Abstract: This paper dissuses thc problem of robot path planning in the presence or static and moving obstacles. Thereare two sub-problems:(1) planning the path to avoid collision with static obstacles;(2) planning the velocity alongthe path to avoid collision with moving obstacles. We transform the second sub-problem to a 2-dimensional staticproblem in time-path space. By using rational parametric function, a collision-free trajectory for robots can beobtained.