On the Manipulability of Velocity-constrained Serial Robotic Manipulators

Abstract: This paper presents a performance metric for the manipulability of constrained serial manipulators. The manipulability measure and manipulability ellipsoid are found from the manipulability Jacobian, which is easily found for serial manipulators as the standard Jacobian matrix, or for parallel manipulators as the Jacobian that gives the mapping from the active joint velocities to the end-effector velocities. For serial manipulators with constraints on the kinematic chain, however, this measure is not straightforwardly found because the manipulability Jacobian cannot be found in the same way as for the cases above. In this paper we propose to use the Constrained Jacobian Matrix, i.e., an analytical mapping between the end-effector and joint velocities that also takes the chain constraints into account. This analytical representation of the Constrained Jacobian Matrix allows us to find a performance metric describing the manipulability of a serial manipulator with chain constraints in the same way as for non-constrained kinematic chains and parallel manipulators. The approach allows us to compare the manipulability of the end effector of non-constrained serial manipulators and constrained serial manipulators and we study the important case of robotics-assisted minimally invasive surgery where the arm is constrained at the entry point.