Optimal Motion Planning for Multiple Robotrj Having Independent Goals

This work makes two contributions to geometric mo t ion planning f o r multiple robots: i ) mo t ion plans can be determined that simultaneously optimize a n independent performance criterzon f o r each robot; i i ) a general spectrum is defined between decoupled and centralized planning. B y 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 mo t ion planning approaches that consider optimality combine individual criteria in to a single criterion. A s a result, these methods can fail t o f ind m a n y potentially useful mo t ion plans. W e present implemented, multiplerobot mot ion planning algorithms that are derived f r o m the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: a) coordination along fixed, independent paths; ia) coordination along independent roadmaps; i i i ) general, unconstrained mot ion planning. Several computed examples are presented f o r all three problem classes that illustrate the concepts and algori thms.