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State Complexes for Metamorphic Robots

Department of Mathematics, University of Georgia, Athens, GA 30602, USA

R. Ghrist

Department of Mathematics, University of Illinois, Urbana, IL 61801, USA

A metamorphic robotic system is an aggregate of homogeneous robot units which can individually and selectively locomote in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and analyzing general metamorphic robots. With this formal structure, combined with ideas from geometric group theory, we define a new type of configuration space for metamorphic robots—the state complex—which is especially adapted to parallelization. We present an algorithm for optimizing an input reconfiguration sequence with respect to elapsed time. A universal geometric property of state complexes—non-positive curvature—is the key to proving convergence to the globally timeoptimal solution obtainable from the initial path.

Key Words: metamorphic robot • configuration space • cubical complex • curvature

The International Journal of Robotics Research, Vol. 23, No. 7-8, 811-826 (2004)
DOI: 10.1177/0278364904045468


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