A Virtual Torque-Based Approach to Kinematic Control of Redundant Manipulators

This paper presents an inverse kinematics algorithm for a redundant manipulator. The proposed approach combines analytical and numerical methods to solve generalized inverse kinematics problems simultaneously in both free and constrained working spaces. The method introduces a virtual repulsive torque imposed by the topological configuration of robot links, joint limits, and obstacles with motion trajectories. The method calculates the shortest distances between joint limit, links, and obstacles. Links of manipulator and obstacles are modeled in ellipsoids so as to evaluate the minimum distances between obstacles and links of a redundant robot. Virtual repulsive torques imposed on links are estimated based on the shortest distances between these ellipsoidal objects. A numerical method obtains the tendency of major joints’ movements and calculates their potential velocities by composing these acting torques. In trajectory tracking, collision avoidance occurring on links can finally be achieved by utilizing the characteristics of joint redundancy. The validity and efficiency of the proposed method are measured in simulations of movement along trajectories in terms of a defined index of motion availability, by which it verifies that the method is not only feasible to constrained motions but also has better performances in free motions than inverse Jacobian techniques.