基于动态参数扩展控制障碍函数的无人机时变编队最优跟踪控制

doi:10.12382/bgxb.2024.0260

摘要/Abstract

摘要：

针对多约束条件下无人机时变编队控制中的能耗优化问题,提出一种基于动态参数扩展高阶控制障碍函数的优化控制方法。对现有的高阶控制障碍函数进行改进,综合考虑无人机与障碍物的运动状态建立扩展状态的动力学模型,将动态目标避障的安全性约束条件在扩展状态动力学模型上展开,得到用于建立动态目标避障的扩展高阶控制障碍函数;针对扩展高阶控制障碍函数约束的可解性与保守性问题,设计K类函数参数的自适应规则得到动态参数扩展高阶控制障碍函数,在提高含约束优化问题可解性的同时降低解的保守性。利用控制障碍函数与动态参数扩展高阶控制障碍函数建立多约束条件,基于一致性条件与哈密顿分析建立目标函数,将时变编队的能耗优化问题转化为多约束优化问题,并用二次规划进行求解得到最优控制输入。仿真结果表明,所提方法比固定参数扩展高阶控制障碍函数以及人工势场法具有更好的避障效果与更低的能耗。

关键词: 时变编队跟踪控制, 最优控制, 控制障碍函数, 状态观测器

Abstract:

Aiming at the issue of optimal energy consumption of UAV time-varying formation under multiple constraints,an optimal control method based on an dynamic parameter extended high-order control barrier function is proposed.The method is used to improve the existing high-order control barrier function.In consideration of the motion states of UAV and obstacles,an the extended state dynamics model is established.The safety constraints of dynamic target obstacle avoidance are expanded on the extended state dynamics model,and the extended high-order control barrier function used to establish dynamic target obstacle avoidanceis obtained.For the feasibility and conservatism of the extended high-order control barrier function constraints,the adaptive rules of the class K function parameter are designed to obtain the dynamic parameter extended high-order control barrier function,which improves the feasibility and reduces the conservatism for the solution of constraint optimization problem.The control barrier function and the extended high-order control barrier function are used to establish the multi-constraints,and an objective function is established by the consistency condition and Hamiltonian analysis.The energy consumption optimization problem of time-varying formation is transformed into a multi-constraint optimization problem,and the quadratic programming is used to solve the problem to obtain the optimal control input.Simulated results demonstrate that the proposed method has superior obstacle avoidance and lower energy consumption compared to the fixed parameter high-order control obstacle functions and the artificial potential field.

Key words: time-varying formation tracking control, optimal control, control barrier function, state observer

中图分类号:

TJ301

吴俊岐, 吴碧, 邓宏彬, 周智千. 基于动态参数扩展控制障碍函数的无人机时变编队最优跟踪控制[J]. 兵工学报, 2025, 46(4): 240260-.

WU Junqi, WU Bi, DENG Hongbin, ZHOU Zhiqian. Time-varying UAV Formation Optimal Tracking Control with Dynamic Parameter Extended Control Barrier Functions[J]. Acta Armamentarii, 2025, 46(4): 240260-.

图/表 12

图1 轨迹保守性与可解性示意图

Fig.1 Conservatism and feasibility of trajectory

图2 K类函数参数自适应规则

Fig.2 Class K function adaptive rules

图3 控制系统框架

Fig.3 Control system framework

图4 编队通讯拓扑

Fig.4 Formation communication topology

图5 速度观测器观测结果

Fig.5 Observation results of velocity observer

图6 不同时刻无人机编队状态

Fig.6 UAV formation state at different times

图7 不同时刻无人机与障碍物之间的距离

Fig.7 Distance between UAV and obstacle at different times

图8 K类函数参数值

Fig.8 Class K function parameter values

图9 不同K类函数参数条件下的无人机避障轨迹

Fig.9 UAV obstacle avoidance trajectories with different class K function parameters

图10 不同K类函数参数下的控制输入

Fig.10 Control inputs with different class K function parameters

表1 不同避障方法所消耗的能量

Table 1 The energy consumptions of different obstacle avoidance methods

方法	参数	UAV1	UAV2	UAV3	UAV4
E-HOCBF方法	p=0.1	4.33×10³	1.21×10⁴	1.40×10⁴	3.70×10³
	p=0.3	3.67×10³	1.07×10⁴	1.26×10⁴	3.21×10³
	p=0.5	3.68×10³	1.07×10⁴	1.24×10⁴	3.16×10³
DPE-HOCBF 方法	p=p_ik	3.29×10³	1.01×10⁴	1.21×10⁴	3.02×10³
APF方法		4.56×10³	1.04×10⁴	1.25×10⁴	3.70×10³

表2 跟踪误差与平均仿真时间

Table 2 Tracking error and mean simulation time

仿真条件	方法		平均仿真时间/s
无人机数量4、障碍物数量3	APF方法	0.7472	1.6062
无人机数量4、障碍物数量3	DPE-HOCBF方法	0.5064	1.6282
无人机数量8、障碍物数量6	APF方法	0.9407	1.5856
无人机数量8、障碍物数量6	DPE-HOCBF方法	0.6207	1.6078

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