CG 伪谱法在欠驱动航天器姿态机动最优控制中的应用

摘要

使用Chebyshev?Gauss(CG)伪谱法研究带动量轮和推力器的欠驱动航天器姿态最优控制问题.基于欧拉姿态角和动量矩定理导出两类航天器姿态运动模型,采用 Clenshaw?Curtis积分近似得到性能指标函数中的积分项,应用重心拉格朗日插值逼近状态变量和控制变量,将连续最优控制问题离散为具有代数约束的非线性规划(NLP)问题,通过序列二次规划(SQP)算法求解.数值仿真结果表明,对两类欠驱动航天器的姿态机动最优控制均能达到设计控制要求,得到的姿态最优曲线与验证得到的曲线几乎完全重叠.%The attitude optimal controls of underactuated spacecraft with momentum wheels and thrusters are dis?cussed by using Chebyshev?Gauss(CG)pseudospectral method,respectively.The equations of motion for the two types of underactuated spacecrafts are formulated based on Euler angle and the theory of angular momentum. The integration of cost function can be approximated by the Clenshaw?Curtis quadrature. The barycentric Lagrange in?terpolation is presented to approximate the state and control variables. The continuous optimal control problem can be converted to a discrete nonlinear programming(NLP)problem. And then, it can be solved by Sequential Quadratic Programming(SQP)algorithm. The simulation results show that the CG pseudospectral method is ef?fective for solving the attitude optimal control of two types of underactuated spacecrafts. The optimal controls can meet the designed requirements. The planned curves of attitude are similar to the solution curves of numerical in?tegration.