An algorithm for planning time-optimal trajectories for given minimum distance paths

The authors address the problem of determining a time-dependent trajectory when a path planner provides a minimal distance path between two points. In contrast with most of the known methods that work in the velocity-time (v-t) space, theirs works directly in the velocity-arc length (v-s) space, which is the data provided by geometrical path planners. In a first instance, the method assumes a linear path to obtain a nonconstrained trajectory in the v-s plane. The dynamical constraints are then projected into this space to limit the original solution. As the algorithm uses discretized data, the authors provide its cost on space and time and the exact evaluation for the approximation error which depends on the desired accuracy