Dynamic Programming-Based Redundancy Resolution for Path Planning of Redundant Manipulators Considering Breakpoints

This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while ensuring that the angles, velocities, and accelerations of each joint do not exceed the manipulator's constraints. We obtain the analytical solution to the inverse kinematics problem of the manipulator using a parameterization method, transforming the redundancy resolution problem into an optimization problem of determining the parameters at each path point. The constraints on joint velocity and acceleration serve as constraints for the optimization problem. Then all feasible inverse kinematic solutions for each pose under the joint angle constraints of the manipulator are obtained through parameterization methods, and the globally optimal solution to this problem is obtained through the dynamic programming algorithm. On the other hand, if a feasible joint-space path satisfying the constraints does not exist, the proposed algorithm can compute the minimum number of breakpoints required for the path and partition the path with as few breakpoints as possible to facilitate the manipulator's operation along the path. The algorithm can also determine the optimal selection of breakpoints to minimize the global cost function, rather than simply interrupting when the manipulator is unable to continue operating. The proposed algorithm is tested using a manipulator produced by a certain manufacturer, demonstrating the effectiveness of the algorithm.