基于精确凸松弛的固定翼无人机实时轨迹规划

doi:10.12382/bgxb.2024.0362

摘要/Abstract

摘要：

针对固定翼无人机轨迹规划问题,提出一种基于精确凸松弛的实时轨迹规划方法。该方法包含路径规划和速度优化2个步骤。第1步,设计无人机在多障碍环境下的飞行路径。综合考虑无人机动力学和控制约束条件,提出基于Dubins路径的避障路径规划方法来生成适应固定翼无人机飞行性能限制的避障路径。第2步,计算无人机沿避障路径飞行的速度和控制。提出利用非线性保留和精确凸松弛将强非线性的速度优化问题转化为单个凸优化问题,并理论证明了方法的有效性。因为不需要迭代求解凸优化问题,速度优化算法没有收敛性问题,具有良好的实时性。仿真结果表明:新方法在多障碍环境和未知障碍环境中均能够可靠快速地完成避障轨迹规划,相比于非线性优化和序列凸优化,计算效率明显提升,计算时间仅为数十毫秒。

关键词: 固定翼无人机, 轨迹规划, 实时避障算法, Dubins路径, 凸优化, 精确凸松弛

Abstract:

This paper investigates the trajectory planning issue for fixed-wing UAVs and proposes a real-time trajectory planning method based on exact convex relaxation.This method includes two steps,i.e.path planning and velocity optimization.In the first step,a flight path of UAV in the multi-obstacle environments is designed.In consideration of the dynamics and control constraints,an obstacle avoidance path planning method based on Dubins path is proposed to generate a flyable obstacle avoidance trajectory.In the second step,the velocity and control of a fixed-wing UAV flying along an obstacle avoidance path are calculated such that it can track the obstacle avoidance path.The nonlinearity retention and exact convex relaxation are used to convert the highly nonlinear velocity optimization problem into one single convex optimization problem,and the validity of the proposed method is theoretically proven.Since there is no iterative process of solving the convex optimization problems,the velocity optimization algorithm does not have convergence issues and has remarkable real-time performance.The simulated results demonstrate that the proposed method can realize obstacle avoidance trajectory planning reliably and rapidly in both multi-obstacle environment and unknown obstacle environment,and it significantly improves the computing efficiency compared with the nonlinear programming and successive convex optimization methods.The calculation time is only tens of milliseconds.

Key words: fixed-wing UAV, trajectory planning, real-time obstacle avoidance algorithm, Dubins path, convex optimization, exact convex relaxation

中图分类号:

V279

李雅轩, 刘新福. 基于精确凸松弛的固定翼无人机实时轨迹规划[J]. 兵工学报, 2025, 46(3): 240362-.

LI Yaxuan, LIU Xinfu. Real-time Trajectory Planning for Fixed-wing UAVs Based on Exact Convex Relaxation[J]. Acta Armamentarii, 2025, 46(3): 240362-.

图/表 15

图1 多障碍环境下无人机飞行

Fig.1 Schematic diagram of a UAV flying in a multi-obstacle environment

图2 Dubins路径

Fig.2 Dubins path

图3 单障碍避障

Fig.3 Schematic diagram of single obstacle avoidance

图4 多障碍避障

Fig.4 Schematic diagram of multi-obstacles avoidance

表1 固定翼无人机参数

Table 1 Parameters of fixed-wing UAV

参数	数值	参数	数值
m/kg	11.5	v_max/(m·s^-1)	40
S/m²	0.84	v_min/(m·s^-1)	25
c₀	0.0339	T_max/N	100
c₁	0.1834	T_min/N	10
C_L,max	0.6083	σ_max/(°)	60

图5 避障路径规划

Fig.5 Schematic diagram of obstacle avoidance path planning

图6 搜索过程

Fig.6 Search process

图7 速度和控制曲线

Fig.7 Velocity and control curves

图8 不同目标函数对松弛约束活跃性的影响

Fig.8 Effects of different objective functions on the activity of the relaxed constraint

图9 未知障碍环境下的飞行路径

Fig.9 Flight path in the unknown obstacle environment

图10 未知障碍环境下的速度和控制曲线

Fig.10 Velocity and control curves in the unknown obstacle environment

表2 障碍区域参数

Table 2 Parameters of obstacles

障碍序号	x_O/m	y_O/ m	r_O/m
1	280	90	105
2	640	160	140
3	500	-180	120
4	200	-140	70

图11 本文方法得到的飞行轨迹

Fig.11 Flight paths got by the proposed method

图12 本文方法得到的速度和控制曲线

Fig.12 Velocity and control curves got by the proposed method

表3 不同方法的计算效率对比结果

Table 3 Comparative results of computational efficiencies of different methods

方法	平均迭代次数	平均计算时间/ms
非线性优化^[24]	11.53	2541.52
序列凸优化^[25]	6.62	435.48
本文方法	不需要迭代	12.60

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