A Jacobian-based redundant control strategy for the 7-DOF WAM

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when mapping between the two spaces. This results in using appropriate optimization algorithms to compute along with the Jacobian matrix. Taking the second approach, the Jacobian matrix for a redundant robot will be non-square. One approach to obtain a solution is to use pseudo inverse, this approach is however computational intensive. This paper presents a pragmatic approach by which a joint of a 7-DOF whole arm manipulator (WAM) is initially fixed to facilitate the computation of the squared Jacobian matrix. Based on this approach, appropriate optimization strategies that are outlined in the paper, can then be applied to determine the optimal value of the 'fixed' joint in real time. Experiments are performed to verify the viability of this approach, and the results established that a robust and flexible Cartesian trajectory planning framework can be achieved for general redundant manipulators.