A linear-time algorithm for minimum-time velocity planning of autonomous vehicles

Velocity planning on a path to be followed by a wheeled autonomous vehicle may be difficult when high curvatures and velocities are allowed. A fast, straightforward algorithm to address this problem is presented. It has linear-time computational complexity and provides an optimal minimum-time velocity profile. The algorithm is based on a curvilinear discretization that makes easy to take into account the constraint on the vehicle's maximal normal acceleration. Formal proofs of the algorithm's properties are included. Two examples illustrate the proposed approach.