基于高斯伪谱法的火星表面上升燃耗最优轨迹设计

Minimum-Fuel Mars Ascent Trajectory Design Based on Gauss Peseudospectral Method

火星上升器的设计与其轨迹设计紧密相关,而现有方法大都将MAV(Mars Ascent Vehicle)的分级优化和轨迹优化解耦计算,其计算效率低且鲁棒性较差。提出了一种基于高斯伪谱法的两级MAV分级与轨迹耦合多阶段优化算法,它以MAV的发射总质量最小为目标函数,并考虑了MAV设计约束、MAV的质量模型约束、轨迹的路径约束和控制约束等限制条件。利用该方法可以同时求得发射总质量最小的两级MAV分级参数和一条燃耗最优的上升轨迹,解决了由于不合理的两级MAV分级设计导致的轨迹优化算法无法收敛的问题。数值仿真结果表明该方法具有较快的收敛速度,且对初值选取的敏感度较小、具有较强的鲁棒性。

Mars Ascent Vehicle(MAV)design is closely related to trajectory design.However,the existing method mostly decoupled the staging optimization and trajectory optimization,resulting in computational inefficiency and poor robustness.A coupled staging-trajectory multiphase optimization algorithm is proposed in this paper for a two-stage MAV design.Considering given vehicle,mission,path and control constraints,the objective of the optimization algorithm is to minimize the Gross Lift-off Mass(GLOM)of the two-stage MAV,and the algorithm is based on Gauss pseudospectral method.By using this algorithm,an optimal staging design is obtained,and an optimal trajectory is designed to minimize propellant consumption simultaneously.And the algorithm solves the problem that trajectory optimization algorithm couldn’t converge due to the unreasonable MAV staging design.In addition,numerical simulations show that the coupled staging-trajectory multiphase optimization algorithm have good robustness and strong convergence.