非凸二次约束下航天器姿态机动路径迭代规划方法

针对复杂约束下航天器姿态机动路径规划问题，首先描述和分析了航天器姿态机动过程中面临的动力学和运动学约束、有界约束、姿态指向约束，把姿态指向约束利用非凸二次型进行表述；其次从能量最优角度出发，将该约束机动问题归纳为非凸二次约束二次规划问题；然后引入线性松弛技术，将该问题转化成双线性规划问题，求出其中一个变量的凸包络和凹包络，降低求解复杂度，从而求出原问题的一个线性松弛。同时为了提高求解精度，提出一种基于评价函数的迭代规划算法，利用线性松弛求出的解作为初值，通过评价函数进行迭代规划，最终求出原问题的最优解。仿真结果表明该方法不仅可以满足复杂的姿态约束，得到全局姿态优化路径，而且能够降低能量消耗。

Spacecraft Attitude Maneuver Path Iterative Planning Method Under Nonconvex Quadratic Constraints

The objective of this paper is to design an optimal attitude maneuver path for a rigid body spacecraft under complex constraints. Firstly, dynamics and kinematic constraints, bounded constraints and attitude pointing constraints are described and analyzed. Especially, the attitude pointing constraints are formulized as the nonconvex quadratic form; Secondly, the constrained attitude maneuver problem can be formulated as the nonconvex quadratically constrained quadratic programming with the target that the energy-cost is smallest; Then the linear relaxation technique is introduced, and the problem is converted into a bilinear programming problem, in which convex envelope and concave envelope of one variable can be obtained. By this theory the complexity of solving is reduced and a linear relaxation of the original problem can be obtained. Meanwhile, in order to improve the solution accuracy, an iterative planning algorithm based on evaluation function is presented in this paper. This algorithm makes the solution of linear relaxation as the initial value, and an optimal solution can be achieved by iteration ultimately. Simulation results show that this method not only meets the complex attitude constraints to give an optimal attitude maneuver path, but also reduces energy consumption.