Event Location: GHC 6501

Abstract: Animals often use gaits – cyclic changes in shape producing a net displacement – to move through their environments. In robotics, we are interested in planning motions for artificial systems that can match or exceed the locomotive capabilities of animals. A fundamental question of locomotion is “What are the characteristics of a useful gait?” The geometric mechanics community has made significant progress in answering this question, identifying functions of the system shape that capture the net displacements induced by broad classes of gaits without having to individually test each possible motion. In this proposal, we first introduce these results with the aim of separating them from the specialized language of differential geometry and making them accessible to a broader audience. Following this introduction, we then examine how the choice of generalized coordinates quality of the locomotion functions, a question which has not previously been addressed. Building off of these initial results, we propose to expand the applicability of our methods to systems with other physics, such as low Reynolds number swimmers, and to further explore the fundamental mathematical structures underlying our results. We anticipate that these two avenues of investigation will combine to allow us to address higher-dimensional systems in a principled, geometric fashion.