State complexes for metamorphic robots

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 hype of configuration space,for metamorphic robots-the state complex-which is especially adapted to parallelization. We present an algorithm for optitimizing 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 time-optimal solution obtainable from the initial path.