State complexes for metamorphic robots
<|reference_start|>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. This formal structure, combined with ideas from geometric group theory, leads to a natural extension of a configuration space for metamorphic robots -- the state 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 state complexes -- non-positive curvature -- is the key to proving convergence to the globally time-optimal solution.<|reference_end|>
@article{abrams2003state,
    title={State complexes for metamorphic robots},
    author={A. Abrams and R. Ghrist},
    journal={arXiv preprint arXiv:cs/0307004},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0307004},
    primaryClass={cs.RO cs.CG}
}