Convex Optimization Solution for Inverse Kinematics of a Physically Constrained Redundant Manipulator

Results of redundant manipulator inverse kinematics are likely to exceed the manipulator's physical constraints. To acquire inverse kinematics solution subject to physical bounds, a method using convex optimization is adopted. Firstly, the relation between joint velocity and torque is analyzed, and the manipulator kinetic energy and the repetitive motion are adopted as the optimization criteria, with joint velocity and joint torque as the optimization variables. Then the inverse kinematics problem is transformed into a convex optimization problem and further transformed into a quadratic programming problem. Taking full advantage of the redundancy of the manipulator, physical constraints including the joint position, joint velocity and joint torque are avoided in solving the inverse kinematics. Finally, simulation experiment is carried out on a 7-DOF redundant manipulator KUKA LBR iiwa. Results of the obtained joint variables satisfy the physical constraints and the optimization criteria. The result shows that the proposed method is suitable for solving inverse kinematics of physically constrained redundant manipulator.