Towards the Analytical Computation of Time-Optimal Trajectories for Unicycle Robots in Corridor Environments

This paper presents an analytical formulation for the time-optimal trajectory planning problem for unicycle robots in structured environments. We describe the environment as a sequence of rectangular corridors and compute the trajectory as a sequence of time-optimal motion primitives defined according to Pontryagin's minimum principle. The proposed approach uses a heuristic to place the center of arc maneuvers and, in certain situations, uses a turn on-the-spot primitive as initial or final maneuver to achieve time-optimality and obstacle avoidance. The computation of the trajectory within each corridor is decoupled and, therefore, the results can be applied to an arbitrarily long sequence of corridors while allowing parallel computations. The effectiveness of the approach is demonstrated by means of an example and Monte Carlo simulation: the suboptimality of the analytic motion is less than 1%, while the solution time is two orders of magnitude less than that of an optimal control problem formulation.