29 citations · 65 across the 22 of their papers we have counts for
24 papers
Linear Motility Maps in Nonlinear Viscous Fluids
Yishun Zhou, Shai Revzen
Systems moving in low Reynolds number fluid regimes are known to be governed by a ``motility map'' which linearly relates their shape change rates to they body frame velocity movin…
Walking on Rough Terrain with Any Number of Legs
Zhuoyang Chen, Xinyuan Wang, Shai Revzen
Robotics would gain by replicating the remarkable agility of arthropods in navigating complex environments. Here we consider the control of multi-legged systems which have 6 or mor…
Sample Efficient Learning of Body-Environment Interaction of an Under-Actuated System
Zvi Chapnik, Yizhar Or, Shai Revzen
Geometric mechanics provides valuable insights into how biological and robotic systems use changes in shape to move by mechanically interacting with their environment. In high-fric…
Asymmetric Friction in Geometric Locomotion
Ross L. Hatton, Yousef Salaman, Shai Revzen
Geometric mechanics models of locomotion have provided insight into how robots and animals use environmental interactions to convert internal shape changes into displacement throug…
Learning the Geometric Mechanics of Robot Motion Using Gaussian Mixtures
Ruizhen Hu, Shai Revzen
Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For…
Rapid Integrator for a Class of Multi-Contact Systems
Marion Anderson, Shai Revzen
Many problems in robotics involve creating or breaking multiple contacts nearly simultaneously or in an indeterminate order. We present a novel general purpose numerical integrator…
Modeling multi-legged robot locomotion with slipping and its experimental validation
Ziyou Wu, Dan Zhao, Shai Revzen
Multi-legged robots with six or more legs are not in common use, despite designs with superior stability, maneuverability, and a low number of actuators being available for over 20…
Bridging Walking and Slithering -- Stokesian Locomotion
Shai Revzen, Dan Zhao, Glenna Clifton +2
Both legged locomotion and slithering motions typically utilize periodic gaits -- repeating cycles of body shape change that produce a net motion through the world. Legged locomoti…
Estimating Phase from Observed Trajectories Using the Temporal 1-Form
Simon Wilshin, Matthew D. Kvalheim, Clayton Scott +1
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asympto…
Dandelion-Picking Legged Robot
Sandilya Sai Garimella, Shai Revzen
Agriculture is currently undergoing a robotics revolution, but robots using wheeled or treads suffer from known disadvantages: they are unable to move over rubble and steep or loos…
Phase Response Curves and the Role of Coordinates
Simon Wilshin, Matthew D. Kvalheim, Shai Revzen
The "Phase Response Curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences. We make the observation that the PRC with respect to a coordinate $y\in\m…
Challenges in Dynamic Mode Decomposition
Ziyou Wu, Steven L. Brunton, Shai Revzen
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide ran…
Optimizing Gait Libraries via a Coverage Metric
Brian Bittner, Shai Revzen
Many robots move through the world by composing locomotion primitives like steps and turns. To do so well, robots need not have primitives that make intuitive sense to humans. This…
Representing and computing the B-derivative of an vector field's flow
George Council, Shai Revzen, Samuel A. Burden
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 B…
Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems
Brian Bittner, Ross L. Hatton, Shai Revzen
Systems whose movement is highly dissipative provide an opportunity to both identify models easily and quickly optimize motions. Geometric mechanics provides means for reduction of…
Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits
Matthew D. Kvalheim, David Hong, Shai Revzen
Our recent work established existence and uniqueness results for globally defined linearizing semiconjugacies for flows having a gl…
Recovery of Behaviors Encoded via Bilateral Constraints
George Council, Shai Revzen
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,…
Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits
Matthew D. Kvalheim, Shai Revzen
We consider dynamical systems having an attracting hyperbolic fixed point or periodic orbit and prove existence and uniqueness results for (actually $C^{k,α}_{\text{loc…
Gait modeling and optimization for the perturbed Stokes regime
Matthew D. Kvalheim, Brian Bittner, Shai Revzen
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 geometr…
Global linearization and fiber bundle structure of invariant manifolds
Jaap Eldering, Matthew Kvalheim, Shai Revzen
We study global properties of the global (center-)stable manifold of a normally attracting invariant manifold (NAIM), the special case of a normally hyperbolic invariant manifold (…
Reverse-engineering invariant manifolds with asymptotic phase
Matthew Kvalheim, Shai Revzen
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…
Event-Selected Vector Field Discontinuities Yield Piecewise-Differentiable Flows
Samuel A. Burden, S. Shankar Sastry, Daniel E. Koditschek +1
We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics,…
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
Samuel A. Burden, Shai Revzen, S. Shankar Sastry
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 stab…
Dimension Reduction Near Periodic Orbits of Hybrid Systems
Samuel Burden, Shai Revzen, S. Shankar Sastry
When the Poincaré map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant sub…