Robust finite-time control allocation in spacecraft attitude stabilization under actuator misalignment

A novel combination of finite time control and control allocation with uncertain configuration matrix due to actuator misalignment is investigated for attitude stabilization of a rigid spacecraft. Finite time controller using nonsingular terminal sliding mode technique is firstly designed as virtual control of control allocator to produce the three axis torques, and can guarantee finite time reachability of given attitude motion of spacecraft in the presence of external disturbances. The convergences of this feedback controller for the resulting closed loop systems are also proven theoretically. Then, under the condition of uncertainty included in the configuration matrix due to actuator misalignment, a robust least squares-based control allocation is employed to deal with the problem of distributing the three axis torques over the available actuators under redundancy, in which the focus of this control allocation is to find the optimal control vector of actuator by minimizing the worst-case residual, under the condition of the uncertainty included in actuator configuration matrix and control constraints like saturation. Simulation results using the orbiting spacecraft model show good performance under external disturbances and even uncertain configuration matrix, which validates the effectiveness and feasibility of the proposed scheme.