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Kinematic Cartography for Locomotion at Low Reynolds Numbers

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3 Author(s)

Kinematic motion planning often requires a notion of “distance” between configurations. Euclidean distances on a parameter space are easy to compute, but can drastically distort the effort required to change configuration. Here, we present a framework for characterizing this distortion, based on principles adopted from the cartographic community, and a method for transforming configuration coordinates to better represent actuation costs. As a demonstration of this approach, we derive a true configuration distance metric for an important class of locomoting systems: low Reynolds number swimmers. Applying our cartographic coordinate transformation to these systems both provides intuition for previous numerical results, and allows direct geometric comparison between systems with heterogeneous morphology.