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Differential flatness-based distributed control of underactuated robot swarms

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  • 1. Department of Dynamics and Control, Beihang University, Beijing 100191, China;
    2. Institute of Computer Application Technology, China North Industries Group Corporation Limited, Beijing 100095, China

Received date: 2023-05-09

  Revised date: 2023-08-25

  Online published: 2023-09-25

Supported by

the National Natural Science Foundation of China (Nos.62373025, 12332004, 62003013, and 11932003)

Abstract

This paper proposes a distributed control method based on the differential flatness (DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.

Cite this article

Ningbo AN, Qishao WANG, Xiaochuan ZHAO, Qingyun WANG . Differential flatness-based distributed control of underactuated robot swarms[J]. Applied Mathematics and Mechanics, 2023 , 44(10) : 1777 -1790 . DOI: 10.1007/s10483-023-3040-8

References

[1] ECHETO, J., SANTOS, M., and ROMANA, M. G. Automated vehicles in swarm configuration: simulation and analysis. Neurocomputing, 501, 679-693 (2022)
[2] LIU, Y. B., HUO, L. J., WU, J., and BASHIR, A. K. Swarm learning-based dynamic optimal management for traffic congestion in 6G-driven intelligent transportation system. IEEE Transactions on Intelligent Transportation Systems, 24, 7831-7846 (2023)
[3] ORFANUS, D., DE FREITAS, E. P., and ELIASSEN, F. Self-organization as a supporting paradigm for military UAV relay networks. IEEE Communications Letters, 20, 804-807 (2016)
[4] LIU, D. X., WANG, J. L., XU, K., XU, Y. H., YANG, Y., XU, Y. T., WU, Q. H., and ANPALAGAN, A. Task-driven relay assignment in distributed UAV communication networks. IEEE Transactions on Vehicular Technology, 68, 11003-11017 (2019)
[5] MAJID, M., HABIB, S., JAVED, R., RIZWAN, M., SRIVASTAVA, G., GADEKALLU, T. R., and JERRY, C. W. Applications of wireless sensor networks and internet of things frameworks in the industry revolution 4.0: a systematic literature review. Sensors, 22, 2087 (2022)
[6] TEMENE, N., SERGIOU, C., GEORGIOU, C., and VASSILIOU, V. A survey on mobility in wireless sensor networks. Ad Hoc Networks, 125, 102726 (2022)
[7] WANG, X. H., LI, X. S., HUANG, N. J., and O'REGAN, D. Asymptotical consensus of fractional-order multi-agent systems with current and delay states. Applied Mathematics and Mechanics (English Edition), 40, 1677-1694 (2019) https://doi.org/10.1007/s10483-019-2533-8
[8] MAO, X. C. and WANG, Z. H. Stability, bifurcation, and synchronization of delay-coupled ring neural networks. Nonlinear Dynamics, 84, 1063-1078 (2016)
[9] MU, R. J., CHEN, J. Y., PENG, K. K., ZHANG, X., DENG, Y. P., and CUI, N. G. Finite-time super-twisting controller based on SESO design for RLV re-entry phase. IEEE Access, 7, 37371-37380 (2019)
[10] MAO, X. C., LI, X. Y., DING, W. J., WANG, S., ZHOU, X. Y., and QIAO, L. Dynamics of a multiplex neural network with delayed couplings. Applied Mathematics and Mechanics (English Edition), 42, 441-456 (2021) https://doi.org/10.1007/s10483-021-2709-6
[11] MAO, X. C. and DING, W. J. Nonlinear dynamics and optimization of a vibration reduction system with time delay. Communications in Nonlinear Science and Numerical Simulation, 122, 107220 (2023)
[12] WANG, X. H. and HUANG, N. J. Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control. Applied Mathematics and Mechanics (English Edition), 42, 1799-1816 (2021) https://doi.org/10.1007/s10483-021-2789-6
[13] HE, W. L., XU, B., HAN, Q. L., and QIAN, F. Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies. IEEE Transactions on Cybernetics, 50, 2996-3008 (2019)
[14] LI, D. Y., GE, S. S., and LEE, T. H. Fixed-time-synchronized consensus control of multiagent systems. IEEE Transactions on Control of Network Systems, 8, 89-98 (2020)
[15] LI, X. M., ZHOU, Q., LI, P. S., LI, H. Y., and LU, R. Q. Event-triggered consensus control for multi-agent systems against false data-injection attacks. IEEE Transactions on Cybernetics, 50, 1856-1866 (2019)
[16] ZHAO, W. B., LIU, H., and LEWIS, F. L. Robust formation control for cooperative underactuated quadrotors via reinforcement learning. IEEE Transactions on Neural Networks and Learning Systems, 32, 4577-4587 (2020)
[17] ZHOU, Z., WANG, H. B., WANG, Y. L., XUE, X. J., and ZHANG, M. Q. Distributed formation control for multiple quadrotor UAVs under Markovian switching topologies with partially unknown transition rates. Journal of the Franklin Institute, 356, 5706-5728 (2019)
[18] YU, Z. Q., LIU, Z. X., ZHANG, Y. M., QU, Y. H., and SU, C. Y. Distributed finite-time fault-tolerant containment control for multiple unmanned aerial vehicles. IEEE Transactions on Neural Networks and Learning Systems, 31, 2077-2091 (2019)
[19] GU, N., WANG, D., PENG, Z. H., and WANG, J. Safety-critical containment maneuvering of underactuated autonomous surface vehicles based on neurodynamic optimization with control barrier functions. IEEE Transactions on Neural Networks and Learning Systems, 34, 2882-2895 (2021)
[20] LV, M., DE SCHUTTER, B., and BALDI, S. Nonrecursive control for formation-containment of HFV swarms with dynamic event-triggered communication. IEEE Transactions on Industrial Informatics, 19, 3188-3197 (2022)
[21] GONG, J. Y., JIANG, B., MA, Y. L., and MAO, Z. H. Distributed adaptive fault-tolerant formation-containment control with prescribed performance for heterogeneous multiagent systems. IEEE Transactions on Cybernetics (2022) https://doi.org/10.1109/TCYB.2022.3218377
[22] MAHMOOD, A. and KIM, Y. Leader-following formation control of quadcopters with heading synchronization. Aerospace Science and Technology, 47, 68-74 (2015)
[23] OH, K. K. and AHN, H. S. Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space. International Journal of Robust and Nonlinear Control, 24, 1809-1820 (2014)
[24] ZHAO, W. B., LIU, H., and LEWIS, F. L. Data-driven fault-tolerant control for attitude synchronization of nonlinear quadrotors. IEEE Transactions on Automatic Control, 66, 5584-5591 (2021)
[25] LIU, H., MA, T., LEWIS, F. L., and WAN, Y. Robust formation control for multiple quadrotors with nonlinearities and disturbances. IEEE Transactions on Cybernetics, 50, 1362-1371 (2018)
[26] WANG, C. H., JI, J. C., MIAO, Z. H., and ZHOU, J. Udwadia-Kalaba approach based distributed consensus control for multi-mobile robot systems with communication delays. Journal of the Franklin Institute, 359, 7283-7306 (2022)
[27] ZHANG, K. M., ZHENG, X. D., CHENG, Z., LIANG, B., WANG, T. S., and WANG, Q. Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement. Applied Mathematics and Mechanics (English Edition), 43, 93-112 (2022) https://doi.org/10.1007/s10483-022-2811-5
[28] FLIESS, M., LÉVINE, J., MARTIN, P., and ROUCHON, P. Flatness and defect of non-linear systems: introductory theory and examples. International Journal of Control, 61, 1327-1361 (1995)
[29] MELLINGER, D. and KUMAR, V. Minimum snap trajectory generation and control for quadrotors. 2011 IEEE International Conference on Robotics and Automation, IEEE, Shanghai, 2520-2525 (2011)
[30] FAESSLER, M., FRANCHI, A., and SCARAMUZZA, D. Differential flatness of quadrotor dynamics subject to rotor drag for accurate tracking of high-speed trajectories. IEEE Robotics and Automation Letters, 3, 620-626 (2017)
[31] AI, X. L. and YU, J. Q. Fixed-time trajectory tracking for a quadrotor with external disturbances: a flatness-based sliding mode control approach. Aerospace Science and Technology, 89, 58-76 (2019)
[32] ZHOU, D. J., WANG, Z. J., and SCHWAGER, M. Agile coordination and assistive collision avoidance for quadrotor swarms using virtual structures. IEEE Transactions on Robotics, 34, 916-923 (2018)
[33] ZHOU, X., WEN, X. Y., WANG, Z. P., GAO, Y. M., LI, H. J., WANG, Q. H., YANG, T. K., LU, H. J., CAO, Y. J., XU, C., and GAO, F. Swarm of micro flying robots in the wild. Science Robotics, 7, eabm5954 (2022)
[34] REN, W. and CAO, Y. C. Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues, Springer, London (2011)
[35] TEDRAKE, R. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832) (2023) https://underactuated.csail.mit.edu/
[36] LEE, T., LEOK, M., and MCCLAMROCH, N. H. Geometric tracking control of a quadrotor UAV on SE(3). 49th IEEE Conference on Decision and Control, IEEE, Atlanta, GA, 5420-5425 (2010)
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