火星大气进入轨迹伪谱凸优化设计方法

Pseudospectral Convex Programming Approach for Mars Atmospheric Entry Trajectory Planning

为解决火星大气进入末端高度最大化问题,提出Legendre伪谱凸优化(LPCP)方法进行求解。首先以纵向航程角为自变量建立火星进入模型,从而将末端时间自由问题转化为末端纵向航程角固定问题,避免优化末端时间;同时相比基于能量的模型,不必已知末端高度和速度,因此可以求解末端高度最大化问题。然后将状态微分方程在Legendre-Gauss-Lobatto(LGL)配点处离散,将微分方程转化为代数等式约束,并通过一阶泰勒展开凸化过程约束。最后,采用基于虚拟控制技术的凸优化算法迭代求解上述凸优化问题。数值仿真结果表明,相比自适应伪谱法和一般序列凸优化方法,提出的LPCP算法在保证最优性的同时计算效率更高。

To generate the Mars atmospheric entry trajectory with maximum terminal altitude,the Legendre pseudospectral convex programming(LPCP)algorithm is proposed.Firstly,the Mars entry dynamics is reformulated by taking the downrange angle as the independent variable so as to convert the free-final-time problem into the fixed-final-downrange angle one,thereby avoiding the optimization of final time;and compared with the energy-based formulation,there is no need to know the terminal altitude and velocity in advance,hence the maximum terminal altitude problem can be included.Then,the reformulated dynamics is discretized into a series of algebraic equalities at Legendre-Gauss-Lobatto(LGL)points,and the path constraints are convexified via the first-order Taylor series approximation.Finally,the transcribed convex problem is addressed via successive convex optimization and virtual control techniques.The numerical simulation results show that the algorithm in this paper has higher computational efficiency while ensuring the optimality than the adaptive pseudospectral method and the general sequential convex programming method.