L.E. Bruzzone and R.M. Molfino
Parallel robots, natural invariants of the rotation matrix, impedancecontrol
The problem of controlling the interaction between manipulator and environment through impedance algorithms is strictly related to the representation of the spatial position of the end-effector; there are many possible ways to represent the kinematics of a rigid body, and this leads to different control laws. Exploiting the natural invariants of the rotation matrix and the angular velocity vector for the definition of the closed-loop system behaviour seems to be elegant and intuitive, with some theoretical advantages related to the Euclidean-geometric meaning of these entities. A control law based on this concept and applied to a six-degree-of-freedom parallel manipulator has been assessed through simulations, confirming the effectiveness of the approach.
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