Time-varying UAV Formation Optimal Tracking Control with Dynamic Parameter Extended Control Barrier Functions

doi:10.12382/bgxb.2024.0260

Abstract

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

CLC Number:

TJ301

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-.

Figures/Tables 12

Fig.1 Conservatism and feasibility of trajectory

Fig.2 Class K function adaptive rules

Fig.3 Control system framework

Fig.4 Formation communication topology

Fig.5 Observation results of velocity observer

Fig.6 UAV formation state at different times

Fig.7 Distance between UAV and obstacle at different times

Fig.8 Class K function parameter values

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

Fig.10 Control inputs with different class K function parameters

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

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

References 26

[1]	ZHAO Q L, DONG X W, SONG X, et al. Cooperative time-varying formation guidance for leader-following missiles to intercept a maneuvering target with switching topologies[J]. Nonlinear Dynamics, 2019,95:129-141.
[2]	WANG J H, HAN L, DONG X W, et al. Distributed sliding mode control for time-varying formation tracking of multi-UAV system with a dynamic leader[J]. Aerospace Science and Technology, 2021,111:106549.
[3]	XU K T, GE M F, LIANG C D, et al. Predefined-time time-varying formation control of networked autonomous surface vehicles:a velocity-and model-free approach[J]. Nonlinear Dynamics, 2022, 108(4):3605-3622.
[4]	YU J L, DONG X W, HAN L, et al. Practical time-varying output formation tracking for high-order nonlinear strict-feedback multi-agent systems with input saturation[J]. ISA Transactions, 2020,98:63-74.
[5]	DONG X W, HU G Q. Time-varying formation control for general linear multi-agent systems with switching directed topologies[J]. Automatica, 2016,73:47-55.
[6]	YU J L, DONG X W, LI Q D, et al. Time-varying formation tracking for high-order multi-agent systems with switching topologies and a leader of bounded unknown input[J]. Journal of the Franklin Institute, 2018, 355(5):2808-2825.
[7]	XU X G, WEI Z Y, REN Z, et al. Time-varying fault-tolerant formation tracking based cooperative control and guidance for multiple cruise missile systems under actuator failures and directed topologies[J]. Journal of Systems Engineering and Electronics, 2019, 30(3):587-600.
[8]	LIU J, FANG J A, LI Z, et al. Time-varying formation tracking for second-order multi-agent systems subjected to switching topology and input saturation[J]. International Journal of Control Automation and Systems, 2019, 18(1):991-1001.
[9]	XI J X, WANG X C, LI H Y, et al. Energy-constraint output formation for swarm systems with dynamic output feedback control protocols[J]. ISA Transactions, 2022,120:235-246.
[10]	LI X, QI G Y, ZHANG L M. Time-varying formation dynamics modeling and constrained trajectory optimization of multi-quadrotor UAVs[J]. Nonlinear Dynamics, 2021, 106(4):3265-3284.
[11]	PAN Z H, SUN Z Q, DENG H B, et al. A multilayer graph for multiagent formation and trajectory tracking control based on MPC algorithm[J]. IEEE Transactions on Cybernetics, 2021, 52(12):13586-13597.
[12]	PANG Z H, ZHENG C B, SUN J, et al. Distance and velocity-based collision avoidance for time-varying formation control of second-order multi-agent systems[J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2021, 68(4):1253-1257.
[13]	杜宏宝, 王正杰, 唐礼喜, 等. 基于控制障碍函数的飞行器避障与制导控制[J]. 兵工学报, 2023, 44(9):2814-2823.
	DU H B, WANG Z J, TANG L X, et al. Control barrier function-based control for aircraft avoidance and guidance with dynamic obstacles[J]. Acta Armamentarii, 2023, 44(9):2814-2823. (in Chinese)
[14]	HEGDE A, GHOSE D. Multi-UAV collaborative transportation of payloads with obstacle avoidance[J]. IEEE Control Systems Letters, 2021,6:926-931.
[15]	SINGLETARY A, KLINGEBIEL K, BOURNE J, et al. Comparative analysis of control barrier functions and artificial potential fields for obstacle avoidance[C]// Proceedings of 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems.Prague, Czech Republic: IEEE,2021:8129-8136.
[16]	NGUYEN Q, SREENATH K. Exponential control barrier functions for enforcing high relative-degree safety-critical constraints[C]// Proceedings of 2016 American Control Conference.Boston,MA, US: IEEE,2016:322-328.
[17]	XIAO W, BELTA C. High-order control barrier functions[J]. IEEE Transactions on Automatic Control, 2021, 67(7):3655-3662.
[18]	XU H L, XIAO W, CASSANDRAS C G, et al. A general framework for decentralized safe optimal control of connected and automated vehicles in multi-lane signal-free intersections[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(10):17382-17396.
[19]	XIAO W, CASSANDRAS C G, BELTA C A. Bridging the gap between optimal trajectory planning and safety-critical control with applications to autonomous vehicles[J]. Automatica, 2021,129:109592.
[20]	XIAO W, BELTA C A, CASSANDRAS C G. Feasibility-guided learning for constrained optimal control problems[C]// Proceedings of the 2020 59th IEEE Conference on Decision and Control.Jeju, Korea (South): IEEE,2020:1896-1901.
[21]	KHALIL H. Nonlinear control[M]. London,UK: Pearson, 2015.
[22]	AMES A D, COOGAN S, EGERSTEDT M, et al. Control barrier functions:theory and applications[C]// Proceedings of the 2019 18th European Control Conference.Naples, Italy:IEEE,2019:3420-3431.
[23]	LIANG X, QU X R, HOU Y H, et al. Finite-time unknown observer based coordinated path-following control of unmanned underwater vehicles[J]. Journal of the Franklin Institute, 2021, 358(5):2703-2721.
[24]	MALIKOPOULOS A A, CASSANDRAS C G, ZHANG Y J. A decentralized energy-optimal control framework for connected automated vehicles at signal-free intersections[J]. Automatica, 2018,93:244-256.
[25]	ZHANG Y, CASSANDRAS C G. Decentralized optimal control of connected automated vehicles at signal-free intersections including comfort-constrained turns and safety guarantees[J]. Automatica, 2019,109:108563.
[26]	SOUZA R M J A, LIMA G V, MORAIS A S, et al. Modified artificial potential field for the path planning of aircraft swarms in three-dimensional environments[J]. Sensors, 2022, 22(4):1558.