Optimal Control of Cooperative Multi-Robot Systems using Mixed-Integer Linear Programming

A new planning method for optimal control of multi-robot systems is discussed which accounts for the (continuous) physical locomotion dynamics of the robots and its tight coupling to the distribution and allocation of (discrete) subtasks to the robots to fulfill a joint mission. The point of departure is a nonlinear and nonconvex hybrid optimal control problem (HOCP) formulation which incorporates a detailed hybrid automaton model. Because of the many difficulties involved in solving this problem like large computational times and the lack of good or global convergence properties it is transcribed into a mixedinteger linear program (MILP). This can be solved much more efficiently using existing algorithms. The proposed approach is outlined for an example problem of cooperative soccer robots. The MILP solution itself may serve either as a good initial solution estimate for a method addressing the nonlinear HOCP or may later become the kernel of a model predictive control method for cooperative multi-robot systems. Despite the promising results obtained so far a variety of open questions yet remains to be answered including the ”best” way of transcribing HOCP to MILP with respect to both computational efficiency and good HOCP solution approximation.