再入轨迹多约束模型预测静态凸规划方法

Reentry Trajectory Optimization Based on Constrained Model Predictive Static Convex Programming

针对大升阻比可重复使用飞行器再入滑翔轨迹规划问题,提出了一种基于自适应分段Chebychev伪谱离散的多约束模型预测静态凸规划算法(P-CMPCP),实现了全量终端状态约束及多过程约束作用下再入轨迹的高精度迭代解算。考虑倾侧角翻转导致控制量不连续,传统规划方法难以同时严格满足终端位置、角度约束,且过程约束易超限,采用自适应分段伪谱离散策略,构建全程飞行状态及过程性能指标约束对各配点处控制调整量的敏感度关系,从而将非线性最优控制问题转化为静态凸规划问题,并利用内点法对各分段控制量进行了协调优化。本文所提方法无需对动力学模型进行简化或近似处理,即能以少量积分运算使轨迹满足再入全量模型约束,且控制量平滑,数值精度优于传统规划方法。

A novel adaptive piecewise Chebychev pseudospectral method based-constrained model predictive static convex programming algorithm(P-CMPCP) is proposed for reentry glide trajectory planning of reusable vehicles with large lift-to-drag ratio. The high-precision trajectory solution can be solved iteratively under complete terminal state and multi-process constraints. Firstly, considering the discontinuity of the control quantity caused by the overturning of the bank angle, it is difficult for the traditional planning method to strictly meet the terminal position and angle constraints simultaneously, and the process constraints are liable to exceed the limit, an adaptive piecewise pseudospectral discretization strategy is adopted. Subsequently, the sensitivity relationships among the flight state, process constraint and the control adjustment quantity at each collocation point are derived, so that the nonlinear optimal control problem is transformed into a static convex programming problem. Finally, the interior point method is utilized to optimize the control quantities of each segment. The smooth trajectory solution can be obtained efficiently without any simplification or approximation of the dynamic model. The simulation results indicate that the proposed approach has increased numerical accuracy compared to traditional methods.