SCTOMP: Spatially Constrained Time-Optimal Motion Planning

This work focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows a system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the assumption of a given collision-free geometric reference. Instead, we present a three-stage motion planning method that solely relies on start and goal locations and a geometric representation of the environment to compute a time-optimal trajectory that is compliant with system dynamics and constraints. The proposed scheme first finds collision-free navigation corridors, second computes an obstacle-free Pythagorean Hodograph parametric spline along each corridor, and third, solves a spatially reformulated minimum-time optimization problem at each of these corridors. The spline obtained in the second stage is not a geometric reference, but an extension of the free space associated with its corridor, and thus, time-optimality of the solution is guaranteed. The validity of the proposed approach is demonstrated by a well-established planar example and benchmarked in a spatial system against state-of-the-art methodologies across a wide range of scenarios in highly congested environments. Video: https://youtu.be/zGExvnUEfOY