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Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning. 

Abstract 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. 

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.