Pareto Optimization in Robotics With Acceleration Constraints

Abstract

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. We prove that, when velocity and acceleration are bounded, the finiteness result still holds for systems involving only two robots. In tins setting, we separate acceleration bounds into two opposite assumptions: initial bounded accelerations and terminal bounded accelerations. Initial bounded accelerations are the cases when certain instantaneous stops are allowed. In contrast, terminal bounded accelerations allow infinite accelerations toward moving directions. We shows that either assumption does not alter the finiteness result for Pareto optimal path classes. General bounded accelerations can be derived by combining the two assumptions. However, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give a counter examples involving three robots and explain the result in terms of the geometry of phase space. We also shows that with certain bounds on obstacle distributions finiteness results can be recovered.