Graph minor analysis of reconfiguring state spaces
Thomas Larkworthy and Subramanian Ramamoorthy
In: Proc. Workshop on Modular Robotics: State of the Art, IEEE International Conference on Robotics and Automation, 2010., Anchorage, USA(2010).

Abstract

Efficiently overcoming difficult motion constraints is the prime problem in development of efficient motion planning algorithms for self-reconfiguring systems (SRSs). Metamodularization, and other related techniques, deal with the problem by adding further constraints in a way that simplifies planning. If Rn denotes a raw state space for configurations containing n sub-units, and Cn a further constrained version of Rn then Rn ≤ Cn where ≤ denotes the graph minor relation. Often the choice of Cn is ad hoc (although made on clever intuitions). We wish to study whether there are principles that may guide this choice. We demonstrate one such principle, that is planning is tractable, e.g. in meta-modularized sub-spaces, when Cn ≤ Cn+1, which captures a smooth increase in state-space complexity as more modules are added.

[Edit]