Rocket landing guidance based on second-order Picard-Chebyshev-Newton type algorithm

This paper proposes a rocket substage vertical landing guidance method based on the second-order Picard-Chebyshev-Newton type algorithm. Firstly, the continuous-time dynamic equation is discretized based on the natural second-order Picard iteration formulation and the Chebyshev polynomial. Secondly, the landing problem that considers terminal constraints is transformed into a nonlinear least-squares problem with respect to the terminal constraint function and solved with the Gauss-Newton method. In addition, the projection method is introduced to the iteration process of the Gauss-Newton method to realize the inequality constraints of the thrust. Finally, the closed-loop strategy for rocket substage vertical landing guidance is proposed and the numerical simulations of the rocket vertical landing stage are carried out. The simulation results demonstrate that compared with the sequential convex optimization algorithm, the proposed algorithm has higher computational efficiency. 针对火箭一子级着陆问题, 提出一种基于二阶皮卡-切比雪夫-牛顿类算法的制导方法。基于动力学方程的自然二阶皮卡迭代格式及切比雪夫多项式, 将连续时间动力学方程进行离散化处理; 将考虑终端约束的着陆问题转化为关于终端约束函数的非线性最小二乘问题, 并采用高斯-牛顿方法求解该问题; 在此基础上, 在高斯-牛顿法的迭代过程中引入投影方法, 实现推力的不等式约束。基于上述算法设计闭环制导并完成着陆段数值仿真。仿真结果表明, 该制导方法具有较好的终端精度及计算效率。