Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints

TL;DR

This paper introduces a computationally efficient trajectory optimization method for linear control systems with input and state constraints, utilizing flatness-based parameterization and quadratic programming for real-time applications.

Contribution

It proposes a novel polynomial-based parameterization of trajectories and constraints, enabling fast quadratic programming solutions for constrained linear control systems.

Findings

Method achieves real-time trajectory optimization

Applicable to high horizon control problems

Demonstrated on motor torque control

Abstract

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented.