Optimal motion planning for multiple robots having independent goals

This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning. By considering independent performance criteria, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory research. Previous multiple-robot motion planning approaches that consider optimality combine individual criteria into a single criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multi-robot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: i) coordination along fixed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Several computed examples are presented for all three problem classes that illustrate the concepts and algorithms.