Robust Hybrid Global Dual Quaternion Pose Control of Spacecraft-Mounted Robotic Systems

We propose a nonlinear hybrid dual quaternion feedback control law for multibody spacecraft-mounted robotic systems (SMRSs) pose control. Indeed, screw theory expressed via a unit dual quaternion representation and its associated algebra can be used to compactly formulate both the forward (position and velocity) kinematics and pose control of N-degree-of-freedom robot manipulators. Recent works have also established the necessary theory for expressing the rigid multibody dynamics of an SMRS in dual quaternion algebra. Given the established framework for expressing both kinematics and dynamics of general N-body SMRSs via dual quaternions, this paper proposes a dual quaternion control law that achieves simultaneous global asymptotically stable pose tracking for the end effector and the spacecraft base of an SMRS. The proposed hybrid control law is robust to chattering caused by noisy feedback and avoids the unwinding phenomenon innate to continuous-based (dual) quaternion controllers. Additionally, an actuator allocation technique is proposed in the neighborhood of system singularities to ensure bounded control inputs, with minimum deviation from the specified spacecraft base and end-effector trajectories during controller execution.