A solution of the minimum-time velocity planning problem based on lattice theory

TL;DR

This paper introduces a lattice-theoretic approach to solve the minimum-time velocity planning problem for vehicles, providing a necessary and sufficient feasibility condition and an operator based on differential equations to compute optimal solutions.

Contribution

It presents a novel lattice-based framework and a simple differential equation operator for efficiently solving the minimum-time velocity planning problem.

Findings

Feasibility set forms a lattice structure.

Operator computes optimal velocity law satisfying constraints.

The approach guarantees optimality if the feasible set is non-empty.

Abstract

For a vehicle on an assigned path, we find the minimum-time speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We present a necessary and sufficient condition for the feasibility of the problem and a simple operator, based on the solution of two ordinary differential equations, which computes the optimal solution. Theoretically, we show that the problem feasible set, if not empty, is a lattice, whose supremum element corresponds to the optimal solution.