Application of the Rotation Matrix Natural Invariants to Impedance Control of Purely Rotational Parallel Robots

Force control of parallel robots with rotational degrees of freedom through impedance algorithms is considerably influenced by the representation method of the end-effector orientation. Using the natural invariants of the rotation matrix and the angular velocity vector in the impedance control law has some theoretical advantages, which derive from the Euclidean-geometric meaning of these entities. These benefits are particularly evident in case of robotic architectures with three rotational degrees of freedom (serial or parallel wrists with spherical motion). The behaviour of a 3-CPU parallel robot controlled by an impedance algorithm based on this concepts is assessed through multibody simulations, and the results confirm the effectiveness of the proposed approach.