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 tenfold 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.

It is challenging to perform system 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 control of the system’s internal configuration. This method constructs a series of connected models comprising actuator and locomotor dynamics based on data points from stochastically perturbed, repeated behaviors. By deriving these connected models from general formulations of dissipative Lagrangian systems with symmetry, we offer a method that can be applied broadly to robots with first-order, low-pass actuator dynamics, including swelling-driven actuators used in hydrogel crawlers. These models accurately capture the dynamics of the system shape and body movements of a simplified swimming robot model. We further apply our approach to a stimulus-responsive hydrogel simulator that captures the complexity of chemomechanical interactions that drive shape changes in biomedically relevant micromachines. Finally, we propose an approach of numerically optimizing control signals by iteratively refining models, which is applied to optimize the input waveform for the hydrogel crawler. This transfer to realistic environments provides promise for applications in locomotor design and biomedical engineering.

The gaits of locomoting systems are typically designed to maximize some sort of efficiency, such as cost of transport or speed. Equally important is the ability to modulate such a gait to effect turning maneuvers. For drag-dominated systems, geometric mechanics provides an elegant and practical framework for both ends—gait design and gait modulation. Within this framework, “constraint curvature” maps can be used to approximate the net displacement of robotic systems over cyclic gaits. Gait optimization is made possible under a previously reported “soap-bubble” algorithm. In this work, we propose both local and global gait morphing algorithms to modify a nominal gait to provide single-parameter steering control. Using a simplified swimmer, we numerically compare the two approaches and show that for modest turns, the local approach, while suboptimal, nevertheless proves effective for steering control. A potential advantage of the local approach is that it can be readily applied to soft robots or other systems where local approximations to the constraint curvature can be garnered from data, but for which obtaining an exact global model is infeasible.