The concurrent position and attitude (pose) tracking of a rigid spacecraft is addressed in the presence of actuator faults, mass and inertia uncertainties, and unknown external disturbances. The control design relies on a novel hybrid dual-quaternion integral sliding mode that incorporates a hysteretic switching to avoid the quaternion unwinding problem. On the sliding mode, the pose tracking error is globally finite-time convergent. The resultant control law has a simple structure and consists of a nominal control input, which realizes the sliding mode in the fault-free uncertainty-free case, and an adaptive part, which dynamically compensates for the perturbations due to actuator faults and other uncertainties. Moreover, a real-time control allocation algorithm is devised to deliver the control command to position and attitude actuators in proportion to the effectiveness degree of each actuator. Rigorous proof shows that the proposed strategies can stabilize the spacecraft pose trajectory to a small neighborhood of the sliding mode in finite time. Formation flying of earth-orbiting spacecraft and asteroid body-fixed hovering are simulated to demonstrate the efficacy and broad applicability of the proposed method.

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.

The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding-mode attitude controller is designed using attitude and angular velocity estimates from an arbitrary stable stand-alone observer. Rigorous analysis shows that the controller ensures robust stability of the entire closed-loop system as long as the observer yields state estimates with uniformly ultimately bounded estimation errors. In addition, a sequential Lyapunov analysis is utilized to obtain a convergent sequence of analytical successively tighter upper bounds on the steady-state tracking error. Therefore, our results can be used to predict steady-state performance bounds given selected gains or facilitate gain selection given steady-state performance bounds. Numerical examples demonstrate the utility of the proposed theory.