A sequential approach for speed planning under jerk constraints

TL;DR

This paper introduces a sequential line-search algorithm for efficiently computing minimum-time speed profiles under velocity, acceleration, and jerk constraints, improving robustness over traditional NLP solvers in industrial speed planning tasks.

Contribution

The paper presents a novel sequential line-search method that exploits problem structure to solve jerk-constrained speed planning more efficiently and robustly.

Findings

The proposed algorithm outperforms existing NLP solvers in computational experiments.

It effectively handles non-convex jerk constraints in speed profile optimization.

The method enhances robustness and efficiency in industrial automation contexts.

Abstract

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and non-convex jerk constraints, which, thus, represent the main source of difficulty. While existing non-linear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this paper. At each iteration a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach which strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proved through different computational experiments.