A Finite Element Method Approach for Trajectory Generation via Time-Optimal Control and Model Predictive Control Tracking

TL;DR

This paper introduces a finite element method-based framework combining time-optimal control and model predictive control to generate and track optimal trajectories for systems like Dubins' car, improving robustness and avoiding initialization issues.

Contribution

It presents a novel finite element approach for solving time-optimal control problems using GWRM and SCP, integrated with MPC for robust trajectory tracking.

Findings

Successfully generates optimal trajectories for Dubins' car.

Avoids reliance on shooting methods and their initialization.

Demonstrates robustness through disturbance rejection.

Abstract

In this paper a framework for solving the time optimal control (TOC) using Galerkin's Weighted Residuals Method (GWRM) and Sequential Convex Programming (SCP) is proposed. The proposed method solves the two-point boundary value problem, avoiding the use of shooting methods that rely heavily on the appropriate initialization of the adjoint state and optimal time. Since TOC yields an open-loop controller, a Model Predictive Control (MPC) scheme is employed to track both the optimal trajectory and controller, allowing the system to reject disturbances. The approach is validated using the Dubins' car dynamics for optimal time trajectory generation.