General parameterization of holonomic kinematic inversion algorithms for redundant manipulators

Redundant robotic manipulators under kinematic control may exhibit unpredictable behaviours at joint level. When the end-effector describes a closed trajectory, the joint angles may not return to their initial values and final configuration in the joint space may depend on the trajectory followed by the end-effector. In this paper, a complete parameterization of holonomic local control strategies that avoid these problems is proposed. Only a basis of the null-space of the Jacobian matrix is required in order to design all the possible holonomic control strategies. The effectiveness of the proposed approach is verified on a simple case study and on a real industrial manipulator.