Adaptive Fault-Tolerant Attitude Tracking Control of Rigid Spacecraft on Lie Group with Fixed-Time Convergence

This paper investigates the fixed-time attitude tracking problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The logarithm map is first utilized to transform the tracking problem on SO(3) into the stabilization one on its associated Lie algebra (so(3)). A novel nonsingular fixed-time-based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault-tolerant control law is constructed, in which an online adaptive law is incorporated to estimate the upper boundary of the lumped uncertainties. The combined control scheme enforces the system state to reach a neighborhood of the sliding surface in the sense of the fixed-time concept. The key feature of the resulting control scheme is that it can accommodate actuator failures under limited control torque without the knowledge of fault information. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed fixed-time controllers.