Abstract
A metamorphic robotic system is an aggregate of identical robot units which can individually detach and reattach in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and analyzing general metamorphic systems. This formal structure combined with ideas from geometric group theory leads to a natural extension of a configuration space for metamorphic systems — the shape complex — which is especially adapted to parallelization. We present an algorithm for optimizing reconfiguration sequences with respect to elapsed time. A universal geometric property of shape complexes — non-positive curvature — is the key to proving convergence to the globally time-optimal solution.
Supported in part by National Science Foundation Grant DMS-0134408.
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Ghrist, R. (2004). Shape Complexes for Metamorhpic Robots. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_12
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DOI: https://doi.org/10.1007/978-3-540-45058-0_12
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