Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version)

TL;DR

This paper introduces a new theoretical framework and a trajectory planning method for solving the challenging problem of time-optimal control in high-order chain-of-integrators systems with full state constraints and arbitrary terminal states, demonstrating superior performance.

Contribution

It develops a novel notation system, theoretical switching laws, and the manifold-intercept method (MIM) for efficient trajectory planning under complex constraints.

Findings

MIM outperforms baselines in computational time

MIM achieves higher accuracy and trajectory quality

Theoretical framework clarifies switching law properties

Abstract

Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further comprehension of the problem, this paper establishes a novel notation system and theoretical framework, providing the switching manifold for high-order problems in the form of switching laws. Through deriving properties of switching laws regarding signs and dimension, this paper proposes a definite condition for time-optimal control. Guided by the developed theory, a trajectory planning method named the manifold-intercept method (MIM) is developed. The proposed MIM can plan time-optimal jerk-limited trajectories with full state constraints, and can also plan near-optimal non-chattering higher-order trajectories with negligible extra motion time compared to optimal profiles. Numerical results indicate that the proposed MIM outperforms all baselines in computational time, computational accuracy, and trajectory quality by a large gap.