| Abstract: |
| The tools of geometric mechanics pioneered by Bloch and others provide a compact representation of locomotion dynamics as ``the reconstruction equation``. We have found this equation yields a convenient form for estimating models directly from observation data. We have applied data-driven geometric mechanics models toward optimizing robot gaits both physical and simulated, exploring the optimality of animal movement, and efficiently creating libraries of maneuvers that are to be used as building blocks for higher level robot tasks. Our methods employed the tools of Data-Driven Floquet Analysis, providing a phase that we used as a means of grouping related measurements, allowing us to estimate a reconstruction equation model as a function of phase and in the neighborhood of an observed behavior. This allowed us to build models at unanticipated scales of complexity and speed. Our use of a perturbation expansion for the geometric terms also allowed us to prove that this ``geometric`` case is conjugate to the dynamics of a range of highly damped cases, leading to an improved estimation procedure for models in low but non-zero Reynolds number. The talk will focus on results, simulated and physical, and the surprising practicality of data-driven geometric mechanics. |
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