基于梯度下降法的翼伞系统最优分段航迹规划

传统最优控制航迹规划一般以逆风精确着陆、控制能量小为优化目标，但传统最优控制的操纵过程一般是一条连续变化的曲线，工程上不易实施；与之相比，传统分段航迹规划操纵简单，工程上容易实施，能实现逆风精确着陆的目标，但控制能耗大。为了兼顾逆风精确着陆、能耗低和控制操作简单等目标，提出了一种基于梯度下降法的翼伞最优分段航迹规划方法。该方法将控制变量参数化，将逆风精确着陆、控制能耗小、能实现避障等多目标优化问题转化为加权单目标优化问题，并通过梯度下降法求解得到分段常值最优归航航迹。所提算法与基于伪谱法的最优控制规划航迹和基于遗传算法的分段规划航迹进行了对比，算法仿真结果表明本文提出的最优分段航迹规划法既可以实现着陆精度高、控制能量小、逆风着陆和避障的优化目标，同时规划的航迹又由分段常值实现控制，工程上容易实施，兼顾了最优控制航迹规划和分段航迹规划的优点。

Optimal segment constant trajectory planning for parafoil system based on gradient descent method

Traditional optimal control trajectory planning algorithms take precise landing against the wind and low energy consumption as the optimization objectives. However, the control process is usually a continuous curve, which is difficult to implement in engineering. Though the traditional multiphase trajectory planning algorithm can achieve the goal of precise upwind landing with a simple control process, the control energy consumption is large. To balance the objectives of precise upwind landing, low energy consumption, obstacle avoidance, and simple control operations, an optimal segment constant trajectory planning algorithm for parafoil systems based on the gradient descent method is proposed in this paper. In this algorithm, the control variable is parameterized, and the multi-objective optimization problems such as precise upwind landing, low control energy consumption and obstacle avoidance are transformed into weighted single objective optimization problems, and the optimal problem is solved using the gradient descent method. This paper further compares the proposed trajectory planning algorithm, the Gaussian pseudo-spectral optimal control trajectory planning algorithm, and the genetic multiphase trajectory planning algorithm, showing that the proposed optimal segment constant trajectory planning algorithm can achieve high landing precision, low control energy consumption, upwind landing and obstacle avoidance, with the control value being segment constant, which is easy to implement in engineering.