talks

More Legs are Different: The Surprising Simplicity of Multi-Legged Locomotion

Most of the animals that move with legs in the world do so with six or more legs, yet humans have focused primarily on bipeds and quadrupeds in designing legged robots. This talk will present some theoretical and experimental results that suggest that multi-legged robots with six or more legs exhibit some surprising properties that challenge our anthropocentric intuitions about locomotion. Modeling multi-legged motion fairly accurately, at single percentage points of relative error, turns out to be much easier than naively expected. This is both due to event-selected hybrid systems resolving multi-contact collisions in a smooth way, and due to the surprisingly high accuracy of geometric mechanics models on dry friction problems to which they shouldn't really apply. Together our results suggest that modeling and learning how to move with many legs might be much easier than has previously been thought. (Given at the USC ECE CPS seminar; 2024-10-09)

Why do periodic gaits exist?

This talk will show that the appearance of periodic gaits in multi-legged animals should be surprising from the mechanical perspective, and propose a novel hypothesis for why they exist. Most terrestrial animals move using legs that push against a substrate. Viewed from the animal's body frame, the legs undergo rhythmic oscillations which are often modeled as a periodic solution to some mechanical equation of motion - a "periodic gait". First we will review some of the vast biomechanical literature that attempts to explain why periodic gaits exist and why animals select different gaits under different conditions. This will demonstrate that these explanations do not apply to small animals with many legs, leaving a puzzle, which will lead to a new hypothesis for why periodic gaits are biologically prevalent, and potentially, why they are a good idea for multi-legged robot designs. The talk will be suitable for an audience with an interest in mechanics, biomechanics, robotics, or control, and an undergraduate level background in dynamics or dynamical systems, and can serve in part as an introduction to the biomechanical literature on animal gaits. This work was funded in part by ARO MURI W911NF-17-1-0306, NSF CMMI 1825918, NSF CPS 2038432, and D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education Autonomous Systems Mega-Project.

Multi-Contact Collisions are Surprisingly Smooth

In many practical situations in robotics and biomechanics, objects collide along multiple contact points which form contacts in a state-dependent order. Examples include a human catching a basketball -- 10 contacts forming in an unknown order -- or a quadrupedal robot trotting -- forming two contacts in unknown order. Modeled as hybrid systems, these examples represent a challenge because the ensemble of trajectories spans an area where the guard functions representing the contact events intersect, meaning that over an infinitesimal change in initial conditions the system could be subject to vastly different dynamics. The hybrid systems that appear in these collision problems are not arbitrary; they have the property that the equations of motion depend only on the set of contacts created but not on the order of creation of those contacts. These are "Event Selected Systems (ESS)", and in recent work we have shown that an ESS where forces change because of position dependent guards will always have a continuously smooth state-space flow. To illustrate this we built a three legged hopper whose legs generate measurably distinct dynamics individually, yet the arbitrarily ordered triple contact leads to the same outcome up to affine approximation. In other words, even though each leg moves the robot in a different way as the contacts build up, correctly suggesting a non-differentiable flow after the first impact, the dynamics from aerial phase to after all three legs have landed are smooth -- continuous and differentiable. The implication of our results is that many multi-contact problems that may seem non-smooth and difficult to control are in fact smooth and may be amenable to conventional non-linear control approaches. The talk will introduce event selected systems, and be suitable for an audience familiar with multivariate calculus. The work was funded by ARO MURI W911NF-17-1-0306, NSF CPS 2038432, and the D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education Autonomous Systems Mega-Project. (given at Technion Mechanical Engineering Department 2023-12)

Ground Robots for Space Exploration: The Case for in-situ Built Robots

Achieving a meaningful presence on other bodies in our solar system is one of the greatest technological challenges facing humanity. It is also of crucial strategic importance in the growing competition between geo-political superpowers. The key limiting factor is mass: moving matter to other planetary bodies is hard, and forming matter into useful field robots requires components dependent on a supply chain of global extent. Current robotic technology relies on precision electronics and electromechanical components, powerful magnets and motors, and fast and accurate computations that require delicate semiconductor circuits to operate. Biology suggests that this dependency on accuracy, speed, and power is not an inherent requirement. Arthropods out-perform our best robots while suffering from none of these exacting requirements. Over the past 20 years Revzen and collaborators have focused on various bio-inspired insights for modeling, control, and robot fabrication to enable useful robots to be built from only a few, low-quality materials. The talk will present these insights and how they come together, including a discussion of some next steps toward a higher TRL. Intended for an audience with a solid background in the physical sciences, but relying on no field specific expertise. (Talk given June 2023, JHU APL)

Multi-legged Slipping is Simpler Than You Think

Multi-contact sliding mechanics in general and multilegged slipping in particular have long been considered difficult to model. As a consequence roboticists have avoided building multilegged systems and designing motion plans which include intentional slipping. I present a series of experiments and mathematical advances that demonstrate how these problems become easier with more contacts. These advances have allowed us to create fast learning algorithms that identify highly predictive models for the interaction physics of multi-contact gaits from a few dozen cycles of motion. The consequences are multifold: gait optimization algorithms for slipping and soft robots, speeding up simulations from linear to logarithmic dependence in the planning horizon, a deeper understanding of the relationship between Coulomb and Viscous friction, and perhaps some tantalizing hints as to the evolutionary origins of animals' motor control. The work presented was funded by the NSF CMMI 1825918, ARO W911NF-14-1-0573, ARO W911NF-17-1-0306, and the D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education Autonomous Systems Mega-Project. (Given at UPenn, GRASP seminar 2022)"

Learning Locomotion the Easy Way

It seems that animals are very good at learning how to move, and how to recover the ability to move after injury. Roboticists have attempted to imbue the same capabilities in robots with only moderate success. Through pursuing a deeper understanding of the underlying mathematics and physics of locomotion, I present the idea of using limit cycle oscillators as the key mathematical object to consider. Using tools developed for modeling the oscillators that appear in biological locomotion and combining them with insights from geometric mechanics, we created robots that can learn how to move with an optimization that lasts only a few dozens of cycles. The talk will present these ideas at a high level, primarily focusing on experimental results from animals, robots, and simulated robots. The work presented was funded by the NSF CMMI 1825918, ARO W911NF-14-1-0573, ARO W911NF-17-1-0306, and the D. Dan and Betty Kahn Michigan-Israel Partnership for Research and Education Autonomous Systems Mega-Project. (Given at Technion Autonomous Systems' Seminar (2022))

How walking is a lot like slithering

Legged movement is the most prevalent mode of terrestrial locomotion, and is typically viewed as qualitatively different from slithering or swimming. In this talk we present arguments and evidence to the contrary. We demonstrate that walking multilegged animals are governed by the same simplified physics as low Reynolds number ("Stokesian") swimmers. Using automated body and foot tracking of walking ants across 1 million steps we find that a Stokesian model accurately predicts this motion, and that of similarly analyzed multilegged robots. We also apply these analysis tools to nematodes and cockroaches. Using an allometric scaling examination of muscle force, muscle power, and walking contact mechanics we reveal that small walking animals are capable of overriding their inertia so rapidly that it can reasonably be dropped out of the equations of motion. This motivates us to define a new parameter, the ``stopping ratio'', which corresponds with Reynolds numbers in fluids, but also applies to legged locomotion. We define the (non-dimensional) stopping ratio as the number of motion cycles that are required for an animal to come to rest. We conclude that locomotion with small stopping ratios is often "Stokesian", and admits vast simplifications in control and planning. This suggests that the evolutionary origins of animal locomotion lie in this universally applicable class of Stokesian motion, that our physical intuitions of locomotion are quite misleading due to our bipedalism and size, and that the control of animal motion might be easier than we realize. Joint work with N. Gravish, G. Clifton, B. Bittner, and D. Zhao. (given at U. Michigan EEB department seminary (2022))

Facing the Unknown, with Robots

Is there anyway we can prepare to face the unknown? Can we develop robots that are fluid in function? Shai Revzen is an Assistant Professor of Electrical Engineering, of Ecology and Evolutionary Biology, and Robotics at the University of Michigan. He’s been a video game programmer, an experimental biologist, and Chief Architect in a Silicon Valley tech company. He has co-founded a biomedical start-up, authored several patents, and published academically in robotics, biology, and applied mathematics.