A Feasible Sequential Linear Programming Algorithm with Application to Time-Optimal Path Planning Problems

TL;DR

This paper introduces a Feasible Sequential Linear Programming algorithm with a trust-region approach for solving time-optimal control problems, ensuring global convergence and feasibility, demonstrated on crane motion planning.

Contribution

The paper presents a novel FSLP algorithm that guarantees feasibility and quadratic convergence for time-optimal control problems with nonlinear constraints.

Findings

Efficiently solves time-optimal control problems with nonlinear constraints.

Ensures global convergence using a trust-region strategy.

Demonstrates effectiveness on crane motion planning case.

Abstract

In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear constraints which arise in motion planning of mechatronic systems. The algorithm applies a trust-region globalization strategy ensuring global convergence. For fully determined problems our algorithm provides locally quadratic convergence. Moreover, the algorithm keeps all iterates feasible enabling early termination at suboptimal, feasible solutions. This additional feasibility is achieved by an efficient iterative strategy using evaluations of constraints, i.e., zero-order information. Convergence of the feasibility iterations can be enforced by reduction of the trust-region radius. These feasibility iterations maintain feasibility for general Nonlinear Programs (NLP). Therefore, the algorithm is applicable to general NLPs. We demonstrate our algorithm's efficiency and the feasibility update strategy on a TOCP of an overhead crane motion planning simulation case.