基于Legendre伪谱法的固体运载火箭轨迹优化研究

Trajectory optimization of solid launch vehicle based on Legendre pseudospectral method

Legendre法则是一种高阶积分近似法则,用较大积分步长得到较高精度。以结点伪谱法处理不连续问题后,可以把一个无限维的动态最优控制问题转化为有限维的静态优化问题,大大降低了问题复杂性。将其应用于轨迹优化,力求使其成为一种求轨迹优化问题的通用算法。以三级固体运载火箭为例,在惯性直角坐标系中建立动力学模型,给出轨迹优化模型。轨迹优化算例结果验证了Legendre伪谱法在弹道时间和精度优化的正确性和有效性。

Legendre pseudospectral （PS） is a sort of high-order integral approximate rule, and high-precision value can be obtained by using the bigger integral step length. The discontinuous problem was treated by using Knotting Pseudospectral Method, which can convert infinite dimension dynamic optimal control problem into finite dimension static optimization problem so as to reduce the complexity of the problem. This method was used for trajectory optimization of three-stage solid launch vehicle to obtain a general algorithm. Taking three-stage solid launch vehicle as an example, the dynamics model can be derived in the inertia rectangular coordinate system, and trajectory optimization model was gained. The results demonstrate validity of this method for optimizing trajectory time and accuracy.