基于Gauss伪谱法的欠驱动航天器姿态优化控制

现代航天器一般可以通过三正交反作用动量飞轮对其进行姿态机动控制并任意定位.研究了当其中某一个动量飞轮失效而不能输出完整三轴控制力矩时的欠驱动航天器姿态优化控制问题.在系统动量矩等于零时，其姿态控制问题可以转化为无漂移系统的非完整运动规划问题.采用Gauss伪谱法(GPM)将带有两个反作用动量飞轮的航天器姿态非完整运动规划问题转换为非线性规划问题(NLP)，再通过SQP(sequential quadratic programming)算法求解.通过数值仿真、优化控制能达到设计的零边界控制要求，方便伺服电机对动量飞轮的控制；规划得到的姿态曲线与数值积分得到的曲线几乎完全重叠；权衡最终的优化目标值、运行时间和精度三因素找到合适的插值配点个数；结果表明了该方法对欠驱动航天器的姿态优化控制是有效的.

Optimal Attitude Control of Underactuated Spacecrafts With the Gauss Pseudospectral Method

The attitude and orientation of modern spacecrafts generally can be controlled by 3 orthogonal reaction momentum wheels. The attitude control of underactuated spacecrafts with only 2 momentum wheels and failed out of complete 3-axis controlling torques, was investigated. The control problem was converted to a nonholonomic motion planning problem of a drift-free system with zero angular momentum. The attitude motion planning problem of a spacecraft with 2 momentum wheels was converted to a nonlinear programming problem (NLP) with the Gauss pseudospectral method, and then solved with the SQP algorithm. Through numerical simulation the optimal control met the design requirements of zero boundaries, so the wheels can be controlled easily by servomotors; the planned attitude curves were almost identical to the numerically integrated solutions; the number of suitable collocation points was found through balancing among 3 factors: the target function value, the running time and the solution error. The results show that the proposed method is effective for the optimal attitude control of underactuated spacecrafts.