To achieve high-dexterity motion planning on floating-base systems, the base dynamics induced by arm motions must be treated carefully. In general, it is a significant challenge to establish a fixed-base frame during tasking due to forces and torques on the base that arise directly from arm motions (e.g. arm drag in low Reynolds environments and arm momentum in high Reynolds environments). While thrusters can in theory be used to regulate the vehicle pose, it is often insufficient to establish a stable pose for precise tasking, whether the cause be due to underactuation, modeling inaccuracy, suboptimal control parameters, or insufficient power. We propose a solution that asks the thrusters to do less high bandwidth perturbation correction by planning arm motions that induce zero perturbation on the base. We are able to cast our motion planner as a nonholonomic rapidly-exploring random tree (RRT) by representing the floating-base dynamics as pfaffian constraints on joint velocity. These constraints guide the manipulators to move on zero-perturbation manifolds (which inhabit a subspace of the tangent space of the internal configuration space). To invoke this representation (termed a perturbation map) we assume the body velocity (perturbation) of the base to be a joint-defined linear mapping of joint velocity and describe situations where this assumption is realistic (including underwater, aerial, and orbital environments). The core insight of this work is that when perturbation of the floating-base has affine structure with respect to joint velocity, it provides the system a class of kinematic reduction that permits the use of sample-based motion planners (specifically a nonholonomic RRT). We show that this allows rapid, exploration-geared motion planning for high degree of freedom systems in obstacle rich environments, even on floating-base systems with nontrivial dynamics.

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.