Redundancy-Resolution Algorithms for Isotropic Robots

A real-time redundancy-resolution scheme for an isotropic, redundant robot is the subject of this paper. In redundant robots, the extra degrees of freedom can be used to minimize a performance index. The proposed index is quadratic in the joint variables, its weighting function having units of frequency. It is shown how this performance index can produce cyclic trajectories in a simple manner, thereby eliminating the undesired drift of the joint angles upon tracking a closed Cartesian trajectory. Moreover, isotropic robots can be postured in such a way that the condition number of their Jacobian matrices can attain a minimum value of unity, a feature that is closely related to the performance of the robot. It is claimed that trajectories that are close to the set of isotropic postures are performed with smaller errors than trajectories lying far from that set.