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

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.