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.