A dual quaternion linear-quadratic optimal controller for trajectory tracking

This work addresses the task-space design problem of a linear-quadratic optimal tracking controller for robotic manipulators using the unit dual quaternion formalism. The efficiency, compactness, and lack of singularity of the representation render the unit dual quaternion a suitable framework for simultaneously describing the attitude and the position of the end-effector. Motivated by the advantages of this kinematic description, we propose a new task-space linear-quadratic optimal tracking controller in order to find an optimal trajectory for the end-effector, providing a tool to balance more conveniently the end-effector error and its task-space velocity. This is possible because the kinematic control problem using the dual quaternion transformation invariant error can be reduced to an affine time-varying system. The proposed optimal tracking controller allows the compensation of trajectory induced disturbances, as well as other modeled additive disturbances and known bias. Simulation results with different design parameters provide a performance overview, in comparison with standard kinematic controllers with and without a feed-forward term, for tracking a desired reference.