基于改进保守凸可分近似的高超声速飞行器轨迹规划方法  

A Hypersonic Vehicle Trajectory Planning Method Based on an Improved Conservative Convex Separable Approximation

作　　者：祝静娴 王剑颖 罗云皓 王永海 ZHU Jingxian;WANG Jianying;LUO Yunhao;WANG Yonghai(School of Aeronautics and Astronautics,Sun Yat-sen University,Shenzhen 518107,China;Science and Technology on Space Physics Laboratory,Beijing 100076,China)

机构地区：[1]中山大学航空航天学院,深圳518107 [2]空间物理重点实验室,北京100076

出　　处：《宇航学报》2024年第6期935-947,共13页Journal of Astronautics

摘　　要：面向高超声速飞行器轨迹在线规划需求,提出一种改进的保守凸可分近似规划方法,以解决当前序列凸优化的振荡不收敛问题。首先,基于序列凸化、松弛变量、罚函数等方法将高超声速飞行器轨迹规划这一非凸原问题转化为凸的子问题。其次,针对凸优化中的振荡不收敛问题,设计一种使迭代序列趋于聚点的信赖域更新策略,并验证该策略能有效避免迭代中后期进程缓慢的“振荡现象”。进一步地,结合改进的信赖域更新策略,提出基于改进保守凸可分近似的轨迹规划方法,并对算法进行等效性和收敛性分析,证明该算法能够收敛到原问题的一个驻点。最后,以复杂约束条件下的高超声速飞行器轨迹规划问题为例,对随机初始猜测值和随机终点两种工况进行仿真验证,并与序列二次规划方法的规划结果进行对比,结果表明本文算法在满足求解精度的要求下,具有较快的求解速度、以及较好的收敛性和鲁棒性。Aiming at the requirements of online trajectory planning of hypersonic vehicles,an improved conserved convex separable approximations programming method is proposed to solve the nonconvergence issue called solution chattering of the current sequence convex optimization.Firstly,based on the methods of sequence convexity,relaxation variables,penalty functions and others,the non-convex original problem of hypersonic vehicle trajectory planning is transformed into a convex subproblem.Secondly,aiming at the problem of oscillation non-convergence in convex optimization,a trust region update strategy is proposed to make the iterative sequence tend to converge,and it is verified that the strategy can effectively avoid the“crawling phenomenon”in the middle and late stages of iteration.Furthermore,with the improved trust domain update strategy,a trajectory planning method based on improved conservative convex separable approximation is proposed,and the equivalence and convergence analysis of the algorithm are carried out to prove that the algorithm can converge to a station point of the original problem.Finally,taking the hypersonic vehicle trajectory planning problem under complex constraints as an example,the simulation verification is carried out by two working conditions:random initial guess value and random endpoint,one of them is compared with the planning results of the sequential quadratic programming method,the results show that the proposed algorithm has fast solution speed,good convergence and robustness under the condition of satisfying the requirements of solution accuracy.

关 键 词：在线轨迹规划 序列凸优化 保守凸可分近似 信赖域 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]