Explicit Time-Optimal Speed Profiles for Planar Paths with Monotone Curvature

TL;DR

This paper presents an explicit, exact method for computing time-optimal speed profiles along planar paths with monotonic curvature, considering various boundary conditions and constraints, with rigorous proof of global optimality.

Contribution

It introduces a novel explicit and exact approach for minimum-time speed profiling on paths with monotonic curvature, ensuring global optimality under mild conditions.

Findings

Explicit construction of time-optimal profiles

Handles various boundary speed conditions

Numerical implementation is straightforward

Abstract

Minimum-time speed profiles are constructed for planar paths with smooth strictly-monotonic signed curvature, subject to constraints on velocity, normal acceleration and tangential acceleration. The construction is explicit and exact, and global optimality is rigorously established from first principles under mild regularity conditions on the path. Free, fixed, and inequality-constrained boundary speeds are all accommodated. Numerical implementation is straightforward.