The Geometry of Optimal Gait Families for Steering Kinematic Locomoting Systems

Motion planning for locomotion systems typically requires translating high-level rigid-body tasks into low-level joint trajectories-a process that is straightforward for car-like robots with fixed, unbounded actuation inputs but more challenging for systems like snake robots, where the mapping depends on the current configuration and is constrained by joint limits. In this paper, we focus on generating continuous families of optimal gaits-collections of gaits parameterized by step size or steering rate-to enhance controllability and maneuverability. We uncover the underlying geometric structure of these optimal gait families and propose methods for constructing them using both global and local search strategies, where the local method and the global method compensate each other. The global search approach is robust to nonsmooth behavior, albeit yielding reduced-order solutions, while the local search provides higher accuracy but can be unstable near nonsmooth regions. To demonstrate our framework, we generate optimal gait families for viscous and perfect-fluid three-link swimmers. This work lays a foundation for integrating low-level joint controllers with higher-level motion planners in complex locomotion systems.

Adaptive Gait Modeling and Optimization for Principally Kinematic Systems

Robotic adaptation to unanticipated operating conditions is crucial to achieving persistence and robustness in complex real world settings. For a wide range of cutting-edge robotic systems, such as micro- and nano-scale robots, soft robots, medical robots, and bio-hybrid robots, it is infeasible to anticipate the operating environment a priori due to complexities that arise from numerous factors including imprecision in manufacturing, chemo-mechanical forces, and poorly understood contact mechanics. Drawing inspiration from data-driven modeling, geometric mechanics (or gauge theory), and adaptive control, we employ an adaptive system identification framework and demonstrate its efficacy in enhancing the performance of principally kinematic locomotors (those governed by Rayleigh dissipation or zero momentum conservation). We showcase the capability of the adaptive model to efficiently accommodate varying terrains and iteratively modified behaviors within a behavior optimization framework. This provides both the ability to improve fundamental behaviors and perform motion tracking to precision. Notably, we are capable of optimizing the gaits of the Purcell swimmer using approximately 10 cycles per link, which for the nine-link Purcell swimmer provides a factor of ten improvement in optimization speed over the state of the art. Beyond simply a computational speed up, this ten-fold improvement may enable this method to be successfully deployed for in-situ behavior refinement, injury recovery, and terrain adaptation, particularly in domains where simulations provide poor guides for the real world.

A Data-Driven Approach to Geometric Modeling of Systems with Low-Bandwidth Actuator Dynamics

It is challenging to perform identification on soft robots due to their underactuated, high dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory), that can be applied to systems with low-bandwidth actuation of the shape space. By exploiting temporal asymmetries in actuator dynamics, our approach enables the design of robots that can be driven by a single control input. We present a method for constructing a series connected model comprising actuator and locomotor dynamics based on data points from stochastically perturbed, repeated behaviors around the observed limit cycle. We demonstrate our methods on a real-world example of a soft crawler made by stimuli-responsive hydrogels that locomotes on merely one cycling control signal by utilizing its geometric and temporal asymmetry. For systems with first-order, low-pass actuator dynamics, such as swelling-driven actuators used in hydrogel crawlers, we show that first order Taylor approximations can well capture the dynamics of the system shape as well as its movements. Finally, we propose an approach of numerically optimizing control signals by iteratively refining models and optimizing the input waveform.