  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.
