基于二阶锥优化的饱和及禁区约束下的航天器姿态控制

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

研究了姿态禁区约束、角速度和控制力矩饱和约束下的航天器姿态机动问题。为了解决实际问题中的强非线性和非凸问题,提出了采用二阶锥优化方法来求解路径。具体来说,非线性的运动学和动力学通过松弛和转化为标准的仿射形式,并采用线性化和L1罚函数方法将问题中的非凸约束进行凸化。提出了基于角速度的二次性能指标,采用逐次迭代的二阶锥优化算法得到航天器姿态机动路径。最终,通过数值仿真验证了算法的有效性。

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.