A rapid trajectory optimization method is proposed to solve the fuel-optimal Earth-landing problem of reusable rockets, in which the nonlinear aerodynamic drag force is non-negligible. To enable the online and autonomous operation ability, the method is designed based on convex optimization, which features rapid and deterministic convergence properties, and a homotopic-iterative strategy is proposed to convexify the nonlinear system dynamics of the rocket. In the proposed iterative algorithm, the problem is first solved based on the lossless convexification method while the drag force is considered to be zero. Then, during subsequent iterations, the drag profile is approximated by the last solution and homotopically added to the problem. Thus, the nonlinear drag is gradually included while the problem remains convex. Because the convexification of the nonlinear terms is not based on linearization, no reference trajectory or initial guess is needed, which greatly enhances the autonomy of the algorithm. Numerical experiments are provided to demonstrate the effectiveness, rapidness, and accuracy of the proposed algorithm.

提出了一种快速轨迹优化方法，解决了可重复使用火箭燃料最优的着陆问题，其中非线性气动阻力不可忽略。为了实现在线和自主操作能力，基于凸优化设计了该方法，该方法具有快速确定的收敛特性，并提出了一种同态迭代策略来凸显火箭的非线性系统动力学。在提出的迭代算法中，首先基于无损凸化方法解决了该问题，同时将阻力设为零。然后，在随后的迭代中，阻力曲线由最后一个解决方案近似并同义地添加到问题中。因此，非线性阻力逐渐包括在内，而问题仍然凸出。因为非线性项的凸化不是基于线性化的，所以不需要参考轨迹或初始猜测，这大大提高了算法的自治性。数值实验表明了该算法的有效性，快速性和准确性。