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Time optimality and completeness are desired properties for robot trajectory planning, which ensure that robotic systems work reliably and efficiently. However, there is great difficulty to design planning algorithms that simultaneously guarantee time optimality and completeness. In this paper, a complete, time-optimal and real-time algorithm for path-constrained trajectory planning is proposed under both torque and velocity constraints. The time optimality and completeness of the proposed algorithm are theoretically proven with rigorous mathematical analysis. Moreover, the proposed approach is general and applicable on different robotic systems, and two examples are given on a two-link manipulator and an active-caster-based omnidirectional wheeled mobile robot. Comparative simulation and experimental results are provided to demonstrate the superior performance of the proposed algorithm.
Shen et al. (Wed,) studied this question.