Spacecraft Attitude Control with Saturation and Attitude Forbidden Constraints via Second-Order Cone Programming

This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints, angular velocity saturation and actuator saturation simultaneously. A second-order cone programming (SOCP) technology is developed to solve the strong nonlinear and non-convex control problem in real time. Specifically, the nonlinear attitude kinematic and dynamic are transformed and relaxed to a standard affine system, and linearization and L1 penalty technique are adopted to convexify non-convex inequality constraints. With the proposed quadratic performance index of angular velocity, the optimal control solution is obtained with high accuracy using the successive SOCP algorithm. Finally, the effectiveness of the algorithm is validated by numerical simulation.