An efficient computation algorithm for time optimal trajectory planning with physical constraints

Time optimal trajectory planning under various hard physical constraints plays a significant role in simultaneously meeting the requirements on high productivity and high accuracy in the fields of both machining tools and robotics. In this paper, the problem of time optimal trajectory planning is first formulated, and then a novel back and forward check algorithm is proposed to solve the minimum time feed-rate optimization problem. The proposed time optimal trajectory planning algorithm is very computationally efficient because the optimal solution at each node is analytically obtained by four lemmas presented in the paper. Moreover, the algorithm can incorporate general velocity-dependent constraints explicitly. An eight profile and a Lissajous curve are used as case studies to verify the effectiveness of the proposed algorithm. Computation results show that the proposed algorithm can indeed provide an optimal and feasible solution to the minimum time trajectory planning problem, and the short execution time of the algorithm demonstrates that the proposed algorithm is very computationally efficient.