Time Optimal Trajectories for a Mobile Robot Under Explicit Acceleration Constraints

Mobile robots are becoming increasingly important for different tasks in various industries. The time-optimal path planning problem in two-dimensional for a point mass robot, navigating in an obstacle free environment, is the focus of this research work. The main challenge is to compute an explicit solution path which takes into account the constraints on the robot's along-track and cross-track accelerations, while minimizing the overall travel time. We analyze this problem by employing Pontryagin's minimum principle and Kelley's condition, to derive time-optimal path primitives. Using these path primitives, the paper proposes a methodology that synthesizes time-optimal paths, and analytically solves (up to simple quadratures) for the corresponding adjoint vector in order to prove compliance with necessary conditions for optimality. Representative examples are studied in order to demonstrate the method, and are compared with numerical results using direct collocation.