Time-Optimal Switching Surfaces for Triple Integrator under Full Box Constraints
For control engineers and researchers, this work solves a fundamental optimal control problem with practical constraints, offering an efficient and complete solution.
This paper provides a complete characterization of time-optimal switching surfaces for triple integrator under full box constraints, including asymmetric constraints and active position constraints. The proposed algorithm achieves a 100% success rate with computational times of about 10 μs per trajectory, a 5-order-of-magnitude reduction over optimization-based methods.
Time-optimal control for triple integrator under full box constraints is a fundamental problem in the field of optimal control, which has been widely applied in the industry. However, scenarios involving asymmetric constraints, non-stationary boundary conditions, and active position constraints pose significant challenges. This paper provides a complete characterization of time-optimal switching surfaces for the problem, leading to novel insights into the geometric structure of the optimal control. The active condition of position constraints is derived, which is absent from the literature. An efficient algorithm is proposed, capable of planning time-optimal trajectories under asymmetric full constraints and arbitrary boundary states, with a 100% success rate. Computational time for each trajectory is within approximately 10$μ$s, achieving a 5-order-of-magnitude reduction compared to optimization-based baselines.