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

This paper proposes a robust dual-quaternion based H-infinity task-space controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, kinematic singularities, and their influence upon the kinematics of the end-effector pose (i.e., position and orientation), we adapt H-infinity techniques--suitable only for additive noises--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 H-infinity conditions derived in this paper are extended to conceive a new kinematic singularity avoidance technique suitable for the proposed non-Euclidean task-space manifold, which ensures proper behavior throughout the task space. The effectiveness and performance overview of the proposed strategies are evaluated within different realistic simulated scenarios.