The reduced gradient method for solving redundancy in robot arms

An efficient computational scheme for solving inverse kinematic problems in redundant robot arms is presented. When following a given end-effector trajectory, successive internal arm configurations are in general selected by local optimization of a given performance criterion. Typically, joint displacements are derived using the Projected Gradient method, involving pseudoinversion fo the robot Jacobian and projection in its null-space. However, this technique is computationally intensive. In this paper, an alternative approach is proposed based on the Reduced Gradient method, which allows to deal explicitly only with the reundant degrees of freedom. The superiority of this technique for solving redundancy is illustrated analytically in a simple case, and numerically by simulation of a four-link planar arm. Optimization of various criteria like manipulability, available joint range, and distance form obstacles is considered. Extensions of the method are also briefly discussed.