Kinematic control of redundant manipulators for higher efficiency and mechanical advantage

The joint torques and the joint velocities of a robot manipulator depend on the joint configuration of the manipulator. In a near singular configuration, the joint velocities required to move the end-effector in certain directions get extremely high. In some configurations, the joint torques required for the end-effector to apply a force along a certain direction may also get extremely high. Redundant manipulators allow the end-effector to reach a desired position and orientation with an infinite number of joint configurations. Thus joint configurations requiring lower joint velocities or torques may be chosen to follow a desired trajectory.

Choosing configurations requiring lower (minimum norm) joint velocities to track a desired end-effector trajectory results in minimum overall movement of the joints. We refer to such manipulator motion as efficient motion. Efficient motion is achieved by maximizing the Manipulator Velocity Ratio (MVR) [2] in the direction of motion, or in the direction in which it is minimum, depending on the nature of the end-effector trajectory. Improving the performance criterion that utilizes the Manipulability Measure [14] also results in low joint velocities in certain directions.

Choosing configurations that require the minimum joint torques for a certain magnitude of external force is also desired in some cases. In order to lower the joint torques, a performance criterion that is based on the Manipulator Mechanical Advantage (MMA) [2] is maximized. Maximizing MMA in the direction of the applied force results in configurations requiring lower joint torques for a desired end-effector force. The control schemes utilized in this thesis use kinematic and local optimization techniques which are based on the gradient projection method.

The control schemes mentioned above are applied to the NASA Laboratory Telerobotic Manipulator (LTM). Simulations were performed using a solid model of the LTM on the Silicon Graphics workstation. The software was written in "C" language for higher speed and portability.