arXiv subjects

Shai Revzen

Publications and source records attributed to Shai Revzen.

At least 19 recordsLinked to original sources

arXiv2026

Linear Motility Maps in Nonlinear Viscous Fluids

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 moving through the fluid. A consequence of this is ``Purcell's Scallop Theorem'' -- a locomotion system that undergoes shape changes that follow the same path forward and backward in time (reciprocal body deformations) cannot achieve net displacement, regardless of pacing of those changes.We show that linear-in-velocity motility maps extend to any power law viscosity (a.k.a. Ostwald--de Waele fluid), and therefore to many biological fluids in intermediate shear ranges. We also show that the linear-in-velocity property can be violated in Carreau-Yasuda fluids to produce net motion using an ``inchworm'' model consisting of two unequal masses with unequal drag coefficients performing reciprocal motions. Interestingly, the direction of motion can be switched by changing speeds. Our results show that the linear motility map of geometric mechaincs can be used to analyze and design locomotion in power-law fluids, and that some nonlinear drag relationships such as Carreau-Yasuda can be exploited to generate net locomotion in seeming violation of the ``scallop theorem''.

cs.RO↗

arXiv2026

Walking on Rough Terrain with Any Number of Legs

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 more legs. Current multi-legged control strategies in robots include large black-box machine learning models, Central Pattern Generator (CPG) networks, and open-loop feed-forward control with stability arising from mechanics. Here we present a multi-legged control architecture for rough terrain using a segmental robot with 3 actuators for every 2 legs, which we validated in simulation for robots with 6 to 16 legs. Segments have identical state machines, and each segment also receives input from the segment in front of it. Our design bridges the gap between WalkNet-like event cascade controllers and CPG-based controllers: it tightly couples to the ground when contact is present, but produces fictive locomotion when ground contact is missing. The approach may be useful as an adaptive and computationally lightweight controller for multi-legged robots, and as a baseline capability for scaffolding the learning of machine learning controllers.

cs.RO↗

arXiv2026

Sample Efficient Learning of Body-Environment Interaction of an Under-Actuated System

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-friction environments it provides that the entire interaction is captured by the ``motility map''. Here we compare methods for learning the motility map from motion tracking data of a physical robot created specifically to test these methods by having under-actuated degrees of freedom and a hard to model interaction with its substrate. We compared four modeling approaches in terms of their ability to predict body velocity from shape change within the same gait, across gaits, and across speeds. Our results show a trade-off between simpler methods which are superior on small training datasets, and more sophisticated methods, which are superior when more training data is available.

cs.RO↗

arXiv2025

Asymmetric Friction in Geometric Locomotion

Geometric mechanics models of locomotion have provided insight into how robots and animals use environmental interactions to convert internal shape changes into displacement through the world, encoding this relationship in a ``motility map''. A key class of such motility maps arises from (possibly anisotropic) linear drag acting on the system's individual body parts, formally described via Riemannian metrics on the motions of the system's individual body parts. The motility map can then be generated by invoking a sub-Riemannian constraint on the aggregate system motion under which the position velocity induced by a given shape velocity is that which minimizes the power dissipated via friction. The locomotion of such systems is ``geometric'' in the sense that the final position reached by the system depends only on the sequence of shapes that the system passes through, but not on the rate with which the shape changes are made. In this paper, we consider a far more general class of systems in which the drag may be not only anisotropic (with different coefficients for forward/backward and left/right motions), but also asymmetric (with different coefficients for forward and backward motions). Formally, including asymmetry in the friction replaces the Riemannian metrics on the body parts with Finsler metrics. We demonstrate that the sub-Riemannian approach to constructing the system motility map extends naturally to a sub-Finslerian approach and identify system properties analogous to the constraint curvature of sub-Riemannian systems that allow for the characterization of the system motion capabilities.

cs.RO↗

arXiv2025

Learning the Geometric Mechanics of Robot Motion Using Gaussian Mixtures

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 robots with a useful number of DoF, these geometric mechanics models can only be constructed in the neighborhood of a gait. Here we show how Gaussian Mixture Models (GMM) can be used as a form of manifold learning that learns the structure of the Geometric Mechanics "motility map" and demonstrate: [i] a sizable improvement in prediction quality when compared to the previously published methods; [ii] a method that can be applied to any motion dataset and not only periodic gait data; [iii] a way to pre-process the data-set to facilitate extrapolation in places where the motility map is known to be linear. Our results can be applied anywhere a data-driven geometric motion model might be useful.

cs.RO↗

arXiv2024

Rapid Integrator for a Class of Multi-Contact Systems

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 based on the theory of Event Selected Systems (ESS). Many multicontact models are ESS, which has recently been shown to imply that despite a discontinuous vector field, the flow of these systems is continuous, piecewise smooth, and has a well defined orbital derivative for all trajectories, which can be rapidly computed. We provide an elementary proof that our integrator is first-order accurate and verify numerically that it is in fact second-order accurate as its construction anticipated. We also compare our integrator, implemented in NumPy, to a MuJoCo simulation on models with 2 to 100 contacts, and confirm that the increase in simulation time per contact is nearly identical. The results suggest that this novel integrator can be invaluable for modelling and control in many robotics applications.

cs.RO↗

arXiv2023

Modeling multi-legged robot locomotion with slipping and its experimental validation

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 years. This may be in part due to the difficulty in modeling multi-legged motion with slipping and producing reliable predictions of body velocity. Here we present a detailed measurement of the foot contact forces in a hexapedal robot with multiple sliding contacts, and provide an algorithm for predicting these contact forces and the body velocity. The algorithm relies on the recently published observation that even while slipping, multi-legged robots are principally kinematic, and employ a friction law ansatz that allows us to compute the shape-change to body-velocity connection and the foot contact forces. This results in the ability to simulate motion plans for a large number of potentially slipping legs. In homogeneous environments, this can run in (parallel) logarithmic time of the planning horizon

cs.RO↗

arXiv2022

Bridging Walking and Slithering -- Stokesian Locomotion

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 locomotion can be viewed from the perspective of piece-wise contact constraint formation and removal. Slithering and low Reynolds number swimming operate under continuous constraints of force balance, wherein dissipation removes the ability to accumulate momentum. Here we discuss how to bridge the gap between these domains of motion, thereby, among other benefits, producing models for the space of legged locomotion with slipping. The connective fabric is the use of a "Stokesian", or "local connection" model.

cs.RO↗

arXiv2022

Estimating Phase from Observed Trajectories Using the Temporal 1-Form

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 asymptotic phase can be estimated using a carefully chosen series expansion which directly computes the phase response curve and provide an algorithm for estimating the co-efficients of this series. Unlike all previously available data driven phase estimation methods, our algorithm can: (i) use observations that are much shorter than a cycle; (ii) recover phase within any forward invariant region for which sufficient data are available; (iii) recover the phase response curves (PRC-s) that govern weak oscillator coupling; (iv) show isochron curvature, and recover nonlinear features of isochron geometry. Our method may find application wherever models of oscillator dynamics need to be constructed from measured or simulated time-series.

math.DS↗

arXiv2021

Dandelion-Picking Legged Robot

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 loose ground, and they trample continuous strips of land thereby reducing the viable crop area. Legged robots offer an alternative, but existing commercial legged robots are complex, expensive, and hard to maintain. We propose the use of multilegged robots using low-degree-of-freedom (low-DoF) legs and demonstrate our approach with a lawn pest control task: picking dandelions using our inexpensive and easy to fabricate BigANT robot. For this task we added an RGB-D camera to the robot. We also rigidly attached a flower picking appendage to the robot chassis. Thanks to the versatility of legs, the robot could be programmed to perform a ``swooping'' motion that allowed this 0-DoF appendage to pluck the flowers. Our results suggest that robots with six or more low-DoF legs may hit a sweet-spot for legged robots designed for agricultural applications by providing enough mobility, stability, and low complexity.

cs.RO↗

arXiv2021

Phase Response Curves and the Role of Coordinates

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 $y\in\mathbb{R}$ actually depends on the full choice of coordinates $(x,y)$, $x\in\mathbb{R}^d$. We give a coordinate-free definition of the PRC making this observation obvious. We show how by controlling $y$, using delay coordinates of $y$, and postulating the dynamics of $x$ as a function of $x$ and $y$, we can sometimes reconstruct the PRC with respect to the $(x,y)$ coordinates. This suggests a means for obtaining the PRC of, e.g., a neuron via a voltage clamp.

q-bio.QM↗

arXiv2021

Challenges in Dynamic Mode Decomposition

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 range of fields, including fluid mechanics, robotics, and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modeling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables. Our numerical models include system and measurement noise. We explore the influences of dataset metrics, the spectrum of the latent dynamics, the normality of the system matrix, and the geometry of the dynamics. Our results show that even for these very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability. Our work is motivated by our experience modeling multilegged robot data, where we have encountered great difficulty in reconstructing time series for oscillatory systems with slow transients, which decay only slightly faster than a period.

math.DS↗

arXiv2021

Optimizing Gait Libraries via a Coverage Metric

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 becomes of paramount importance when robots are damaged and no longer move as designed. Here we propose a goal function we call "coverage", that represents the usefulness of a library of locomotion primitives in a manner agnostic to the particulars of the primitives themselves. We demonstrate the ability to optimize coverage on both simulated and physical robots, and show that coverage can be rapidly recovered after injury. This suggests that by optimizing for coverage, robots can sustain their ability to navigate through the world even in the face of significant mechanical failures. The benefits of this approach are enhanced by sample-efficient, data-driven approaches to system identification that can rapidly inform the optimization of primitives. We found that the number of degrees of freedom improved the rate of recovery of our simulated robots, a rare result in the fields of gait optimization and reinforcement learning. We showed that a robot with limbs made of tree branches (for which no CAD model or first principles model was available) is able to quickly find an effective high-coverage library of motion primitives. The optimized primitives are entirely non-obvious to a human observer, and thus are unlikely to be attainable through manual tuning.

cs.RO↗

arXiv2021

Representing and computing the B-derivative of an $EC^r$ vector field's $PC^r$ flow

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.

math.DS↗

arXiv2020

Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems

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 the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to ``Shape-Underactuated Dissipative Systems (SUDS)'' -- systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly those robots using highly damped series elastic actuators. Whether involved in locomotion or manipulation, these robots are often used to interface less rigidly with the environment. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs suggesting that systems with soft pneumatic actuators or dielectric elastomers can be modeled with the tools presented. 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.

cs.RO↗

arXiv2020

Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits

Our recent work established existence and uniqueness results for $\mathcal{C}^{k,\alpha}_{\text{loc}}$ globally defined linearizing semiconjugacies for $\mathcal{C}^1$ 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" $\mathcal{C}^\infty$ flows having a globally attracting hyperbolic fixed point or periodic orbit, the $\mathcal{C}^\infty$ Koopman eigenfunctions can be completely classified, generalizing a result known for analytic systems. For such systems, every $\mathcal{C}^\infty$ eigenfunction is uniquely determined by its eigenvalue modulo scalar multiplication.

math.DS↗

arXiv2020

Recovery of Behaviors Encoded via Bilateral Constraints

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 template 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.

cs.RO↗

arXiv2019

Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits

We consider $C^1$ dynamical systems having an attracting hyperbolic fixed point or periodic orbit and prove existence and uniqueness results for $C^k$ (actually $C^{k,\alpha}_{\text{loc}}$) linearizing semiconjugacies -- of which Koopman eigenfunctions are a special case -- defined on the entire basin of attraction. 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. Using our main results we also prove new existence and uniqueness statements for $C^k$ Koopman eigenfunctions, including a complete classification of $C^\infty$ eigenfunctions assuming a $C^\infty$ dynamical system with semisimple and nonresonant linearization. We give an intrinsic definition of "principal Koopman eigenfunctions" which generalizes the definition of Mohr and Mezi\'{c} for linear systems, and which includes the notions of "isostables" and "isostable coordinates" appearing in work by Ermentrout, Mauroy, Mezi\'{c}, 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 \cite{mohr2016koopman} is unique under certain conditions. We also discuss the limit used to define the "faster" isostable coordinates in \cite{wilson2018greater,monga2019phase} in light of our main results.

math.DS↗