Investigations on the Use of the Cayley Form for Feedback Controller Design
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A novel approach for designing feedback controllers for mechanical systems by extending spacecraft attitude controllers to N-dimensional rotations is presented. The approach is enabled by the Cayley form, which represents the motion of mechanical systems as the rotation of N-dimensional rigid bodies. In particular an attempt is made to extend to N-dimensions a proof of global asymptotic stability of linear feedback of the Rodrigues parameters and angular velocity. The complexity of N-dimensional rotational kinematics, however, disallows a direct generalization of the three-dimensional proof. Two alternative nonlinear feedback controllers are presented and analyzed for their optimality and performance. These controllers are applied to a three-link manipulator system and found in one example to have superior performance to conventional controllers. Additionally, a new set of quasi velocities is developed that does provide globally asymptotically stable linear feedback for general mechanical systems.
author list (cited authors)
Sinclair, A., Hurtado, J., & Junkins, J.