktitle = {Animal Abstracts},
  year = {2012},
  pages = {A1.31}
}
Revzen, S., Koditschek, D.E. and Full, R.J. Testing feedforward control models in rapid running insects using large perturbations (abstract only) 2006
Vol. 46(suppl 1)Integrative and comparative biology, pp. e1-162 
conference DOI  
Abstract: Sensory feedback dominates limb coordination in walking. By contrast,
insects are capable of stable running over rough surfaces with no
detectable change in motor output to major leg muscles. Passive,
dynamic models suggest self-stabilization. A central pattern generator
forcing a mass-spring system can model these observations. RHex,
a rapid running, bio-inspired hexapedal robot is a physical realization
of these models. The robot can self-stabilize over simple terrain
when its leg motors are driven with feedforward ``clock'' (CPG-like)
signals only. However, RHex requires sensory feedback to its clock
to attain comparable speeds over complex terrain. With such feedback,
traversal of significant obstacles induces phase shifts in motor
timing to coordinate legs. We examined high-speed running in cockroaches
to determine whether neural feedback shifts leg phase and/or frequency
after encountering an obstacle. Cockroaches were tripped with a hip-high
hurdle while running at 25 cm/s on a treadmill. High-speed video
tracked the body and distal portion of all six legs versus time.
Perturbations struck different legs in different locations, but always
caused a significant disruption to the mechanical system for the
several strides traversing the obstacle. Cockroaches incurred significant
phase and frequency changes. When the pattern of leg motions was
extrapolated from before the obstacle to after the obstacle, it failed
to match the animals' pattern after recovery in 17 of 22 trials.
Results suggest that sensory feedback is likely sent to a CPG-like
clock driving leg movements, as required by our physical model. We
reject the hypothesis that animals use a feed-forward clock without
neural feedback when challenged with large perturbations in rapid
running.
BibTeX:
@conference{revzen-2006-SICB,
  author = {S Revzen and D E Koditschek and R J Full},
  title = {Testing feedforward control models in rapid running insects using large perturbations (abstract only)},
  booktitle = {Integrative and comparative biology},
  year = {2006},
  volume = {46},
  number = {suppl 1},
  pages = {e1-162},
  doi = {https://doi.org/10.1093/icb/icl056}
}
Revzen, S., Koditschek, D.E. and Full, R.J. Selecting among Neuromechnical Control Architectures using Kinematic Phase and perturbation experiments (poster) 2007 Yearly meeting of the American Society of Biomechanics  conference  
Abstract: We use an experimental paradigm grounded in dynamical systems (DS)
theory to select which among several competing neuro-mechanical control
architectures (NCA) could be in use in a given rhythmic motor behavior
by using kinematic data alone. Our method allows us to extrapolate
animal motions based on a few consecutive video frames, and compare
the predicted motion to perturbation experiment outcomes. We apply
the method to the study of control of running in the cockroach Blaberus
discoidalis, and discuss its broader utility in a variety of biomechanical
problems, e.g. in potential clinical application of motor learning
tasks
BibTeX:
@conference{revzen-2007-ASB,
  author = {S Revzen and D E Koditschek and R J Full},
  title = {Selecting among Neuromechnical Control Architectures using Kinematic Phase and perturbation experiments (poster)},
  booktitle = {Yearly meeting of the American Society of Biomechanics},
  year = {2007}
}
Revzen, S., Bishop-Moser, J., Spence, A.J. and Full, R.J. Testing Control Models In Rapid Running Insects Using Lateral Ground Translation (abstract only) 2007
Vol. 47(suppl 1)Integrative and comparative biology, pp. e1-152 
conference DOI  
Abstract: Perturbation of simple passive, dynamic models of legged locomotion
suggest the possibility of self-stabilization with minimal neural
feedback. Rapid recovery from brief impulses to the body of fast,
sprawled-posture runners and the absence of muscle activation pattern
changes while traversing rough terrain support the hypothesis of
recovery by mechanical feedback alone. Large and complex perturbations
to rapid running insects imposed by a single, hip-high hurdle do
produce significant leg phase and frequency changes showing that
sensory feedback must play a role in recovery. To better determine
the interrelationship between neural and mechanical feedback, we
designed a trackway with a 10 x 25 cm platform insert that could
translate laterally to a maximum acceleration of 10g in 50 msec.
Cockroaches (Blaberus discoidalis; n=14) running at 308 cm/sec at
a step frequency of 11.52.7 Hz onto a movable platform were accelerated
laterally at 1g in a 100 msec interval providing a 563 cm/sec specific
impulse. By automatically tracking body position and orientation
and leg (tarsus) positions, we found no change in leg motion timing
for at least 50 msec. Following this delay, animals decreased step
frequency for one stride, and then partially recovered frequency
thereafter. Results are consistent with previous research showing
that the initial rapid recovery is accomplished by mechanical feedback
promoting self-stabilization followed by neural feedback modulation
of a central pattern generator at a slower rate occurring after a
delay comparable to the duration of a step. Funded by NSF FIBR Grant.
BibTeX:
@conference{revzen-2007-SICB,
  author = {S Revzen and J Bishop-Moser and A J Spence and R J Full},
  title = {Testing Control Models In Rapid Running Insects Using Lateral Ground Translation (abstract only)},
  booktitle = {Integrative and comparative biology},
  year = {2007},
  volume = {47},
  number = {suppl 1},
  pages = {e1-152},
  doi = {https://doi.org/10.1093/icb/icm104}
}
Revzen, S. and Guckenheimer, J.M. A Dynamical Systems Analysis of Running Cockroaches 2008 MBI Workshop 4: Neuromechanics of Locomotion  conference URL 
Abstract: We use methods from dynamical systems theory to analyze movement of
/Blaberus discoidalis/ cockroaches. One of our key objectives is
to derive dimensionally reduced models that describe the biomechanical
synergies used by an animal steadily running on flat ground. By modeling
the motion as a stable periodic orbit in a body centered frame of
reference, we may apply Floquet theory to the problem. In the absence
of noise, the theory predicts a change of coordinates which rectifies
the motion transverse to the orbit to a time invariant linear system
with modes that decay exponentially. These Floquet modes can be divided
into those that are highly damped and those that are weakly damped.
Preliminary results give evidence for few weakly damped modes, and
for many highly damped modes that decay in less than a stride. We
hypothesize that the weakly damped modes form a template for the
neuromechanical control of locomotion. We describe our use of diverse
tools from motion tracking, numerical analysis, visualization and
geometric statistics to fit these periodic orbit models to video
recordings of running cockroaches. Our focus is on the numerical
estimation of a phase variable and of the linearized first return
map, with quantified levels of statistical confidence in the presence
of noisy data.
BibTeX:
@conference{revzen-2008-MBI,
  author = {S Revzen and J M Guckenheimer},
  title = {A Dynamical Systems Analysis of Running Cockroaches},
  booktitle = {MBI Workshop 4: Neuromechanics of Locomotion},
  year = {2008},
  url = {https://mbi.osu.edu/event/?id=69}
}
Revzen, S., Berns, M.S., Koditschek, D.E. and Full, R.J. Determining Neuromechanical Control Architecture Using Kinematic Phase Response to Perturbations 2008 Yearly meeting of the Society for Integrative and Comparative Biology  conference  
Abstract: We define several neuromechanical control architectures that represent
rhythmic motion. The first class is a mass-spring system interacting
with the environment whose motions are triggered by specific events.
The second class is a mass-spring system driven by the feedforward
signal of a CPG-like clock. The third class is a mass-spring system
coupled to a clock, but with proprioceptive feedback that tracks
a trajectory without altering the dynamics of the clock. The fourth
class is similar to the third, but allows feedback to modulate the
clock dynamics. We propose that a battery of perturbations to an
animal can provide outcomes that allow identification of an architecture.
To define these architectures, we selected a vertical hopping model
that has received analytical treatment in both robotics and biomechanics,
because it is a simple model that captures the essential phase and
frequency responses of a neural pattern generator coupled to a mechanical
oscillator. We assume that kinematically derived measurements of
mechanical phase reflect the coupled internal neural clock phase
and can be used to capture aspects of the various motor systems'
phase response curves during rhythmic behavior. We subjected the
four models to three perturbations that include a bump, a step, and
an incline. In the first class phase and frequency change continuously.
In the second, frequency is preserved by the clock and phase exhibits
several discrete values. Both phase and frequency are preserved by
the third class, whereas the fourth is similar in outcomes to the
first, but at much longer time scales. Experiments on polypedal running
animals will reveal the true empirical power of these architectural
hypotheses.
BibTeX:
@conference{revzen-2008-SICB,
  author = {Revzen, S and Berns, M S and Koditschek, D E and Full, R J },
  title = {Determining Neuromechanical Control Architecture Using Kinematic Phase Response to Perturbations},
  booktitle = {Yearly meeting of the Society for Integrative and Comparative Biology},
  year = {2008},
  note = {(abstract only)}
}
Revzen, S., Guckenheimer, J.M. and Full, R.J. Study of the neuromechanical control of rhythmic behaviors by floquet analysis (abstract only) 2009 Yearly meeting of the Society for Integrative and Comparative Biology  conference  
Abstract: The control of rhythmic behaviors like locomotion is difficult to
study when compared with control of fixed-point behaviors such as
standing. The problem is largly due to dynamics: perturbations away
from the typical cycle may have surprising and counter-intuitive
consequences later on the in the same cycle or even several cycles
in the future. These causal relationships between seemingly different
perturbations at different phases of motion can make conclusions
drawn from PCA and other matrix factorization methods misleading
or erroneous. Dynamical systems theory describes the interrelation
of perturbations in different parts of a cycle using Floquet Theory.
The theory guarantees the existence of a change of coordinates that
rectifies the dynamics to the simple linear form found in fixed-point
systems. We developed our method for estimating a Floquet structure
from kinematics to test the ``Templates and Anchors Hypothesis.''
This hypothesis states that rapid locomotion is controlled by restricting
the many degrees of freedom of the animal's morphology, as represented
by an ``anchored'' model, to follow low dimensional ``template''
dynamics. The presence of a template would express itself in the
Floquet structure as having a few weakly damped modes that decay
over multiple strides and span the template, and many strongly damped
modes that decay within a stride or a step, and span the remainder
of the degrees of freedom of the anchor. Our preliminary results
suggest that running death's-head cockroaches (Blaberus discoidalis)
posses a template that can be distinguished in the Floquet structure
of the animals' kinematics. We believe our methodology can be applied
to the study of neuromechanical control in a broad range of rhythmic
behaviors.
BibTeX:
@conference{revzen-2009-SICB,
  author = {S Revzen and J M Guckenheimer and R J Full},
  title = {Study of the neuromechanical control of rhythmic behaviors by floquet analysis (abstract only)},
  booktitle = {Yearly meeting of the Society for Integrative and Comparative Biology},
  year = {2009}
}
Revzen, S., Guckenheimer, J.M. and Full, R.J. Subtle differences in gaits: the perspective of data driven Floquet analysis 2011 Yearly meeting of the Society for Integrative and Comparative Biology  conference  
Abstract: Most rapid forms of animal locomotion involve producing a gait - a rhythmic sequence of body motions that propels the body through space by acting on the environment.
Gaits are stable with respect to environmental perturbations.
Data driven Floquet analysis promises a quantitative model of gait derived purely from kinematic measurements.
The model encompasses familiar concepts such as averaged cycles, phase response curves and stability eigenvalues, as well as the less familiar Floquet modes.
Our models of gait provide a prediction of future animal motions against which neuromechanical control hypothesis may be statistically tested.
By computing Floquet modes of seemingly similar gaits, we can expose the fact that these gaits are sensitive to perturbations in very different ways -- producing testable hypotheses can that separate these gaits empirically.
BibTeX:
@conference{revzen-2011-sicb,
  author = {Revzen, S and Guckenheimer, J M and Full, R J},
  title = {Subtle differences in gaits: the perspective of data driven Floquet analysis},
  booktitle = {Yearly meeting of the Society for Integrative and Comparative Biology},
  year = {2011}
}
Revzen, S., Ilhan, B.D. and Koditschek, D.E. Dynamical trajectory replanning for uncertain environments 2012 IEEE Conference on Decision and Control, pp. 3476-3483  conference DOI  
Abstract: We propose a dynamical reference generator equipped with an augmented
transient "replanning" subsystem that modulates a feedback controller's
efforts to force a me- chanical plant to track the reference signal.
The replanner alters the reference generator's output in the face
of unanticipated disturbances that drive up the tracking error. We
demonstrate that the new reference generator cannot destabilize the
tracker, that tracking errors converge in the absence of disturbance,
and that the overall coupled reference-tracker system cannot be destabilized
by disturbances of bounded energy. We report the results of simulation
studies exploring the performance of this new design applied to a
two dimensional point mass particle interacting with fixed but unknown
terrain obstacles.
BibTeX:
@conference{revzen-2012-drg,
  author = {S Revzen and Ilhan, B D and Koditschek, D E},
  title = {Dynamical trajectory replanning for uncertain environments},
  booktitle = {IEEE Conference on Decision and Control},
  year = {2012},
  pages = {3476-3483},
  doi = {https://doi.org/10.1109/CDC.2012.6425897}
}
Revzen, S., Burden, S.A., Koditschek, D.E. and Sastry, S.S. Pinned equilibria provide robustly stable multilegged locomotion 2013 Dynamic Walking  conference URL 
BibTeX:
@conference{revzen-2013-DW,
  author = {Revzen, S and Burden, S A and Koditschek, D E and Sastry, S S},
  title = {Pinned equilibria provide robustly stable multilegged locomotion},
  booktitle = {Dynamic Walking},
  year = {2013},
  note = {https://www.youtube.com/watch?v=omKEjL7YIAk&list=PLVqaARCrz-m9aFEsen8fkW4ZjdaFqRoGL&feature=player_detailpage&t=649teaser talk video},
  url = {http://www.cmu.edu/dynamic-walking/files/abstracts/Revzen_2013_DW.pdf}
}
Revzen, S. Facing the Unknown Challenge - Structure and Modularity in Morphological Computation 2013 International Workshop on Soft Robotics and Morphological Computation  conference URL 
BibTeX:
@conference{revzen-2013-soro,
  author = {Revzen, S},
  title = {Facing the Unknown Challenge - Structure and Modularity in Morphological Computation},
  booktitle = {International Workshop on Soft Robotics and Morphological Computation},
  year = {2013},
  url = {https://pdfs.semanticscholar.org/5037/ffda980eab88cd4aea0075e6a544645deeb2.pdf}
}
Revzen, S. Lessons from animal locomotion: extending Floquet theory to hybrid limit cycle oscillators 2014 Annual meeting of the SIAM  conference  
BibTeX:
@conference{revzen-2014-lfal,
  author = {Revzen, S},
  title = {Lessons from animal locomotion: extending Floquet theory to hybrid limit cycle oscillators},
  booktitle = {Annual meeting of the SIAM},
  year = {2014},
  note = {MS8: Locomotion in Terrestrial and Granular Environments}
}
Revzen, S. Synchronization and Dimensionality Reduction in Networks of Hybrid Phase Oscillators: A Perspective from Legged Locomotion 2015 Network Frontiers Workshop  conference URL 
Abstract: Phase oscillators are a common reduced model for oscillatory systems.
When the equations of motion of a network of phase oscillators are
discontinuous (and meet some technical requirements), the resulting
model is a hybrid dynamical system. Such models can arise for power
grids, for neural nets, and in describing legged locomotion of animals
and robots. I present recent results on the dynamics of this class
of models, which show surprising advantages for control and stabilization
of locomotion thanks to the use of legs. The results apply broadly
to networks of hybrid oscillators.
BibTeX:
@conference{revzen-2015-nfw,
  author = {Revzen, S},
  title = {Synchronization and Dimensionality Reduction in Networks of Hybrid Phase Oscillators: A Perspective from Legged Locomotion},
  booktitle = {Network Frontiers Workshop},
  year = {2015},
  url = {http://netfrontier.northwestern.edu/documents/Slides_NFW2015_Revzen.pdf}
}
Revzen, S. and Hatton, R. Phase Helps Find Geometrically Optimal Gaits 2017 Bulletin of the APS  conference URL 
BibTeX:
@conference{Revzen-2017-aps,
  author = {S Revzen and R Hatton},
  title = {Phase Helps Find Geometrically Optimal Gaits},
  booktitle = {Bulletin of the APS},
  year = {2017},
  url = {http://absimage.aps.org/image/MAR17/MWS_MAR17-2016-004710.pdf}
}
Revzen, S. In defense of Aristotle: is there a Connection for multi-legged locomotion? 2017 MBI workshop 4: Sensori-Motor Control of Animals and Robots  conference URL 
BibTeX:
@conference{revzen-2017-mbi,
  author = {Revzen, S},
  title = {In defense of Aristotle: is there a Connection for multi-legged locomotion?},
  booktitle = {MBI workshop 4: Sensori-Motor Control of Animals and Robots},
  year = {2017},
  url = {https://mbi.osu.edu/event/?id=11043schedule}
}
Revzen, S., Council, G. and Kvalheim, M. Is Legged Locomotion Almost Smooth? 2019 (446)Dynamic Walking  conference URL 
Abstract: Hexapods stand out among legged systems in their stability over unstructured terrain. We have recently discovered that slipping is a routine part of cockroach locomotion,[1] as well as showing that some robotic hexapods can noticeably improve performance by including gaits with slipping. The nonnegligible slipping challenges conventional mechanical analysis and simulation tools locomotion. The indeterminacy of inter-leg force distribution and the combinatorial complexities of possible contact states also result in unreliable motion planning. Our group has found a highly simplified model for friction dominated multi-legged locomotion which produces unexpectedly good motion predictions. Because experimental data on ground contact forces of hexapods is scarce, we designed a hexapedal robot platform equipped with Force/Torque (F/T) transducers and intended to produce the data needed to study why our model was successful. Here we present this robot’s mechanics and some preliminary force data collected with it.
BibTeX:
@conference{revzen-2019-dw,
  author = {S Revzen and G Council and M Kvalheim},
  title = {Is Legged Locomotion Almost Smooth?},
  booktitle = {Dynamic Walking},
  year = {2019},
  number = {446},
  url = {https://docs.google.com/document/d/155IGklc5VWjCga3UaZyJ66UeFiV2_94IlAl5AmnqK7Y/view}
}
Revzen, S. Tutorial 1 presentation: Templates and Anchors for analysis and synthesis of control 2008 MBI Workshop 4: Neuromechanics of LocomotionTutorial 1 presentation  conference URL 
BibTeX:
@conference{RevzenTut1,
  author = {S Revzen},
  title = {Tutorial 1 presentation: Templates and Anchors for analysis and synthesis of control},
  booktitle = {MBI Workshop 4: Neuromechanics of Locomotion},
  year = {2008},
  url = {https://mbi.osu.edu/event/?id=69}
}
Revzen, S. Tutorial 2 presentation: Phase estimation from kinematic data 2008 MBI Workshop 4: Neuromechanics of Locomotion  conference URL 
BibTeX:
@conference{RevzenTut2,
  author = {S Revzen},
  title = {Tutorial 2 presentation: Phase estimation from kinematic data},
  booktitle = {MBI Workshop 4: Neuromechanics of Locomotion},
  year = {2008},
  url = {https://mbi.osu.edu/event/?id=69}
}
Sachdva, V., Zhao, D. and Revzen, S. Slipping Matters 2017 Dynamic Walking  conference  
BibTeX:
@conference{sachdva-2017-dw,
  author = {V Sachdva, D Zhao, S Revzen},
  title = {Slipping Matters},
  booktitle = {Dynamic Walking},
  year = {2017}
}
Sarin, A., Abbot, D., Revzen, S. and Avestruz, A.-T. Bidirectional Capacitive Wireless Power Transfer for Energy Balancing in Modular Robots 2020 Applied Power Electronics Conference and Exposition, pp. 852-859  conference DOI  
Abstract: A modular approach to the complex robotic systems is desireable due to advantages such as ease of development, reconfigurability, and re-usability. Powering these dynamic structures while maintaining ease of assembly and versatile form-factor is a challenge. One promising solution is to exchange energy between modules which each have a small battery. Performing this exchange of energy using mechanical connections is not only unreliable but also limits the reconfigurability of the modules. In this paper, we present a bidirectional capacitive wireless power transfer scheme for energy balancing between different robot modules. A modified CMCDE topology is also presented to make the power transfer resilient to the changes in the robot dimensions. The concept is verified by demonstrating 20 W of power transfer between two modules at 13.56 MHz achieving a dc-dc efficiency of 79 % that is resilient to the changes in the track length.
BibTeX:
@conference{sarin-2020-wirelessPower,
  author = {A Sarin and D Abbot and S Revzen and A-T Avestruz},
  title = {Bidirectional Capacitive Wireless Power Transfer for Energy Balancing in Modular Robots},
  booktitle = {Applied Power Electronics Conference and Exposition},
  publisher = {IEEE},
  year = {2020},
  pages = {852-859},
  doi = {https://doi.org/10.1109/APEC39645.2020.9124139}
}
Sastra, J., Revzen, S. and Yim, M. Softer legs allow a modular hexapod to run faster 2012 Climbing and Walking Robotics (CLAWAR)  conference  
BibTeX:
@conference{sastra-2012-clawar,
  author = {Sastra, J and Revzen, S and Yim, M},
  title = {Softer legs allow a modular hexapod to run faster},
  booktitle = {Climbing and Walking Robotics (CLAWAR)},
  year = {2012}
}
Spence, A.J., Revzen, S., Yeates, K., Mullens, C. and Full, R.J. Insects running on compliant surfaces 2007
Vol. 47(suppl 1), pp. e1-152 
conference DOI  
Abstract: Human runners and hoppers attempt to adjust their leg stiffness to
maintain similar center of mass (COM) dynamics when confronted with
a compliant substrate. Dynamic materials testing of cockroach legs
shows that their behavior in the sagittal plane is largely determined
by passive exoskeletal properties. We tested the hypothesis that
rapid running cockroaches maintain their COM mechanics by compensating
for a compliant substrate. Cockroaches Blaberus discoidalis ran from
a rigid Plexiglas surface onto an elastic substrate of stiffness
(8-13 N/m) equal to 2/3 its virtual leg spring stiffness (15 N/m
for all three legs of a tripod). We directly measured the animals
COM dynamics using a novel 3-axis, MEMs accelerometer configured
as a backpack placed near its COM. Vertical acceleration of the COM
on the elastic surface had smaller peak-to-peak amplitudes (9.3 0.012
m/s2, n = 374 steps on elastic substrate, vs. 12 0.007 m/s2, n =
879 steps on rigid substrate; p<0.0001). Step duration was slightly
longer (44.7 0.044 ms, elastic versus 42.6 0.016 ms rigid; p = 0.019)
and forward velocity was actually faster on the elastic substrate
(35.6 0.004 cm/s on elastic substrate, versus 33.4 0.002 cm/s on
rigid substrate; p < 0.0001). We conclude that the cockroach does
not maintain similar vertical accelerations and therefore COM trajectories
when encountering an elastic substrate. Despite their inability to
maintain constant COM dynamics, cockroaches moved effectively on
complaint substrates. Funded by NSF FIBR.
BibTeX:
@conference{spence-2007-SICB,
  author = {A J Spence and S Revzen and K Yeates and C Mullens and R J Full},
  title = {Insects running on compliant surfaces},
  year = {2007},
  volume = {47},
  number = {suppl 1},
  pages = {e1-152},
  note = {(abstract only)},
  doi = {https://doi.org/10.1093/icb/icm104}
}
Sun, Y. and Revzen, S. A hexapedal robot designed for ground contact force analysis 2019 (544)Dynamic Walking  conference URL 
Abstract: Commonly, legged locomotion is modeled using non-smooth (hybrid) dynamical systems. We have previously shown that many of the forms of non-smoothness that appear in legged systems are rectifiable to the smooth case. Here we will review recent progress in modeling such systems: algorithmic improvements in computing perturbation models of multi-contact problems, extensions of the reconstruction equation from geometric mechanics to the non-smooth case, and extensions of Koopman operator methods to function spaces that contain non-smooth functions.
BibTeX:
@conference{sun-2019-dw,
  author = {Y Sun and S Revzen},
  title = {A hexapedal robot designed for ground contact force analysis},
  booktitle = {Dynamic Walking},
  year = {2019},
  number = {544},
  url = {https://docs.google.com/document/d/155IGklc5VWjCga3UaZyJ66UeFiV2_94IlAl5AmnqK7Y/view}
}
Wilshin, S., Haynes, G.C., Reeve, M., Revzen, S. and Spence, A.J. How is dog gait affected by natural rough terrain? 2012 Integrative and comparative biology  conference  
Abstract: n nature legged animals depend on locomotion over uneven terrain for
survival and reproduction. One way in which animals may optimize
their locomotor behaviour for this task is by adjusting the relative
timing of their leg recirculation, or gait. Therefore, we asked how
the relative leg timing of quadrupeds changes during locomotion over
natural, uneven terrain, and compared this to our idealised notions
of the walk, trot and gallop. Five male dogs of shoulder height 522.0
+/- 62.6 mm (mean +/- s.d.) and body mass 20.0 +/- 2.5 kg (mean +/-
s.d.) were trialled at nominal walk, trot, and gallop speeds over
flat and uneven terrain. Mean perturbation size on uneven terrain
was 54.8 +/- 44.6 mm versus 4.2 +/- 3.1 mm on flat. Dogs were fitted
with a wirelessly synchronized suite of five sensors, comprised of
Global Position System and inertial measurement units. One device
was attached to the proximal-most segment of each leg, and a fifth
on the midline of the back at the front legs. Raw sensor data were
used to compute animal speed, position, and a continuous estimate
of leg phases. The centroids of relative leg phase (averaged across
time within each stride), describing the gait used by the dog on
each terrain at each nominal gait speed, were significantly different
on the rough terrain (linear mixed-model; n=5 dogs, p<0.05). At walking
speeds on the rough terrain, dog gait moves towards the trot. Averages
and distances between gaits in relative leg phase space do not account
for the dynamical and geometric structure of these phase variables,
however. Theoretical developments required to handle these data will
be discussed. To explain why we observe these changes in dog gait,
we propose experiments in a physical model, the robot XRL.
BibTeX:
@conference{wilshin-2012-sicb,
  author = {Wilshin, S and Haynes, G C and Reeve, M and Revzen, S and Spence, A J},
  title = {How is dog gait affected by natural rough terrain?},
  booktitle = {Integrative and comparative biology},
  year = {2012}
}
Wilshin, S. and Revzen, S. Phase driven models of unperturbed locomotion 2014 Integrative and comparative biology, pp. E226  conference  
BibTeX:
@conference{wilshin-2014-sicb,
  author = {Wilshin, S and Revzen, S},
  title = {Phase driven models of unperturbed locomotion},
  booktitle = {Integrative and comparative biology},
  year = {2014},
  pages = {E226}
}
Zhao, D. and Revzen, S. Slipping helps steering in a multilegged robot 2016 Dynamic Walking  conference  
BibTeX:
@conference{zhao-2016-dw,
  author = {Zhao, D and Revzen, S},
  title = {Slipping helps steering in a multilegged robot},
  booktitle = {Dynamic Walking},
  year = {2016}
}
Zhao, D. and Revzen, S. Slip Matters in Hexapedal Steering 2017 IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology  conference URL 
BibTeX:
@conference{zhao-2017-iros,
  author = {Zhao, D and Revzen, S},
  title = {Slip Matters in Hexapedal Steering},
  booktitle = {IEEE International Conference On Intelligent Robots and Systems, Workshop on Robotics Inspired Biology},
  year = {2017},
  url = {http://gravishlab.ucsd.edu/iros2017/posters/Zhao_ConferenceAbstract.pdf}
}
Zhao, D., Sachdva, V. and Revzen, S. Modeling Multilegged Locomotion: the Friction Dominated Limit 2018 Integrative and Comparative Biology  conference  
Abstract: Work on a variety of organisms suggests that at moderate to high speeds animals can select their gaits for many goals, optimizing the cost of transport, speed, or chances of avoiding injury. Here we examine the motion of the nematode Caenorhabditis elegans using a newly developed geometric gait optimization tool. For animals operating in friction dominated regimes, such as viscous swimming, the locomotion is governed by a "connection" as used in the theory of geometric mechanics. By combining tools of kinematic phase analysis with those of geometric mechanics, our gait optimization tool models the connection governing a gait, allowing the computer to climb the gradient of goal functions such as the cost of transport. Using swimming data kindly provided by the Penn Complex Fluids Lab, we validated a Purcell swimming model and discovered that its moment equation contributed little (< 1 per cent) to the motion per cycle. Using a simplified model absent the moment equation, we optimized gaits for extremal motion (maximum displacement per cycle) and for cost of transport, using the animals' observed motion as the initial condition. We classified the resulting gaits by the mean time derivative of absolute curvature, and by the mean power. This gave 4.2+/-.27 [rad/mms] and 74.+/-12. [fW] for the animals, falling close to the 5.6 [rad/mms] and 15. [fW] of the optimal cost of transport gait, and further away from the 11. [rad/mms] and 270. [fW] of the extremal gait. We conclude that these nematodes motions are consistent with cost of transport having a significant weight in their choice of gait. Although unused here, our tool is model free, and can model the connection from motion captured gait data. This work may further illuminate how animals select their locomotor patterns and allow hypotheses of optimality to be rapidly tested.
BibTeX:
@conference{zhao-2018-sicb-mml,
  author = {D Zhao and V Sachdva and S Revzen},
  title = {Modeling Multilegged Locomotion: the Friction Dominated Limit},
  booktitle = {Integrative and Comparative Biology},
  year = {2018}
}
Zhao, D., Li, H. and Revzen, S. Design and Undulatory Gait Tests of a Meter-size Modular Centipede Robot 2019 (503)Dynamic Walking  conference URL 
Abstract: Bioinspired legged robots have been widely used for locomotion on challenging unconstructed environments as well as scientific study of biological locomotion. We investigated the motion of a family of robots ranging from 6 to 12 legs. Our modular “Multipod” robot has both pitch and yaw actuation of backbone between segments, making it possible to test a wide range of new gaits. Its meter-size scale offers a better chance to test centipede locomotion performance in some human-centric environments, like stairs, etc. We present results from a preliminary test of an undulatory gait over a range of inter-segmental phase differences. The results show that robots with different numbers of body segments(legs), move the same distance when actuated at the same phase difference. This implies that longer robots might be very similar to a set of shorter robots walking in caravan.
BibTeX:
@conference{Zhap-2019-dw,
  author = {D Zhao and H Li and S Revzen},
  title = {Design and Undulatory Gait Tests of a Meter-size Modular Centipede Robot},
  booktitle = {Dynamic Walking},
  year = {2019},
  number = {503},
  url = {https://docs.google.com/document/d/155IGklc5VWjCga3UaZyJ66UeFiV2_94IlAl5AmnqK7Y/view}
}
Kvalheim, M. and Revzen, S. Bioinspired Legged Locomotion 2016 , pp. 62-78  inbook DOI  
BibTeX:
@inbook{kvalheim-2016-tempanch,
  author = {M Kvalheim and S Revzen},
  title = {Bioinspired Legged Locomotion},
  publisher = {Elsevier},
  year = {2016},
  pages = {62-78},
  doi = {https://doi.org/10.1016/B978-0-12-803766-9.00004-X}
}
Revzen, S., Koditschek, D.E. and Full, R.J. Progress in motor control - a multidisciplinary perspective 2008 , pp. 25-56  inbook DOI  
Abstract: Our objective is to provide experimentalists with neuromechanical
control hypotheses that can be tested with kinematic data sets. To
illustrate the approach, we select legged animals responding to perturbations
during running. In the following sections, we briefly outline our
dynamical systems approach, state our over-arching hypotheses, define
four neuromechanical control architectures (NCAs) and conclude by
proposing a series of perturbation experiments that can begin to
identify the simplest architecture that best represents an animal?s
controller.
BibTeX:
@inbook{revzen-2007-TestArch,
  author = {S Revzen and D E Koditschek and R J Full},
  title = {Progress in motor control - a multidisciplinary perspective},
  publisher = {Springer Science+Business Media, LLC - NY},
  year = {2008},
  pages = {25-56},
  doi = {https://doi.org/10.1007/978-0-387-77064-2%5C%255F3}
}
Revzen, S. and Kvalheim, M. Bioinspired Legged Locomotion 2016 , pp. 97 - 108  inbook DOI  
BibTeX:
@inbook{revzen-2016-locosc,
  author = {S Revzen and M Kvalheim},
  title = {Bioinspired Legged Locomotion},
  publisher = {Elsevier},
  year = {2016},
  pages = {97 - 108},
  doi = {https://doi.org/10.1016/B978-0-12-803766-9.00004-X}
}
Wensing, P.M. and Revzen, S. Bioinspired Legged Locomotion 2016 , pp. 240 - 266  inbook DOI  
BibTeX:
@inbook{wensing-2016-tempctrl,
  author = {P M Wensing and S Revzen},
  title = {Bioinspired Legged Locomotion},
  publisher = {Elsevier},
  year = {2016},
  pages = {240 - 266},
  doi = {https://doi.org/10.1016/B978-0-12-803766-9.00006-3}
}
Banjanin, B., Burden, S., Moore, T., Revzen, S. and Full, R. Estimating predictive dynamical models of legged locomotion from data 2016
Vol. 56Integrative and comparative biology, pp. E11-E11 
inproceedings  
BibTeX:
@inproceedings{banjanin-2016-estimating,
  author = {Banjanin, B and Burden, SA and Moore, TY and Revzen, S and Full, RJ},
  title = {Estimating predictive dynamical models of legged locomotion from data},
  booktitle = {Integrative and comparative biology},
  year = {2016},
  volume = {56},
  pages = {E11--E11}
}
Council, G., Yang, S. and Revzen, S. Deadbeat control with (almost) no sensing in a hybrid model of legged locomotion 2014 Advanced Mechatronic Systems (ICAMechS), 2014 International Conference on, pp. 475-480  inproceedings DOI  
Abstract: Hybrid systems often appear as models of mechatronic devices, and
are used to express the discontinuous transition in dynamics that
occurs when mechanical contacts are made or broken. Contact state
changes can coincide with dramatic shifts in control authority, and
become sources of unwanted disturbance when they are exogenously
driven. In the natural world, such systems appear in rapid legged
locomotion. We present an insight derived from the analysis of running
animals - namely that dynamics can be partially or fully controlled
through geometric encoding of the desired control law in the feedforward
trajectories of the appendages. The resulting systems use no sensing,
or nearly so, yet can exhibit strong (deadbeat) stability. We provide
a theoretical proof of a general result, then a simulation study
of a simplified model of vertical hopping which rejects ground-height
changes without sensing the ground. We thereby show that mechatronic
controllers for non-trivial tasks such as manipulation and legged
locomotion could be implemented mechanically, with little or no sensing,
by encoding the control laws in the open-loop motions chosen. Our
results highlight that identification of a control mechanism in an
existing animal or machine must take into account that such geometric
stabilization may exist without neural or computational feedback.
BibTeX:
@inproceedings{council2014deadbeat,
  author = {Council, G and Yang, S and Revzen, S},
  title = {Deadbeat control with (almost) no sensing in a hybrid model of legged locomotion},
  booktitle = {Advanced Mechatronic Systems (ICAMechS), 2014 International Conference on},
  year = {2014},
  pages = {475-480},
  doi = {https://doi.org/10.1109/ICAMechS.2014.6911592}
}
Council, G. and Revzen, S. Energy and Phased Based Movement Recovery 2019 2019 SIAM Conference on Dynamical Systems  inproceedings URL 
Abstract: Retaining the ability to move despite body damage is a feature legged animals display - through injury, animals often compensate. Legged robots would be advantaged if they also had the ability to preserve a gait through damage, where we take a gait to be an exponentially stable limit cycle for a mechanical Lagrangian with periodic inputs. Given an prior gait, we wish to preserve that limit cycle by finding a control input that compensates for changes in the Lagrangian. We employ asymptotic phase, a cyclic coordinate, to compare the evolution of the original and new systems in a geometric way. To avoid models, we employ optimization. The complex dynamics of legged robots makes this optimization challenging. We enrich the optimization problem with necessary constraints that will improve convergence rate. For mechanical systems, the Lagrangian is determined via energy. We require that the phase evolution of mechanical power is preserved between the two systems, as well as that the new flow continues to be a semi-conjugacy with the original phase map. We see this practical, as energy is a physical quantity that can be found from data. We perform recovery on two systems. One, in simulation on a CT-SLIP, we recover a periodic motion by matching the phasing of kinetic energy. Two, we performed the optimization experimentally on a hexapod robot with springy legs. We see that the optimization produces a similar gait
BibTeX:
@inproceedings{Council-2019-SIAM,
  author = {G Council and S Revzen},
  title = {Energy and Phased Based Movement Recovery},
  booktitle = {2019 SIAM Conference on Dynamical Systems},
  year = {2019},
  url = {https://meetings.siam.org/sess/dsp_talk.cfm?p=99657}
}
Kvalheim, M. and Revzen, S. Testing an extended "Posture Principle" 2018 Integrative and Comparative Biology  inproceedings URL 
Abstract: The locomotion of many animal species, mammalian quadruped walking and cockroach running as examples, appears to be associated with a "posture principle", wherein motion is restricted to family of postures that is consistent across a range of speeds. Often this observation has been made in conjunction with the "templates and anchors" hypothesis that claims animals use control and dynamics to reduce the complexity of their body (anchor) motions to follow that of a simpler (template) system. Our recent work in dynamical systems theory suggests a universal, systematic method exists for anchoring templates that would follow such a "posture principle". We propose an assay to test for: (1) the presence of a posture principle; (2) the posture based anchoring strategy our theoretical results suggest. If posture based anchoring is found, it would suggest that position sensing could be used for anchoring with little or no support from velocity sensing, suggesting implications for the neuroanatomy and sensory physiology associated with locomotion.
BibTeX:
@inproceedings{kvalheim-2018-sicb,
  author = {Kvalheim, M and Revzen, S},
  title = {Testing an extended "Posture Principle"},
  booktitle = {Integrative and Comparative Biology},
  year = {2018},
  url = {http://www.sicb.org/meetings/2018/schedule/abstractdetails.php?id=722}
}
Kvalheim, M. and Revzen, S. Hybrid Oscillators: Phase and Amplitude in a Class of Non-Smooth Systems 2019 2019 SIAM Conference on Dynamical Systems  inproceedings URL 
Abstract: In the last few years there has been a growing interest in composition operator representations of dynamics, also known as `Koopman Theory', where dynamics are encoded in a semigroup Kt which acts on `observables' ψ by advancing them through time. The spectrum of the `Koopman Operator' K and its eigen-observables lead to many useful applications when the spectrum is discrete. The case of `principal' eigen-observables with discrete spectrum generalizes many known results from classical dynamical systems theory.

We present some early results on Bouligand differentiable observables: functions which have a directional derivative which is also a first-order approximation. These functions arise more often than most realize -- the flows of many hybrid systems [Burden, et.al. SIADS 2016], and most commonly used norms are in this class. Of particular interest to the workshop attendees is the latter observation, which is closely related to action variables in action-angle coordinates.

We will show some cases where action-angle coordinates can be obtained for systems described in terms of Bouligand differentiable observables, and discuss some of the related Koopman theory.

BibTeX:
@inproceedings{Kvalheim-2019-hybosc-SIAM,
  author = {M Kvalheim and S Revzen},
  title = {Hybrid Oscillators: Phase and Amplitude in a Class of Non-Smooth Systems},
  booktitle = {2019 SIAM Conference on Dynamical Systems},
  year = {2019},
  url = {https://meetings.siam.org/sess/dsp_talk.cfm?p=98071}
}
Kvalheim, M., Bittner, B. and Revzen, S. Reduced-Order Models for Locomotion in the Perturbed Stokes Regime 2019 2019 SIAM Conference on Dynamical Systems  inproceedings URL 
Abstract: For those creatures living "life at low Reynolds number", locomotion is friction-dominated in the sense that without power expenditure they quickly come to a halt. It is known that for swimming at the viscous or Stokesian limit (zero Reynolds number), motion is purely kinematic and governed by the viscous connection of geometric mechanics (Kelly and Murray, CDC, 1996). Assuming this reduced-order connection model, Bittner et al. developed an algorithm to estimate the dynamics near a periodic orbit (“gait cycle') directly from observational data of shape and body motion (J. Non. Dyn., 2018). In recent work, we extended this algorithm for the perturbed Stokes regime -- where Reynolds number is small but nonzero -- using a “corrected' reduced-order model (J Non. Dyn., submitted). Applications include the study of gait optimality in biology and “hardware-in-the-loop' robotics (with respect to chosen goal functionals). In this talk, we discuss the mathematical foundations of this reduced-order model, which extend work of Eldering and Jacobs (SIADS, 2016). Using noncompact normal hyperbolicity theory in a singular perturbation context, we show that for locomotion in the perturbed Stokes regime having a cocompact symmetry group, there exists an exponentially stable slow manifold which serves as a corrected reduced-order model. This yields a functional relationship between shape velocity and body velocity, but which is no longer connection-like.
BibTeX:
@inproceedings{Kvalheim-2019-SIAM,
  author = {M Kvalheim and B Bittner and S Revzen},
  title = {Reduced-Order Models for Locomotion in the Perturbed Stokes Regime},
  booktitle = {2019 SIAM Conference on Dynamical Systems},
  year = {2019},
  url = {https://meetings.siam.org/sess/dsp_talk.cfm?p=99791}
}
Miller, D., Fitzner, I., Fuller, S. and Revzen, S. Focused Modularity: Rapid Iteration of Design and Fabrication of a Meter-Scale Hexapedal Robot 2015 Assistive Robotics: Proceedings of the 18th International Conference on CLAWAR 2015, pp. 430-438  inproceedings DOI  
BibTeX:
@inproceedings{miller-2015-focused,
  author = {Miller, D and Fitzner, I and Fuller, SB and Revzen, S},
  title = {Focused Modularity: Rapid Iteration of Design and Fabrication of a Meter-Scale Hexapedal Robot},
  booktitle = {Assistive Robotics: Proceedings of the 18th International Conference on CLAWAR 2015},
  year = {2015},
  pages = {430-438},
  doi = {https://doi.org/10.1142/9789814725248_0053}
}
Piccoli, M., Revzen, S. and Yim, M. SEAL Pack: Versatile, Portable, and Rapidly Deployable SEa, Air, and Land Vehicle 2013 IEEE International Symposium on Safety Security and Rescue Robotics, pp. 1-6  inproceedings DOI  
Abstract: There are thirteen categories in the Robotic USAR ontology covering
land air and sea vehicles. We present a robot system that is capable
of four of those categories including aerial, terrestrial and marine
locomotion in a single package that is man-portable and low cost.
Each mode of locomotion has useful capabilities that the others do
not. The land vehicle can travel over 5km with a 500g load. The boat
can travel 0.5 km over water or loiter for 140 minutes. The flyer
can traverse any terrain for short periods of time. The system packs
into a small 33x20x14 cm package weighing 1 kg. We present design
issues and experimental verification.
BibTeX:
@inproceedings{piccoli-2013-seal,
  author = {Piccoli, M and Revzen, S and Yim, M},
  title = {SEAL Pack: Versatile, Portable, and Rapidly Deployable SEa, Air, and Land Vehicle},
  booktitle = {IEEE International Symposium on Safety Security and Rescue Robotics},
  year = {2013},
  pages = {1-6},
  doi = {https://doi.org/10.1109/SSRR.2013.6719362}
}
Revzen, S., Sastra, J., Eckenstein, N. and Yim CKBot Platform for the ICRA 2010 Planetary Challenge 2010 Proceedings of IEEE International Conference on Robotics and Automation, Workshop "Modular Robots: The State of the Art", pp. 11-12  inproceedings  
Abstract: The ICRA Planetary Contingency Challenge 2010 will include 3 teams
that will be using the new CKBot module and software package. This
paper will present some of the new aspects of this hardware, underlying
software architecture for quickly programming the modules and will
include a tutorial for these teams.
BibTeX:
@inproceedings{revzen-2010-icrackbot,
  author = {Revzen, S and Sastra, J and Eckenstein, N and Yim},
  title = {CKBot Platform for the ICRA 2010 Planetary Challenge},
  booktitle = {Proceedings of IEEE International Conference on Robotics and Automation, Workshop "Modular Robots: The State of the Art"},
  year = {2010},
  pages = {11-12}
}
Revzen, S., Bhoite, M., Macasieb, J.A. and Yim, M. Structure synthesis on-the-fly in a modular robot 2011 IEEE International Conference on Intelligent Robots and Systems (IROS), pp. 4797 - 4802  inproceedings DOI  
Abstract: We describe a modular robot system that can generate foam to make
structural elements. The modular mobile system uses CKBot modules
and carries extra modules along with a foam generation device. In
this paper, we demonstrate the system synthesizing new robot morphologies
- such as snake-like or legged robots or use the conforming foam-based
structures to encapsulate objects or modify the environment and discuss
the issues in building and using this technique.
BibTeX:
@inproceedings{revzen-2011-sotf,
  author = {Revzen, S and Bhoite, M and Macasieb, J A and Yim, M},
  title = {Structure synthesis on-the-fly in a modular robot},
  booktitle = {IEEE International Conference on Intelligent Robots and Systems (IROS)},
  year = {2011},
  pages = {4797 -- 4802},
  doi = {https://doi.org/10.1109/IROS.2011.6094575}
}
Revzen, S., Burden, S. and Kvalheim, M. Why the trot? 2014
Vol. 54Integrative and comparative biology, pp. E174-E174 
inproceedings  
BibTeX:
@inproceedings{revzen-2014-trot,
  author = {Revzen, S and Burden, SA and Kvalheim, MD},
  title = {Why the trot?},
  booktitle = {Integrative and comparative biology},
  year = {2014},
  volume = {54},
  pages = {E174--E174}
}
Revzen, S. and Kvalheim, M. Data driven models of legged locomotion 2015 Proc SPIE
Vol. 9467, pp. 1-8 
inproceedings DOI  
Abstract: Legged locomotion is a challenging regime both for experimental analysis
and for robot design. From biology, we know that legged animals can
perform spectacular feats which our machines can only surpass on
some specially controlled surfaces such as roads. We present a concise
review of the theoretical underpinnings of Data Driven Floquet Analysis
(DDFA), an approach for empirical modeling of rhythmic dynamical
systems. We provide a review of recent and classical results which
justify its use in the analysis of legged systems.
BibTeX:
@inproceedings{revzen-2015-spie,
  author = {Revzen, S and Kvalheim, M},
  title = {Data driven models of legged locomotion},
  journal = {Proc SPIE},
  year = {2015},
  volume = {9467},
  pages = {1-8},
  doi = {https://doi.org/10.1117/12.2178007}
}
Revzen, S. When do locomotor appendages get complicated? 2017
Vol. 57Integrative and comparative biology, pp. E385 
inproceedings  
Abstract: Some animals contact the substrate on which they move using simple appendages -- limbs with few degrees of freedom, which interact with the substrate with what is effectively a single rigid contact, such as a horse's hoof. Other animals have large multi-fingered feet, prehensile tails, or multi-segment tarsi. Why do some locomotor appendages have many mechanical degrees of freedom while others have only a few?
From first principles of Newtonian mechanics, it can be seen that when animals need to produce distinct and unanticipated mechanical configurations ("symbols") so rapidly that environmental noise becomes a challenge, this produces a lower bound on the number of degrees of freedom needed in the body.
In particular, if an animal needs to emit N different symbols, the animal's energy budget for emitting each symbol must be at least order of 2N times the energy of typical environmental noise -- otherwise simple bodies cannot work. As this safety margin approaches 1, the number of degrees of freedom needed in the locomotor appendages quickly rises to infinity.
BibTeX:
@inproceedings{revzen-2017-sicb,
  author = {S Revzen},
  title = {When do locomotor appendages get complicated?},
  booktitle = {Integrative and comparative biology},
  year = {2017},
  volume = {57},
  pages = {E385}
}
Revzen, S. Moving with more legs is different: a geometric mechanics perspective 2019
Vol. 59Integrative and comparative biology, pp. E191-E191 
inproceedings  
BibTeX:
@inproceedings{revzen-2019-moving,
  author = {Revzen, S},
  title = {Moving with more legs is different: a geometric mechanics perspective},
  booktitle = {Integrative and comparative biology},
  year = {2019},
  volume = {59},
  pages = {E191--E191}
}
Revzen, S. and Wu, Z. Viscous friction-like relationship arises from a simple Columb friction locomotion model 2019 APS Meeting Abstracts  inproceedings URL 
Abstract: It is well known in thermodynamics that viscosity-like dissipation relationships appear in particle models even after only a small number of collisions was simulated. We present a minimalistic model of a robot moving inchworm-like in a Columb friction regime, which exhibits a similar effect. This model is sufficiently simple to allow the relationship between actuation force and asymptotic average speed to be solved in closed form. For the range of parameters relevant for decimeter to meter length robots, the relationship of force and speed that arises is nearly linear-suggesting that the average behavior of this locomoting system appears similar to pushing through a viscous medium, and that viscosity-like models might be more appropriate to robots than we previously assumed.
BibTeX:
@inproceedings{revzen2019viscous,
  author = {Revzen, Shai and Wu, Ziyou},
  title = {Viscous friction-like relationship arises from a simple Columb friction locomotion model},
  booktitle = {APS Meeting Abstracts},
  year = {2019},
  url = {https://ui.adsabs.harvard.edu/abs/2019APS..MARV64012R/abstract}
}
Yu, M.Y., Liedtk, A. and Revzen, S. Trotting horses synchronize their legs during the second half of stance 2016
Vol. 56Integrative and comparative biology, pp. E247-E247 
inproceedings  
BibTeX:
@inproceedings{yu-2016-trotting,
  author = {Yu, M Y and Liedtk, A and Revzen, S},
  title = {Trotting horses synchronize their legs during the second half of stance},
  booktitle = {Integrative and comparative biology},
  year = {2016},
  volume = {56},
  pages = {E247--E247}
}
Zhao, D., Schaffer, C. and Revzen, S. Steering hexapedal robots 2015 IEEE Robotics Science and Systems conference, Miniature Legged Robots Workshop  inproceedings URL 
BibTeX:
@inproceedings{zhao-2015-RSS,
  author = {D Zhao and C Schaffer and S Revzen},
  title = {Steering hexapedal robots},
  booktitle = {IEEE Robotics Science and Systems conference, Miniature Legged Robots Workshop},
  year = {2015},
  url = {https://sites.google.com/site/miniatureleggedrobots}
}
Revzen, S. Paging on Access Graphs of Minimal Degree 3 2001 School: Hebrew University, Jerusalem  mastersthesis  
Abstract: This paper presents two related results in the field of Paging Algorithms
and in graph theory. It begins in presenting a generalization of
the Access Graph model of paging, dubbed Abstract Access Graphs.
This model is applicable to online problems in general, and its study
motivated my research. Then it is shown that on access graphs (in
the usual sense) with a minimal vertex degree of 3 or more the competitive
ratio is at least k/4 for all deterministic algorithms and H_k/4
for randomized algoorithms. This is derived from a graph theoretical
result showing that such trees contain many leaves. In attempting
to extend this result to abstract access graphs it is found that
such trees (arboresences) do not exist in some directed graphs, even
with arbitrarily high minimal in- and out- degree. Such an example
is constructed, thereby disproving the existence of linearly small
strongly connected directed dominating sets in such graphs.
BibTeX:
@mastersthesis{revzen-2001-MSc,
  author = {S Revzen},
  title = {Paging on Access Graphs of Minimal Degree 3},
  school = {Hebrew University, Jerusalem},
  year = {2001},
  note = {unpublished}
}
Frachtenberg, E. and Revzen, S. Lossless data compression 2003 United States Patent Applicationasssignee: Harmonic Data Systems Ltd.  misc URL 
Abstract: Dictionary based data compression apparatus comprising: a library
of static dictionaries each optimized for a different data type,
a data type determiner operable to scan incoming data and determine
a data type thereof, a selector for selecting a static dictionary
corresponding to said determined data type and a compressor for compressing
said incoming data using said selected dictionary. The apparatus
is useful in providing efficient compression of relatively short
data packets having undefined contents as may be expected in a network
switch.
BibTeX:
@misc{Patent-Comp,
  author = {E Frachtenberg and S Revzen},
  title = {Lossless data compression},
  journal = {United States Patent Application},
  year = {2003},
  note = {20030030575},
  url = {http://www.freepatentsonline.com/20030030575.html}
}
Shani, B., Revzen, S. and Frimerman, A. Analysis of Electrocardiogram Signals 2006 United States Patentassignee: Bio Signal Analysis, LTD  misc URL 
Abstract: Apparatus for graphical representation of a train of ECG complexes,
said ECG complexes comprising an R wave and a T-P interval and having
variable isoelectric levels, the apparatus comprising: an isoelectric
alignment unit for aligning the complexes in terms of isoelectric
level by aligning respective T-P intervals, thereby to provide a
graphical representation of said train of ECG complexes; and a temporal
alignment unit for aligning said complexes temporally using a predetermined
point of respective R waves. The aligned units are superimposed to
provide a distribution of a normalized ECG signal over a series of
pulses or heartbeats.
BibTeX:
@misc{Patent-ECG,
  author = {B Shani and S Revzen and A Frimerman},
  title = {Analysis of Electrocardiogram Signals},
  journal = {United States Patent},
  year = {2006},
  note = {WO/2006/123334},
  url = {http://www.freepatentsonline.com/WO2006123334.html}
}
Revzen, S. Experiments in Legged Locomotion: Animals, Robots and Rethinking Control 2012 Bio-Robotics seminar series, Arizona State University  misc  
BibTeX:
@misc{revzen-2012-ell,
  author = {Revzen, S},
  title = {Experiments in Legged Locomotion: Animals, Robots and Rethinking Control},
  year = {2012}
}
Revzen, S. Facing the Unknown, with Robots 2015 TEDx U of M  misc URL 
BibTeX:
@misc{revzen-2015-tedx,
  author = {S Revzen},
  title = {Facing the Unknown, with Robots},
  year = {2015},
  url = {https://www.youtube.com/watch?v=W1isc7PRrdY}
}
Revzen, S. Morphologically Modulated Dynamics 2017 ARO & ONR Bio-inspired Autonomous Systems Workshop  misc  
BibTeX:
@misc{revzen-2016-aro,
  author = {Revzen, S},
  title = {Morphologically Modulated Dynamics},
  year = {2017}
}
Revzen, S. A Few Reasons Why I Love Legs 2016 Ann Arbor Nerd Night Talk  misc URL 
Abstract: No animals other than ourselves move on wheels. That might seems strange, given how efficient and effective wheels are for moving around on land. Nevertheless, there are many good reasons to love legs. These include more obvious reasons, like the ability to use sparse footholds on rough surfaces, and less obvious reasons, such as newly discovered ways that legs make it easier for animals to control their movements. Insights from the animal world are leading to new and amazingly capable walking and running robots.
BibTeX:
@misc{revzen-2016-nerd,
  author = {S Revzen},
  title = {A Few Reasons Why I Love Legs},
  year = {2016},
  url = {https://annarbor.nerdnite.com/page/3/}
}
Revzen, S. (invited presentation ONR workshop) 2016 ONR workshop on Distributed Sensing, Actuation, and Control for Bioinspired Soft Robotics  misc  
BibTeX:
@misc{revzen-2016-onr,
  author = {Revzen, S},
  title = {(invited presentation ONR workshop)},
  year = {2016}
}
Revzen, S. Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage 2017 Ben-Gurion University, ISRAEL  misc  
BibTeX:
@misc{revzen-2016-ssm-bgu,
  author = {S Revzen},
  title = {Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage},
  year = {2017}
}
Revzen, S. Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage 2016 University of California Berkeley  misc  
BibTeX:
@misc{revzen-2016-ssm-cal,
  author = {S Revzen},
  title = {Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage},
  year = {2016}
}
Revzen, S. Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage 2017 Technion, ISRAEL  misc  
BibTeX:
@misc{revzen-2016-ssm-techn,
  author = {S Revzen},
  title = {Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage},
  year = {2017}
}
Revzen, S. Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage 2016 University of Pennsylvania Special GRASP Seminar  misc  
BibTeX:
@misc{revzen-2016-ssm-upenn,
  author = {S Revzen},
  title = {Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage},
  year = {2016}
}
Revzen, S. Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage 2016 University of Washington Robotics Seminar  misc  
BibTeX:
@misc{revzen-2016-ssm-uw,
  author = {S Revzen},
  title = {Seeking Simple Models for Multilegged Locomotion Hybrid Oscillators, Rapid Manufacturing, and Slippage},
  year = {2016}
}
Revzen, S. (invited presentation ARO workshop) 2016 ARO workshop on The Future of Vibration Energy Transfer in Solids and Structures Needs and Opportunities Workshop  misc  
BibTeX:
@misc{revzen-2017-aro,
  author = {Revzen, S},
  title = {(invited presentation ARO workshop)},
  year = {2016}
}
Revzen, S. Three legs to stand on: vignettes from the study of locomotion 2019 AIM Program Seminar  misc URL 
Abstract: The study of multi-legged locomotion provides a rich collection of mathematical challenges. In this talk I will present three vignettes from our work in recent years and highlight the ongoing progress in each: (1) differentiability of of the flows of some classes of non-smooth (hybrid) dynamical systems and ongoing work on efficient algorithms for estimating those differentials; (2) geometric mechanics at the singular limit of friction and ongoing work on data driven geometric gait optimization; (3) motivating examples for a Koopman theory for non-smooth systems and ongoing work discovering a refined understanding of non-resonance conditions necessary and sufficient for eigenfunction uniqueness. In each of these cases the needs arising from practical problems in robotics and biology lead us to theoretical advances with direct practical applications and implications. I will conclude with some general remarks on how to push the mathematical envelope in highly applied problem domains.
BibTeX:
@misc{revzen-2019-3legs,
  author = {S Revzen},
  title = {Three legs to stand on: vignettes from the study of locomotion},
  year = {2019},
  url = {https://lsa.umich.edu/math/news-events/all-events.detail.html/57434-14193504.html}
}
Revzen, S. How many legs become a snake? 2019 CMU Mechanical Engineering Seminar  misc  
Abstract: Modeling and control problems generally get harder the more Degrees of Freedom (DoF) are involved, suggesting that moving with many legs or grasping with many fingers should be difficult to describe. In this talk I will motivate the claim that when enough legs contact the ground, the complexity associated with momentum is gone, to be replaced by a "snake like" motion with slipping contacts. In this regime, Newtonian equations of motion are replaced by a “connection” which is both simple to estimate in a data driven form, and easy to simulate by adopting some non-conventional friction models. The talk will contain a brief intro to geometric mechanics, and consist mostly of results showing that: (i) this class of models is more general than may seem at first; (ii) they can be used for very rapid hardware in the loop gait optimization of both simple and complex robots; (iii) they motivate a simple motion model that fits experimental results remarkably well. If successful, this research agenda could improve motion planning speeds for multi-contact robotic systems by several orders of magnitude, and explain how simple animals can move so well with many limbs. Much of the work was done with my collaborators and former CMU members Ross Hatton and Brian Bittner.
BibTeX:
@misc{revzen-2019-CMU,
  author = {S Revzen},
  title = {How many legs become a snake?},
  year = {2019}
}
Revzen, S. From slithering, to swimming, to walking : a journey of geometric mechanics 2020 U Michigan Applied Physics Seminar  misc URL 
Abstract: There is hardly a domain where symmetry simplifies the physics more intuitively than in the geometric mechanics developed in the 1990's. These demonstrated how quotienting by a symmetry group, e.g. body frame motions, leads to a "reconstruction equation" that teases apart the influence of group symmetric constraints and group momentum. When applied to proprioceptively controlled movement in animals, or equivalently, high-gain feedback in robots, the reconstruction equation provides a simple and compact representation of the physics of locomotion. Here we present recent results, wherein we applied these insights to produce a fast and sample-efficient data-driven method for modeling the motion of animals and robots. We show the application of our method to Stokes fluid swimming, demonstrate its extension to finite but low Reynolds numbers, apply it to a broad class of compliant mechanisms, and show its surprising relevance to multi-legged systems whose multi-contact mechanics are very difficult to model.
BibTeX:
@misc{Revzen-2020-AppPhys,
  author = {S Revzen},
  title = {From slithering, to swimming, to walking : a journey of geometric mechanics},
  year = {2020},
  url = {https://lsa.umich.edu/appliedphysics/news-events/all-events.detail.html/78351-20012791.html}
}
Revzen, S How walking is a lot like slithering 2020 U Michigan EEB Department Seminar  misc URL 
Abstract: Video https://www.youtube.com/watch?v=RplfzUTBXkA
BibTeX:
@misc{Revzen-2020-EEB-seminar,
  author = {Revzen S},
  title = {How walking is a lot like slithering},
  year = {2020},
  url = {https://lsa.umich.edu/eeb/news-events/all-events.detail.html/76575-19727086.html}
}
Revzen, S. Kahn Autonomous Systems Mega-Project Annual Meeting (organizer) 2020 Kahn Foundation Annual Meeting  misc URL 
BibTeX:
@misc{Revzen-2020-Kahn,
  author = {S Revzen},
  title = {Kahn Autonomous Systems Mega-Project Annual Meeting (organizer)},
  year = {2020},
  url = {https://vision2020.lsevirtualevents.com/en/login}
}
Revzen, S. How the physics of slithering can teach multilegged robots to walk 2020 U Michigan Saltiel Life Sciences Seminar  misc URL 
BibTeX:
@misc{Revzen-2020-LSI-talk,
  author = {S Revzen},
  title = {How the physics of slithering can teach multilegged robots to walk},
  year = {2020},
  url = {https://www.lsi.umich.edu/events/2020-09/saltiel-life-sciences-symposium-2020}
}
Revzen, S Recovering from robot failures by very fast learning 2020 U Cal Santa-Cruz CPSRC Seminar  misc URL 
Abstract: As we begin to deploy more and more robots in the field, we encounter a growing need for both autonomous recovery from failure, and for graceful degradation under damage. Both of these are properties of biological systems. Recently we have shown two different approaches that employ tools and insights from the mathematical modeling of animal locomotion to allow our robots to quickly recover from typical failures. In one approach, our investigation revealed that the physics of multilegged running are a lot closer to swimming in low Reynolds number (Stokesian) fluids than they are to human running. By exploiting this fact, our robots could be made to learn how to move with only a few minutes of physical trials. When a failure occurs, the robots re-learn how to move even faster. In another approach, the reformulation of robot dynamics in terms of simultaneous constraints allowed us to exploit the observation that many common failures are low-rank in terms of the constraints. By augmenting the constraints that survived the failure with a naive learning algorithm, our robots quickly re-learned how to perform the desired behavior. Both approaches suggest that we are moving closer to animal-like abilities of recovery from damage.
BibTeX:
@misc{Revzen-2020-ucsc-seminar,
  author = {Revzen S},
  title = {Recovering from robot failures by very fast learning},
  year = {2020},
  url = {https://www.soe.ucsc.edu/events/cpsrc-seminar-recovering-robot-failures-very-fast-learning}
}
Revzen, S Two approaches to make robots robustly recover from failure 2020 University of Washington Mechanical Engineering Seminar  misc  
Abstract: The essence of autonomy is the ability to persist in performing a desired task in the face of unexpected obstacles and internal failures. In the last few years we have worked on methods which allowed multi-legged robots to persistently move through the world despite lacking an a-priori model of themselves or their interaction with the environment. We rely on tools from geometric mechanics and differential geometry to present two such approaches, would share some common features. Both approaches rely on data-driven floquet analysis (DDFA) tools to create and maintain data-driven models of the interaction of the robot with the environment. With one approach, these tools are then used in conjunction with ideas from geometric mechanics to optimize a library of gaits that enable motion through the plane, and maintain the expressive power of that library even when the robot undergoes internal failures. With the other approach, the DDFA tools are used to derive virtual constraints that can be used in conjunction with both partial physical models and desired “Behavior Specifications” to create a framework that robustly recovers from many practically meaningful forms of failure. This talk will be of interest to roboticists, mechanical engineers, and physicists or applied mathematicians with an interest in mechanics.
BibTeX:
@misc{Revzen-2020-UW-seminar,
  author = {Revzen S},
  title = {Two approaches to make robots robustly recover from failure},
  year = {2020}
}
Council, G. Data Driven Methods to Build Robust Legged Robots 2019 School: University of Michigan  phdthesis URL 
BibTeX:
@phdthesis{council-2019-phd,
  author = {G Council},
  title = {Data Driven Methods to Build Robust Legged Robots},
  school = {University of Michigan},
  year = {2019},
  url = {http://www.birds.eecs.umich.edu/publications/pdfs/2019-Council-PhD.pdf
} }
Revzen, S. Neuromechanical Control Architectures in Arthropod Locomotion 2009 School: Univeristy of California, Berkeley  phdthesis URL 
BibTeX:
@phdthesis{revzen-2009-PhD,
  author = {S Revzen},
  title = {Neuromechanical Control Architectures in Arthropod Locomotion},
  school = {Univeristy of California, Berkeley},
  year = {2009},
  note = {Department of Integrative Biology},
  url = {http://shrevzen.nfshost.com/docs/REVZEN-2009-PhD.pdf}
}