Shai Revzen

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 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''.

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 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.

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 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.

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 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.

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 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.

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, 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.

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 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 (NHIMs). 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.