Robust H-infinity kinematic control of manipulator robots using dual quaternion algebra

This paper proposes a robust dual-quaternion based H-infinity task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon the kinematics of the end-effector pose, we adapt H-infinity techniques\textemdash suitable only for additive noises\textemdash to unit dual quaternions. The noise to error attenuation within the H-infinity framework has the additional advantage of casting aside requirements concerning noise distributions, which are significantly hard to characterize within the group of rigid-body transformations. Using dual quaternion algebra, we provide a connection between performance effects over the end-effector trajectory and different sources of uncertainties and disturbances while satisfying attenuation requirements with minimum instantaneous control effort. The result is an easy-to-implement closed-form H-infinity control design criterion. The performance of the proposed strategy is evaluated within different realistic simulated scenarios and validated through real experiments.