Smooth point-to-point trajectory planning for industrial robots with kinematical constraints based on high-order polynomial curve

Abstract

In this paper, a smooth point-to-point trajectory planning method for industrial robots is proposed. The trajectory is planned in the joint space. The joint motion is divided into three parts, namely accelerated part, constant velocity part and decelerated part. In the accelerated part and decelerated part, the acceleration is planned with fourth-order polynomial formed with the property of the root multiplicity. Then near time-optimal trajectory can be obtained by maximizing the constant velocity part under kinematical constraints. The results show that the fourth-order polynomial formed with the property of the root multiplicity is determined by only one coefficient. Compared to the classical description, the arduous stage of solving the numerous polynomial coefficients can be eliminated. With the proposed trajectory planning method, the displacement, velocity, acceleration and jerk of each joint and end-effector are all continuous. At the initial moment and end moment, the velocity, acceleration and jerk of each joint and end-effector are zero. The velocity, acceleration and jerk of each joint meet the kinematical constraints. The end-effector moves smoothly and the proposed trajectory planning method is very effective.