Gauss伪谱法的再入可达域计算方法.doc

Gauss伪谱法的再入可达域计算方法 王涛1, 张洪波1, 李永远2, 汤国建1 （1.国防科学技术大学 航天科技与工程学院，湖南 长沙 410073；2.中国运载火箭技术研究院 研发中心，北京 100076） 摘要：飞行器再入可达域研究对再入任务规划及应急迫降着陆点选择具有重要意义Landing Footprint Generation of Entry Vehicle Based on Gauss Pseudospectral Method WANG Tao1, ZHANG Hongbo1, LI Yongyuan2, TANG Guojian1 (1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China; 2. Research Development Center, China Academy of Launch Vehicle Technology, Beijing 100076, China) Abstract: Entry Landing footprint is a significant index to flight capability of entry vehicle. The research on footprint generation is useful in trajectory planning and in the case of failed vehicle landing. The paper takes advantage of Gauss pseudospectral method to generate footprint. To reduce calculation time and improve optimization result, attack angle is regarded as a state variable and only bank angle is optimized, which is reasonable since attack angle profile is often predesigned in engineering. Down-range of vehicle is regarded as event constraint, based on which maximum cross-range is calculated. Flight path angle is regarded as path constraint to eliminate skips on the trajectory. Through simulation, the footprint of CAV-H is generated, which is in accordance with the theoretical analysis of the indirect optimization method. Key words: entry; footprint; Gauss pseudospectral method; attack angle; cross-range 引言 飞行器再入可达域是飞行器在满足约束条件下的集合[1]。研究再入可达域对再入任务规划及应急迫降着陆点选择具有重要意义。Ngo[2]以最大横程为优化指标，利用求解倾侧角的表达式，。L[1]假设可达域的周围存在一系列虚拟目标点，使飞行器落点尽可能接近虚拟目标点，从而得到可达域平衡滑翔条件Quasi-Equilibrium Glide Condition，QEGC），利用最优控制原理巧妙地将转化为单个参数问题。Li[3]、Zhang[4]等人对方法进一步研究，提出了更实用的虚拟目标选取方法Saraf[5]基于航天飞机的制导模式提出了一种解析的可达域计算方法，通过规划阻力剖面，得到了近似的可达域。Chang[6]对该方法进行了，[7]~[9]利用直接法求解可达域。其中Fahroo[7][8]利用拉格朗日伪谱法求解再入可达域，由于约束条件处理不当，得到的轨迹并不光滑，可跟踪性较差。文献[10]和文献[11]分别针对超低再入情况和沿赤道再入情况进行研究，采用伪谱法优化出了可达域，然而，这两种情况下地球自转的影响较小，不具有一般性。 近些年来，伪谱法在轨迹优化领域得到了广泛的应用[12][13]。Gauss伪谱法作为伪谱法的一种，在处理约束方面有明显优势[14]。 本文采用Gauss伪谱法计算再入可达域。考虑到再入过程中一般采用