A graph-based approach to multi-robot rendezvous for recharging in persistent tasks

This paper addresses the problem of maintaining persistence in coordinated tasks performed by a team of autonomous robots. We introduce a dedicated team of charging robots to service a team of primary working robots. Given that the trajectories of the working robots are known within a planning interval, the objective is to plan routes for the charging robots such that they rendezvous with and recharge all working robots to guarantee their continuous operation. To this end, the working robot trajectories are discretized to form a finite set of recharging points at which rendezvous can occur. The problem is formulated as a directed acyclic graph with vertex partitions containing sets of charging points for each working robot. Solutions consist of paths through the graph for each of the charging robots. The problem is shown to be NP-hard and a mixed integer linear program formulation is presented and solved for small problem instances. Finally, it is shown that while the optimal solution is not computationally feasible for large problem sizes, it is possible to graphically transform the single charging robot problem to a Traveling Salesman Problem, for which existing heuristic and approximation algorithms can be applied. Simulation results are presented for both single and multiple charging robot scenarios.