Convergence Analysis of Spatial-Sampling-Based Algorithms for Time-Optimal Smooth Velocity Planning

Abstract

For a vehicle on an assigned path, we consider the problem of finding the time-optimal speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We show that the problem can be solved with an arbitrarily high precision by performing a finite element lengthwise path discretization and using a quadratic spline for interpolation. In particular, we show that an $$\epsilon $$-optimal solution can be found in a time which is a polynomial function of $$\epsilon ^{-1}$$, more precisely its eighth power.