Real-time Trajectory Planning for Fixed-wing UAVs Based on Exact Convex Relaxation

doi:10.12382/bgxb.2024.0362

Abstract

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

CLC Number:

V279

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

Figures/Tables 15

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

Fig.2 Dubins path

Fig.3 Schematic diagram of single obstacle avoidance

Fig.4 Schematic diagram of multi-obstacles avoidance

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

Fig.5 Schematic diagram of obstacle avoidance path planning

Fig.6 Search process

Fig.7 Velocity and control curves

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

Fig.9 Flight path in the unknown obstacle environment

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

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

Fig.11 Flight paths got by the proposed method

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

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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