Abstract：Key to the path-constrained trajectory planning is to introduce a path parameter to reduce the problem into a low-dimension one. While the path passing through singularities, joint variable can hardly be presented as analytical functions of task space-defined parameters, which causes difficulties given to conventional trajectory planning. In this paper, a new parameter, arc-length of the solution curve to the path tracking equation, is introduced. Based on this, the path-tracking problem near singularities is addressed, and singular path-constrained trajectory planning is transformed into a standard optimization problem, which can be solved by dynamic programming. Simulation shows the parameterization combined with dynamic programming performs effectively in singular path trajectory planning.
 Bobrow J E, Dubosky S, Gibson J S. Time-optimal Control of robotic manipulators along specified paths. Int J Robotics Res, 1985,4(3):3-17  Shin K G, McKay N D. Minimum-time control robotic manipulators with geometric path constraints. IEEE Trans Automat Contr, 1985,30(6): 531-541  Slotine J J E, Yang H S. Improving the efficiency of path following algorithms. IEEE J Robot Automat, 1989,5(1): 18-124  Shiller Z, Lu H H. Computation of path constrained time optimal motions with dynamic singularities. Trans ASME J Dynamic Syst. Measurement Contr, 1992, 114: 34-40  Shin K G, McKay N D. A dynamic programming approach to trajectory planning of robotic manipulators. IEEE Robot Automat, 1986, AC-31(6): 491-500  Kieffer Jon, Cahill Aidan J, James Matthew R. Robust and Accurate Time-Optimal Path-Trajectory Control for Robot Manipulator. IEEE Trans Robotics and Automation, 1997,13(6): 880-890  蔡大用,白峰杉. 高等数值分析. 北京: 清华大学出版社,1997