Abstract: A geodesic based trajectory planning method for robots is proposed in this paper,which overcomes some shortcomings of traditional trajectory planning method. The planning is performed in joint space and the planning objects can be a line in Cartesian space,the kinetic energy or some combined indices. Angle and velocity of each joint is attained directly and no inverse kinematics and polynomial interpolation are needed. Because arc length of trajectory is regarded as the variant in geodesics based method,it possesses the advantages of non-time based trajectory planning at the same time.