Restricted accessResearch articleFirst published online 2025
Consensus tracking and vibration control for multiple 3D flexible rotating manipulator systems with input amplitude and rate constraints over directed graph
This paper addresses the angle consensus tracking and vibration control problems of a class of leader-following three-dimensional (3D) flexible rotating manipulator (FRM) systems subject to input amplitude and rate constraints (IARCs) over a directed communication graph. Each follower FRM consists of a rotating base and a flexible manipulator, modeled as a distributed parameter system governed by coupled partial differential equations (PDEs). The desired angular positions of the bases and manipulators are regarded as the virtual leader’s signals. To overcome the difficulty in constructing a suitable Lyapunov function caused by the asymmetry of the Laplacian matrix in the directed topology, a set of distributed observers is proposed to estimate the leader’s angular positions. Based on these observers, a distributed boundary control strategy is developed using the backstepping method combined with a smooth hyperbolic tangent function, which effectively handles the IARCs and achieves both consensus tracking and vibration suppression. The stability of the closed-loop systems is rigorously analyzed using Lyapunov’s direct method and LaSalle’s invariance principle. Finally, several simulation examples are presented to verify the effectiveness of the proposed control scheme.
ChenSHeWZhaoZ, et al. (2025) Adaptive control of a flexible manipulator with unknown hysteresis and intermittent actuator faults. IEEE/CAA Journal of Automatica Sinica12(1): 148–158.
2.
FuJWenGHuangT, et al. (2019) Consensus of multi-agent systems with heterogeneous input saturation levels. IEEE Transactions on Circuits and Systems II: Express Briefs66(6): 1053–1057.
3.
GongBJiangLNingX, et al. (2023) Study on mission planning algorithm for multi-target passive tracking based on satellite formation. Aerospace Science and Technology142: 108660.
4.
HanFJiaY (2022) Bipartite consensus and distributed boundary control for multiple flexible manipulators associated with signed digraph. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(5): 3005–3014.
5.
JiNLiuJ (2024) Consensus control and vibration suppression for multiple flexible nonlinear Timoshenko manipulators under undirected communication topology. Communications in Nonlinear Science and Numerical Simulation138: 108200.
6.
JiNLiuZLiuJ, et al. (2018) Vibration control for a nonlinear three-dimensional Euler–Bernoulli beam under input magnitude and rate constraints. Nonlinear Dynamics91: 2551–2570.
7.
JinHZhangZYangGH, et al. (2025) An event-triggered interval observer scheme for fault diagnosis of cyber-physical dc microgrids. IEEE Transactions on Industrial Informatics21(4): 2789–2798.
8.
JinHZuoZWangY, et al. (2024) Event-triggered interval observer fault detection and isolation for multiagent systems. IEEE Transactions on Cybernetics54(7): 4063–4073.
9.
LiLLiuJ (2023) Consensus tracking control and vibration suppression for nonlinear mobile flexible manipulator multi-agent systems based on PDE model. Nonlinear Dynamics111(4): 3345–3359.
10.
LiLZhangQLiuJ (2025) PDE-based leader-following coordination control for flexible manipulators with event-triggered communication over directed graphs. IEEE Transactions on Control of Network Systems12(1): 894–905.
11.
LiangKCuiJLuP, et al. (2024) Minimal learning parameters-based simplified robust adaptive saturated control for dynamic positioning ship with input magnitude and rate saturations. Ocean Engineering297: 117032.
12.
LiuYChenXMeiY, et al. (2022) Observer-based boundary control for an asymmetric output-constrained flexible robotic manipulator. Science China Information Sciences65(3): 139203.
13.
LiuYFuYHeW, et al. (2019) Modeling and observer-based vibration control of a flexible spacecraft with external disturbances. IEEE Transactions on Industrial Electronics66(11): 8648–8658.
14.
LiuZCuiXZhaoZ, et al. (2024) PDE-based consensus control for multiagent systems with event-triggered mechanism. IEEE Transactions on Control of Network Systems11(4): 1768–1777.
15.
LiuZLiuJWangL (2018) Disturbance observer based attitude control for flexible spacecraft with input magnitude and rate constraints. Aerospace Science and Technology72: 486–492.
16.
TrakasPSBechlioulisCP (2023) Robust adaptive prescribed performance control for unknown nonlinear systems with input amplitude and rate constraints. IEEE Control Systems Letters7: 1801–1806.
17.
WangDHeHLiuD (2017) Intelligent optimal control with critic learning for a nonlinear overhead crane system. IEEE Transactions on Industrial Informatics14(7): 2932–2940.
18.
WangGZuoZLiP, et al. (2025) Controllers for multiagent systems with input amplitude and rate constraints and their application to quadrotor rendezvous. IEEE Transactions on Automation Science and Engineering22(6354–6364): 6354–6364.
19.
WangJLiuJJiB, et al. (2023) Vibration suppression and boundary control for nonlinear flexible rotating manipulator in three-dimensional space subject to output restrictions. Communications in Nonlinear Science and Numerical Simulation120: 107151.
20.
WangKWenSXGaoYF, et al. (2024a) Switching anti-windup synthesis for linear systems subject to asymmetric input magnitude and rate saturation: Application to aircraft engines. IEEE Transactions on Aerospace and Electronic Systems60(2): 1924–1936.
21.
WangSTaoJJiangQ, et al. (2024b) Manipulator joint fault localization for intelligent flexible manufacturing based on reinforcement learning and robot dynamics. Robotics and Computer-Integrated Manufacturing86: 102684.
22.
WuDLiJSongD, et al. (2023) Development of a novel ball-and-socket flexible manipulator for minimally invasive flexible surgery. IEEE Transactions on Medical Robotics and Bionics5(2): 278–288.
23.
XingXLiuJ (2021) Vibration and position control of overhead crane with three-dimensional variable length cable subject to input amplitude and rate constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems51(7): 4127–4138.
24.
XingXLiuJYangC (2022) Adaptive neural control of a class of uncertain state and input-delayed systems with input magnitude and rate constraints. IEEE Transactions on Systems, Man, and Cybernetics: Systems52(11): 6837–6851.
25.
YaoXLiuYZhaoW (2023) Adaptive boundary vibration control and angle tracking consensus of networked flexible Timoshenko manipulator systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems53(5): 2949–2960.
26.
YaoXSunHZhaoZ, et al. (2024) Event-triggered bipartite consensus tracking and vibration control of flexible Timoshenko manipulators under time-varying actuator faults. IEEE/CAA Journal of Automatica Sinica11(5): 1190–1201.
27.
ZhangSWuYHeX, et al. (2022a) Cooperative fault-tolerant control for a mobile dual flexible manipulator with output constraints. IEEE Transactions on Automation Science and Engineering19(4): 2689–2698.
28.
ZhangWZuoZWangY (2022b) Active synchronization for double-integrator network systems without velocity information. IEEE Transactions on Circuits and Systems I: Regular Papers69(6): 2589–2600.
29.
ZhangWZuoZWangY (2022c) Networked multiagent systems: Antagonistic interaction, constraint, and its application. IEEE Transactions on Neural Networks and Learning Systems33(8): 3690–3699.
30.
ZhaoWLiuYYaoX (2024) PDE-based boundary adaptive consensus control of multiagent systems with input constraints. IEEE Transactions on Neural Networks and Learning Systems35(9): 12617–12626.
31.
ZhaoZTanZLiuZ, et al. (2023) Adaptive inverse compensation fault-tolerant control for a flexible manipulator with unknown dead-zone and actuator faults. IEEE Transactions on Industrial Electronics70(12): 12698–12707.
32.
ZuoZYangXLiZ, et al. (2021) MPC-based cooperative control strategy of path planning and trajectory tracking for intelligent vehicles. IEEE Transactions on Intelligent Vehicles6(3): 513–522.
