In this paper, a convex optimization algorithm is proposed to solve the online trajectory optimization problem of boost back of vertical take-off/vertical landing reusable launch vehicles. To achieve high-precision landing of launch vehicles, trajectory optimization of the boost-back flight phase considering the accuracy of entry is carried out, especially in emergencies. The trajectory optimization problem is formulated as an optimal control problem with minimum fuel consumption, and then it is transformed into a series of convex optimization subproblems, which can be solved by primal-dual interior-point method accurately and rapidly. During the transformation, flip-Radau pseudospectral discretization method, lossless convexification and successive convexification technology are applied. To drive the vehicle to predetermined entry points at the expected velocity, terminal constraints are expressed as orbital constraints of the endpoint in the boost-back flight phase. Considering the influence of Earth's rotation, the right ascension of the ascending node of the target orbit is updated according to the time and true anomaly at the end of the boost-back flight phase. Furthermore, the homotopy method is applied to the situation where there is no good initial guess when emergency happens. The algorithm presented in this paper performs well upon the simulation experiments of mission change and thrust decline. With good accuracy, high computational efficiency, and excellent robustness, the convex approach proposed has a great potential for onboard application in reusable launch vehicles and other space vehicles.

提出了一种凸优化算法，以解决垂直起飞/垂直着陆可重复使用运载火箭升压后的在线轨迹优化问题。为了实现运载火箭的高精度着陆，考虑到进入的准确性，特别是在紧急情况下，对后推飞行阶段的轨迹进行了优化。将轨迹优化问题公式化为具有最小油耗的最优控制问题，然后将其转化为一系列凸优化子问题，这些问题可以用原始对偶内点法快速准确地解决。在变换过程中，采用了Flip-Radau伪谱离散化方法，无损凸化和逐次凸化技术。为了以期望的速度将车辆驾驶到预定的入口点，终端约束表示为后推飞行阶段中端点的轨道约束。考虑到地球自转的影响，在升空飞行阶段结束时，根据时间和真实异常更新目标轨道上升节点的右升。此外，同构方法适用于在紧急情况发生时没有很好的初始猜测的情况。本文提出的算法在任务变化和推力下降的仿真实验中表现良好。提出的凸方法具有良好的精度，较高的计算效率和出色的鲁棒性，在可重复使用的运载火箭和其他航天器的车载应用中具有很大的潜力。终端约束表示为升后飞行阶段中端点的轨道约束。考虑到地球自转的影响，在升空飞行阶段结束时，根据时间和真实异常更新目标轨道上升节点的右升。此外，同构方法适用于在紧急情况发生时没有很好的初始猜测的情况。本文提出的算法在任务变化和推力下降的仿真实验中表现良好。提出的凸方法具有良好的精度，较高的计算效率和出色的鲁棒性，在可重复使用的运载火箭和其他航天器的车载应用中具有很大的潜力。终端约束表示为升后飞行阶段中端点的轨道约束。考虑到地球自转的影响，在升空飞行阶段结束时，根据时间和真实异常更新目标轨道上升节点的右升。此外，同构方法适用于在紧急情况发生时没有很好的初始猜测的情况。本文提出的算法在任务变化和推力下降的仿真实验中表现良好。提出的凸方法具有良好的精度，较高的计算效率和出色的鲁棒性，在可重复使用的运载火箭和其他航天器的车载应用中具有很大的潜力。