Optimal motion planning for multiple robots having independent goals

This work makes two contributions to geometric motion planning for multiple robots: i) Motion plans are computed that simultaneously optimize an independent performance measure for each robot; ii) A general spectrum is deened between decoupled and centralized planning, in which we introduce coordination along independent roadmaps. By considering independent performance measures, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory literature. Previous multiple-robot motion planning approaches that consider optimality combine individual performance measures into a scalar criterion. As a result, these methods can fail to nd many potentially useful motion plans. We present implemented, multiple-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 xed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Computed examples are presented for all three problem classes that illustrate the concepts and algorithms.