Today I read a paper titled “State complexes for metamorphic robots”
The abstract is:
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.