多无人机吊挂负载运输系统的非线性鲁棒控制设计

doi:10.13229/j.cnki.jdxbgxb.20220882

摘要/Abstract

摘要：

针对多无人机吊挂负载运输系统中负载的位置跟踪和姿态控制问题，提出了一种新型非线性鲁棒控制策略。首先，在存在未知外界扰动和考虑系统内部状态耦合的基础上，基于拉格朗日力学建立了多无人机吊挂负载运输系统的动力学模型。其次，设计了一种基于误差符号函数积分（RISE）和几何控制方法的非线性鲁棒控制策略，用于补偿未知外界扰动的影响，实现了对负载位姿的精确控制。基于Lyapunov方法的稳定性分析证明了闭环系统的稳定性和吊挂负载跟踪误差的渐近收敛。仿真结果表明，本文提出的控制策略可以实现良好的轨迹跟踪效果，并对外界干扰有较好的鲁棒性。

关键词: 控制理论与控制工程, 多无人机, 吊挂负载, 几何控制, 非线性控制, 鲁棒控制

Abstract:

Multi UAVs suspended payload transportation system is a new type of aerial transportation. In this paper， a new nonlinear robust control strategy is proposed for the position tracking and attitude control of the payload. To deal with the unknown external disturbances and strong system states coupling， the dynamic model of multi-UAV suspended payload transportation system is established via the Lagrange method. Then， a nonlinear robust control strategy based on robust-integral-signum-error method and geometric control is designed to compensate for the effects of unknown external disturbances， and accurate control of the payload's attitude and position are achieved. Based on the stability analysis of Lyapunov method， the stability of the closed-loop system and the asymptotic convergence of the suspended load tracking error are proved. The simulation results show that the control strategy proposed in this paper can achieve good trajectory tracking performance and has good robustness to unknown external interference.

Key words: control theory and control engineering, multiple unmanned aerial vehicles, suspended payload, geometric control, nonlinear control, robust control

中图分类号:

TP273

鲜斌,王光怡,蔡佳明. 多无人机吊挂负载运输系统的非线性鲁棒控制设计[J]. 吉林大学学报(工学版), 2024, 54(6): 1788-1795.

Bin XIAN,Guang-yi WANG,Jia-ming CAI. Nonlinear robust control design for multi unmanned aerial vehicles suspended payload transportation system[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(6): 1788-1795.

图/表 10

图 1

表1

符号定义"

符号	单位	所属群	符号描述
$p L$	m	$R 3$	负载质心在惯性坐标系下的位置
$v L$	m/s	$R 3$	负载质心在惯性坐标系下的线速度
$R L$		$S O (3)$	负载在体坐标系下的姿态旋转矩阵
$Ω L$	rad/s	$R 3$	负载在惯性坐标系下的角速度
$m L$	kg	$R$	负载质量
$J L$	m⁴		负载的惯性矩阵
$p i$	m	$R 3$	第 $i$ 架无人机质心在惯性坐标系下的位置
$v i$	m/s	$R 3$	第 $i$ 架无人机质心在惯性坐标系下的线速度
$R i$		$S O (3)$	第 $i$ 架无人机在体坐标系下的姿态旋转矩阵
$Ω i$	rad/s	$R 3$	第 $i$ 架无人机质心在惯性坐标系下的角速度
$m u a v$	kg	$R$	每架无人机的质量
$J i$	m⁴		第 $i$ 架无人机的惯性矩阵
$ω i$	rad/s	$R 3$	第 $i$ 根绳索的角速度

表1

图2

表2

数值仿真相关增益"

增益名称	数值	增益名称	数值
$k p L$	$d i a g ([9.5,11.9,9])$	$β p$	5.0
$k v L$	$d i a g ([1.8,1.6,3.0])$	$c x$	0.05
$α 2$	$d i a g ([3,2.5,0.01])$	$α 1$	26.3
$k t$	$d i a g ([43.7,28.23,17.54])$	$β$	0.01
$k ξ$	$d i a g ([50.1,50,50])$	$k ω$	50

表2

图3

图4

图5

图6

表3

仿真1负载位姿稳态最大误差对比"

稳态最大误差	本文控制器	滑模控制器
$e x$	0.001 4	0.020 2
$e y$	0.005 2	0.022 2
$e z$	0.001 5	0.004 5
$e R L (1)$	$2.007 ? 0 × 10 - 5$	$2.322 ? 5 × 10 - 4$
$e R L (2)$	$4.467 ? 3 × 10 - 5$	$3.391 ? 5 × 10 - 4$
$e R L (3)$	0.550 7	0.807 2

表3

表4

仿真2负载位姿稳态最大误差对比"

稳态最大误差	本文控制器	滑模控制器
$e x$	0.188 5	0.294 8
$e y$	0.195 4	0.279 8
$e z$	0.176 1	0.313 8
$e R L (1)$	0.014 4	0.050 1
$e R L (2)$	0.014 4	0.043 9
$e R L (3)$	0.572 7	0.815 3

表4

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