Since optimization for one robot is already very difficult, it may not be surprising that computing Pareto-optimal plans is even harder. For some problems, it is even possible that a continuum of Pareto-optimal solutions exist (see Example 9.3), which is very discouraging. Fortunately, for the problem of coordinating robots on topological graphs, as considered in Section 7.2.2, there is only a finite number of solutions [386]. A grid-based algorithm, which is based on dynamic programming and computes all unique Pareto-optimal coordination plans, is presented in [606]. For the special case of two polygonal robots moving on a tree of piecewise-linear paths, a complete algorithm is presented in [212].

Steven M LaValle 2020-08-14