Pareto optimal multi-robot coordination with acceleration constraints

We consider a collection of robots sharing a common environment, each robot constrained to move on a roadmap in its configuration space. To program optimal collision-free motions requires a choice of the appropriate notion of optimality. We work in the case where each robot wishes to travel to a goal while optimizing elapsed time and consider vector-valued (Pareto) optima. Earlier work demonstrated a finite number of Pareto-optimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. This paper demonstrates that when velocity and acceleration are bounded, the finiteness result still holds for certain systems, e.g., two robots; however, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give examples and explain the result in terms of the geometry of phase space.