Graph minor analysis of reconfiguring state spaces
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.