A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

Abstract

Kinematically redundant manipulators are advantageous for their increased dexterity and ability to fulfill some secondary requirements along with their primary task to follow the prescribed trajectory. The redundancy results in a non-trivial inverse kinematics problem (IK). Standard methods of redundancy resolution are based on the pseudoinverse of the Jacobian matrix of the manipulator. The excessive degrees of freedom are utilized to perform secondary tasks that are projected onto the null space of the Jacobian matrix. However, the joint constraints satisfaction cannot be easily ensured in this way—even though methods that account for the joint position limits are known, the constraints for joint velocities and especially accelerations are not straightforward to include. In this paper, a novel redundancy resolution method based on a less common quadratic programming (QP) approach is described. The proposed velocity-level IK method allows fulfilment of the joint constraints at the position, velocity, and acceleration levels. In the derived formulas, accelerations instead of the usual velocities are used—the discretized joint state equations allow the use of joint accelerations as decision variables in the QP problem. The developed algorithm is investigated in a series of numerical tests in which the kinematics of the KUKA LWR4+ redundant 7-DOF manipulator is exploited. The newly elaborated QP-based IK method is firstly compared with the classic pseudoinverse-based approach and then tested for its ability to keep the joint accelerations within the prescribed bounds. The prospects of the proposed approach are discussed in the concluding section.

Keywords

• Inverse kinematics
• optimization
• quadratic programming
• redundant manipulators
• redundant robots