Hybrid Global Finite-Time Dual-Quaternion Observer and Controller for Velocity-Free Spacecraft Pose Tracking

Concurrent position and attitude (pose) tracking of a rigid spacecraft is addressed when there are no (both linear and angular) velocity measurements, and only pose information is available. A second-order observer with a simple structure is designed to provide spacecraft velocity estimates. It consists of one part that mimics the six-degrees-of-freedom (6DOF) spacecraft kinematics and dynamics and a correction part driven by the error between pose measurements and estimates. The resultant velocity estimates are then utilized to construct a velocity-free pose tracking controller with a proportional-derivative plus feedforward form. All the theoretical designs and analyses are conducted in a compact dual-quaternion framework and incorporate hybrid control, homogeneous nonsmooth feedback, and Lyapunov theory. Rigorous proof shows that the observer alone and the combined observer-controller both achieve global finite-time convergence, which is an advantageous property compared with existing 6DOF velocity observers and velocity-free pose controllers. Numerical examples are presented to demonstrate the application and effectiveness of the proposed method.