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Technical Brief

Consensus-Based Cooperative Formation Control for Multiquadcopter System With Unidirectional Network Connections

[+] Author and Article Information
Toru Namerikawa

Department of Integrated Design Engineering,
Graduate School of Science and Technology,
Keio University,
Yokohama 223-8522, Japan
e-mail: namerikawa@sd.keio.ac.jp

Yasuhiro Kuriki

Department of Integrated Design Engineering,
Graduate School of Science and Technology,
Keio University,
Yokohama 223-8522, Japan
e-mail: yasuhiro@nl.sd.keio.ac.jp

Ahmed Khalifa

Department of Industrial Electronics and
Control Engineering,
Faculty of Electronic Engineering,
Menoufia University,
Menoufia 32952, Egypt
e-mail: ahmed.khalifa@el-eng.menofia.edu.eg

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 2, 2016; final manuscript received October 19, 2017; published online December 14, 2017. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 140(4), 044502 (Dec 14, 2017) (8 pages) Paper No: DS-16-1224; doi: 10.1115/1.4038375 History: Received May 02, 2016; Revised October 19, 2017

In this paper, we consider cooperative control issues for a multi-unmanned aerial vehicle (UAV) system. We propose a cooperative formation control strategy with unidirectional network connections between UAVs. Our strategy is to apply a consensus-based algorithm to the UAVs so that they can cooperatively fly in formation. First, we show that UAV models on the horizontal plane and in the vertical direction are expressed as a fourth- and second-order system, respectively. Then, we show that the stability discriminants of the multi-UAV system on the horizontal plane and in the vertical direction are expressed as polynomials. For a network structure composed of bidirectional or unidirectional network connections under the assumption that the network has a directed spanning tree, we provide conditions for formation control gains such that all roots of the polynomials have negative real parts in order for the UAVs to asymptotically converge to the positions for a desired formation by using the generalized Routh stability criterion. The proposed control algorithms are validated through simulations, and experiments are performed on multiple commercial small UAVs to validate the proposed control algorithm.

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References

Murray, R. , 2007, “ Recent Research in Cooperative Control of Multivehicle Systems,” ASME J. Dyn. Syst. Meas. Control, 129(5), pp. 571–583. [CrossRef]
Ma, C.-Q. , and Zhang, J.-F. , 2010, “ Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems,” IEEE Trans. Autom. Control, 55(5), pp. 1263–1268. [CrossRef]
Dong, X. , Zhou, Y. , Ren, Z. , and Zhong, Y. , 2016, “ Time-Varying Formation Control for Unmanned Aerial Vehicles With Switching Interaction Topologies,” Control Eng. Pract., 46, pp. 26–36. [CrossRef]
Li, Z. , Liu, X. , Ren, W. , and Xie, L. , 2013, “ Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input,” IEEE Trans. Autom. Control, 58(2), pp. 518–523. [CrossRef]
Turpin, M. , Michael, N. , and Kumar, V. , 2012, “ Trajectory Design and Control for Aggressive Formation Flight With Quadrotors,” Auton. Robots, 33(1–2), pp. 143–156. [CrossRef]
Kan, Z. , Yucelen, T. , Doucette, E. , and Pasiliao, E. , 2017, “ A Finite-Time Consensus Framework Over Time-Varying Graph Topologies With Temporal Constraints,” ASME J. Dyn. Syst. Meas. Control, 139(7), p. 071012. [CrossRef]
Xi, J. , Shi, Z. , and Zhong, Y. , 2012, “ Consensus and Consensualization of High-Order Swarm Systems With Time Delays and External Disturbances,” ASME J. Dyn. Syst. Meas. Control, 134(4), p. 041011. [CrossRef]
Olfati-Saber, R. , and Murray, R. , 2004, “ Consensus Problems in Networks of Agents With Switching Topology and Time-Delays,” IEEE Trans. Autom. Control, 49(9), pp. 1520–1532. [CrossRef]
Olfati-Saber, R. , Fax, J. , and Murray, R. , 2007, “ Consensus and Cooperation in Networked Multi-Agent Systems,” Proc. IEEE, 95(1), pp. 215–233. [CrossRef]
Ren, W. , 2010, “ Consensus Tracking Under Directed Interaction Topologies: Algorithms and Experiments,” IEEE Trans. Control Syst. Technol., 18(1), pp. 230–237. [CrossRef]
Meng, Z. , Ren, W. , Cao, Y. , and You, Z. , 2011, “ Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology,” IEEE Trans. Syst. Man Cybern., 41(1), pp. 75–88. [CrossRef]
Zelazo, D. , and Allgöwer, F. , 2012, “ Growing Optimally Rigid Formations,” American Control Conference (ACC), Montreal, QC, Canada, June 27–29, pp. 3901–3906.
Yang, A. , Naeem, W. , Irwin, G. W. , and Li, K. , 2014, “ Stability Analysis and Implementation of a Decentralized Formation Control Strategy for Unmanned Vehicles,” IEEE Trans. Control Syst. Technol., 22(2), pp. 706–720. [CrossRef]
Porfiri, M. , Roberson, D. G. , and Stilwell, D. J. , 2007, “ Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach,” Automatica, 43(8), pp. 1318–1328. [CrossRef]
Listmann, K. D. , Masalawala, M. V. , and Adamy, J. , 2009, “ Consensus for Formation Control of Nonholonomic Mobile Robots,” IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, May 12–17, pp. 3886–3891.
Anderson, R. P. , and Milutinović, D. , 2014, “ Stochastic Optimal Enhancement of Distributed Formation Control Using Kalman Smoothers,” Robotica, 32(2), pp. 305–324. [CrossRef]
Kuriki, Y. , and Namerikawa, T. , 2013, “ Formation Control of UAVs With a Fourth-Order Flight Dynamics,” IEEE 52nd Annual Conference on Decision and Control (CDC), Florence, Italy, Dec. 10–13, pp. 6706–6711.
Kuriki, Y. , and Namerikawa, T. , 2014, “ Consensus-Based Cooperative Formation Control With Collision Avoidance for a Multi-UAV System,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 2077–2082.
Kuriki, Y. , and Namerikawa, T. , 2015, “ Experimental Validation of Cooperative Formation Control With Collision Avoidance for a Multi-UAV System,” Sixth International Conference on Automation, Robotics and Applications (ICARA), Queenstown, New Zealand, Feb. 17–19, pp. 531–536.
Godsil, C. , and Royle, G. , 2001, Algebraic Graph Theory, Springer, New York. [CrossRef]
Egerstedt, M. , and Hu, X. , 2001, “ Formation Constrained Multi-Agent Control,” IEEE Trans. Rob. Autom., 17(6), pp. 947–951. [CrossRef]
Leonard, N. E. , and Fiorelli, E. , 2001, “ Virtual Leaders, Artificial Potentials and Coordinated Control of Groups,” 40th IEEE Conference on Decision and Control (CDC), Orlando, FL, Dec. 4–7, pp. 2968–2973.
Xie, X. , 1985, “ Stable Polynomials With Complex Coefficients,” IEEE 24th Annual Conference Decision and Control (CDC), Fort Lauderdale, FL, Dec. 11–13, pp. 324–325.

Figures

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Fig. 1

Desired formation for three UAVs and leader

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Fig. 4

Trajectory on horizontal plane using formation control algorithm (7) with control gains for convergence (case I)

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Fig. 5

Difference from the desired positions on horizontal plane using formation control algorithm (7) with control gains for convergence (case I)

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Fig. 2

Network structure for simulations and experimental validation

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Fig. 3

AR.Drone: control structure

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Fig. 6

Trajectory on horizontal plane using formation control algorithm (7) with control gains for divergence (case II)

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Fig. 7

Difference from the desired positions on horizontal plane using formation control algorithm (7) with control gains for divergence (case II)

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Fig. 8

Simulation results in vertical direction using formation control algorithm (28) with control gains for divergence (case II)

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Fig. 9

Simulation and experimental results in vertical direction using formation control algorithm (28) with control gains for convergence (case I)

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