RBF Neural Network Compensation Sliding Mode Control Strategy for Flexible Space Manipulators

doi:10.12068/j.issn.1005-3026.2024.09.006

Abstract

Abstract:

Flexible structures cause the dynamic parameters of flexible space manipulators to change with time， which reduces the accuracy of tracking control. The lighter mass and the larger ratio of length to radius may result in the vibration of flexible space manipulators during their movement. To solve the above problems， a dynamic model of a flexible space manipulator considering two?dimensional deformation and disturbance torque is established， and a simplified non?linear dynamic formula is derived. On this basis， a control law is designed to identify and compensate for the time?varying term and disturbance torque in the flexible space manipulator using the radial basis function （RBF） neural network. Then， using the hyperbolic tangent function as the approximation rate， a sliding mode control strategy is proposed. Finally， through simulation and ground physical prototype experiment， it can be concluded that in the design of control laws for flexible space manipulators， the control strategy with neural network compensation effectively reduces the impact of disturbance torque on the flexible space manipulator. By using the tanh function instead of the sgn function， the fluctuation of input torque can be reduced， and the effectiveness of the RBF neural network compensation sliding mode control strategy is verified.

Key words: flexible space manipulator, neural network compensation, dynamic modeling, sliding mode control

CLC Number:

TH 113.1

Xiao-peng LI, Jia-xing FU, Hai-long LIU, Meng YIN. RBF Neural Network Compensation Sliding Mode Control Strategy for Flexible Space Manipulators[J]. Journal of Northeastern University(Natural Science), 2024, 45(9): 1258-1267.

Figures/Tables 11

Fig.1 Equivalent physical model diagram of the flexible space manipulator

Fig.2 RBF neural network structure

Fig.3 Control block diagram of the flexible space manipulator using RBF neural network compensation control strategy

Table 1 Parameters of the flexible space manipulator

参数	值
柔性连杆长度l /m	2.5
柔性连杆质量m /kg	3
末端负载M /kg	1
弯曲刚度σ/（N·m²）	100
控制器参数 Z	51
控制器参数 γ	diag[6,6]
控制器系数κ	0.01
控制器参数 *K_v*	151
控制器参数δ_N	12

Fig.4 Rotating simulation results of the flexible space manipulator under different strategies

Fig.5 Deformation simulation results of the flexible space manipulator

Fig.6 Simulation results of input torque of the flexible space manipulator

Fig.7 Trajectory simulation results of the flexible space manipulator

Table 2 Parameters of the ground control

参数	值
柔性空间机械臂长度l/m	0.6
尖端有效载荷M/kg	0.8
柔性空间机械臂质量m/kg	2.5
柔性空间机械臂线密度ρ/（kg·m^-1）	4.17
柔性空间机械臂厚度H/mm	2
柔性空间机械臂弹性模量E/GPa	70
柔性空间机械臂宽度W/mm	200

Fig.8 Experimental results of the ground control experiment platform for the flexible space manipulator

Table 3 Evaluation indexes of different control strategies

评价指标	NNSMC（tanh）	NNSMC（sgn）	SMC
平均绝对误差/rad	0.198	0.209	0.276
标准误差	0.219	0.234	0.254
平均加速度/（m·s^-2）	0.069	0.076	0.104
加速度标准差	0.067	0.088	0.096

References 23

1	Gasbarri P， Pisculli A.Dynamic/control interactions between flexible orbiting space‑robot during grasping，docking and post‑docking manoeuvres［J］.Acta Astronautica，2015，110：225-238.
2	Zhao J D， Zhao Z Y， Yang X H，et al.Inverse kinematics and workspace analysis of a novel SSRMS-type reconfigurable space manipulator with two lockable passive telescopic links［J］.Mechanism and Machine Theory，2023，180：105152.
3	Shang D Y， Li X P， Yin M，et al.Dynamic modeling and fuzzy adaptive control strategy for space flexible robotic arm considering joint flexibility based on improved sliding mode controller［J］.Advances in Space Research，2022，70（11）：3520-3539.
4	Zhang D G.Recursive Lagrangian dynamic modeling and simulation of multi‑link spatial flexible manipulator arms［J］.Applied Mathematics and Mechanics，2009，30（10）：1283-1294.
5	Korayem M H， Heidari A， Nikoobin A.Maximum allowable dynamic load of flexible mobile manipulators using finite element approach［J］.The International Journal of Advanced Manufacturing Technology，2009，45（11）：1232.
6	Nair A P， Selvaganesan N， Lalithambika V R.Lyapunov based PD/PID in model reference adaptive control for satellite launch vehicle systems［J］.Aerospace Science and Technology，2016，51：70-77.
7	Chen S， Xue W C， Zhong S，et al.On comparison of modified ADRCs for nonlinear uncertain systems with time delay［J］.Science China （Information Sciences），2018，61（7）：70223.
8	Yang Z J， Fukushima Y， Qin P.Decentralized adaptive robust control of robot manipulators using disturbance observers［J］.IEEE Transactions on Control Systems Technology，2012，20（5）：1357-1365.
9	Dong C Y， Liu C， Wang Q，et al.Switched adaptive active disturbance rejection control of variable structure near space vehicles based on adaptive dynamic programming［J］.Chinese Journal of Aeronautics，2019，32（7）：1684-1694.
10	Qiao J Z， Wu H， Yu X.High‑precision attitude tracking control of space manipulator system under multiple disturbances［J］.IEEE Transactions on Systems，Man，and Cybernetics：Systems，2021，51（7）：4274-4284.
11	王宏，郑天奇.基于滑模补偿的六轴机械臂RBF网络自适应控制［J］.东北大学学报（自然科学版），2017，38（11）：1601-1606.
	Wang Hong， Zheng Tian‑qi.RBF network adaptive control based on SMC compensation for six‑axis manipulator［J］.Journal of Northeastern University（Natural Science），2017，38（11）：1601-1606.
12	曾晨东，艾海平，陈力.空间机械臂在轨插、拔孔操作力/位姿阻抗控制［J］.机械工程学报，2022，58（3）：84-94.
	Zeng Chen‑dong， Ai Hai‑ping， Chen Li.Operation force/pose impedance control of space manipulator in orbit［J］.Chinese Journal of Mechanical Engineering，2022，58（3）：84-94.
13	吴昊，毛新涛，刘鹭航，等.柔性关节空间机械臂的自适应滑模控制［J］.宇航学报，2019，40（6）：703-710.
	Wu Hao， Mao Xin‑tao， Liu Lu‑hang，et al.Adaptive sliding mode control for flexible joint space mechanical arms［J］.Journal of Astronautics，2019，40（6）：703-710.
14	Yin X M， Wang B， Liu L，et al.Disturbance observer‑based gain adaptation high‑order sliding mode control of hypersonic vehicles［J］.Aerospace Science and Technology，2019，89：19-30.
15	Yao Q J.Adaptive trajectory tracking control of a free‑flying space manipulator with guaranteed prescribed performance and actuator saturation［J］.Acta Astronautica，2021，185：283-298.
16	张建宇，高天宇，于潇雁，等.基于自适应时延估计的空间机械臂连续非奇异终端滑模控制［J］.机械工程学报，2021，57（11）：177-183.
	Zhang Jian‑yu， Gao Tian‑yu， Yu Xiao‑yan，et al.Continuous non‑singular terminal sliding mode control of space manipulator based on adaptive time delay estimation［J］.Journal of Mechanical Engineering，2021，57（11）：177-183.
17	Wu S X， Chen L， Zhang D X，et al.Disturbance observer‑based fixed time sliding mode control for spacecraft proximity operations with coupled dynamics［J］.Advances in Space Research，2020，66（9）：2179-2193.
18	Jia S Y， Shan J J.Finite‑time trajectory tracking control of space manipulator under actuator saturation［J］.IEEE Transactions on Industrial Electronics，2020，67（3）：2086-2096.
19	Johanastrom K， de Canudas W C.Revisiting the LuGre friction model［J］.IEEE Control Systems Magazine，2008，28（6）：101-114.
20	Shang D Y， Li X P， Yin M，et al.Tracking control strategy for space flexible manipulator considering nonlinear friction torque based on adaptive fuzzy compensation sliding mode controller［J］.Advances in Space Research，2023，71（9）：3661-3680.
21	Gu H C， Song G B， Malki H.Chattering‑free fuzzy adaptive robust sliding‑mode vibration control of a smart flexible beam［J］.Smart Materials and Structures，2008，17（3）：035007.
22	Shang D Y， Li X P， Yin M，et al.Vibration suppression for two‑inertia system with variable‑length flexible load based on neural network compensation sliding mode controller and angle‑independent method［J］.IEEE/ASME Transactions on Mechatronics，2023，28（2）：848-859.
23	尚东阳，李小彭，尹猛，等.采用RBF神经网络辨识的柔性机械臂抑振控制策略［J］.西安交通大学学报，2022，56（6）：76-84.
	Shang Dong‑yang， Li Xiao‑peng， Yin Meng，et al.Vibration suppression control strategy of flexible manipulator based on RBF neural network identification［J］.Journal of Xi'an Jiaotong University，2022，56（6）：76-84.

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