Handbook of Unmanned Aerial Vehicles pp 1987-2019 | Cite as

# UAV Swarms: Models and Effective Interfaces

## Abstract

This chapter examines modeling and the design of effective control interfaces, for human operators, of unmanned aerial vehicle (UAV) swarms. The swarm is modeled as a two-component hierarchical system consisting of the interaction dynamics among the UAVs in the swarm, referred to as the *network dynamics*, and the *UAV dynamics* itself. Human operators are assumed to be able to interface with the swarm via the network dynamics, which in turn has adopted a *leader-follower consensus model.* The system-theoretic and topological features of the network dynamics are then examined in order to design effective mechanisms for interfacing with the swarm. Specifically, the open loop ℋ_{2} norm of the network is selected as a performance metric for reasoning about effective human-swarm interaction. The role of topological features of the network is highlighted in the context of this metric and is related through the effective resistance of the corresponding electrical network. This is then followed by exploiting such topological features for designing a network rewiring protocol to maximize the ℋ_{2} norm. These topology design tools are applied to wind-gust rejection in disturbed swarming scenarios, demonstrating the viability of topology-assisted design for improved swarm performance. A network-based model reduction is also proposed to form a lower-order model of the network which is easier for the human operators to conceptualize and manage. The reduction process involves a novel partitioning scheme, dubbed *leader partition*, in order to fuse “similar” states in the UAV network and to form a graph-theoretic method for model reduction. This model reduction technique is then applied to derive improved swarming performance in the presence of wind gusts.

## References

- P. Barooah, J.P. Hespanha, Graph effective resistance and distributed control: spectral properties and applications, in
*Proceedings of the 45th IEEE Conference on Decision and Control*, San Diego, 2006, pp. 3479–3485Google Scholar - B. Bollobás,
*Modern Graph Theory*(Springer, New York, 1998)CrossRefzbMATHGoogle Scholar - F. Bullo, J. Cortes, S. Martinez,
*Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms*(Princeton University Press, Princeton, 2009)Google Scholar - A. Chapman, M. Mesbahi, Semi-autonomous networks: network resilience and adaptive trees, in
*Proceedings of the 49th IEEE Conference on Decision and Control*, Atlanta, no. 2, 2010, pp. 7473–7478Google Scholar - A. Chapman, M. Mesbahi, Semi-autonomous consensus: network measures and adaptive trees. IEEE Trans. on Autom. Control
**58**(1), 19–31 (2013)CrossRefMathSciNetGoogle Scholar - T. Cheviron, Robust control of an autonomous reduced scale helicopter in presence of wind gusts, in
*AIAA Guidance*,*Navigation*,*and Control Conference and Exhibit*, Keystone, 2006, pp. 1–22Google Scholar - R. Diestel,
*Graph Theory*(Springer, Berlin, 2000)Google Scholar - J.A. Drezner, R.S. Leonard, G. Sommer,
*Innovative Management in the DARPA High Altitude Endurance Unmanned Aerial Vehicle Program: Phase II Experience*(RAND, Washington, DC, 1999)Google Scholar - G.E. Dullerud, F. Paganini,
*A Course in Robust Control Theory – A Convex Approach*(Springer, New York, 2000)CrossRefGoogle Scholar - D.D. Fulghum, Miniature air vehicles fly into army’s future. Aviat. Week Space Technol.
**147**, 37–38 (1998)Google Scholar - A. Ghosh, S. Boyd, Growing well-connected graphs, in
*Proceedings of the 45th IEEE Conference on Decision and Control*, San Diego, 2006, pp. 6605–6611Google Scholar - A. Ghosh, S. Boyd, A. Saberi, Minimizing effective resistance of a graph. SIAM Rev.
**50**(1), 37–66 (2008)CrossRefzbMATHMathSciNetGoogle Scholar - S. Griffiths, J. Saunders, A. Curtis, B. Barber, T. McLain, R. Beard,
*Advances in Unmanned Aerial Vehicles: State of the Art and the Road to Autonomy*, ed. by K.P. Valavanis (Springer, Dordrecht, 2007)Google Scholar - J. Hall, Lateral control and observation of a micro aerial vehicle, in
*45th AIAA Aerospace Sciences Meeting and Exhibit*, Reno, 2007, pp. 8–11Google Scholar - J.P. How, B. Bethke, A. Frank, D. Dale, J. Vian, Real-time indoor autonomous vehicle test environment. IEEE Control Syst. Mag.
**28**(2), 51–64 (2008)CrossRefMathSciNetGoogle Scholar - Y. Kim, M. Mesbahi, On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian. IEEE Trans. on Autom. Control
**51**(1), 116–120 (2006)CrossRefMathSciNetGoogle Scholar - X. Li, L. Cao, Largest Laplacian eigenvalue predicts the emergence of costly punishment in the evolutionary ultimatum game on networks. Phys. Rev. E
**80**(6 Pt 2), 066101 (2009)CrossRefGoogle Scholar - S. Martini, M. Egerstedt, A. Bicchi, Controllability decompositions of networked systems through quotient graphs, in
*Proceedings of the 47th IEEE Conference on Decision and Control*, Cancun, 2008, pp. 5244–5249.Google Scholar - D. Mellinger, V. Kumar, Minimum snap trajectory generation and control for quadrotors, in
*International Conferences on Robotics and Automation*, Shanghai, 2011, pp. 2520–2525Google Scholar - M. Mesbahi, M. Egerstedt,
*Graph Theoretic Methods in Multiagent Networks*(Princeton University Press, Princeton, 2010)zbMATHGoogle Scholar - N. Meskin, K. Khorasani, C.A. Rabbath, A hybrid fault detection and isolation strategy for a network of unmanned vehicles in presence of large environmental disturbances. IEEE Trans. Control Syst. Technol.
**18**(6), 1422–1429 (2010)Google Scholar - N. Michael, D. Mellinger, Q. Lindsey, V. Kumar, The GRASP multiple micro-UAV testbed. IEEE Robot. Autom. Mag.
**17**(3), 56–65 (2010)CrossRefGoogle Scholar - TJ. Mueller (ed.),
*Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications*(AIAA, Danvers, 2001)Google Scholar - L. Mutuel, R. Douglas, Controller design for low speed flight in turbulence, in
*AIAA Guidance*,*Navigation*,*and Control Conference*, New Orleans, 1997, pp. 1111–1121Google Scholar - R. Olfati-Saber, Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Auto. Control
**51**(3), 401–420 (2006)CrossRefMathSciNetGoogle Scholar - R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE
**95**(1), 215–233 (2007)CrossRefGoogle Scholar - D. J. Pines, F. Bohorquez, Challenges facing future micro-air-vehicle development. J. Aircr.
**43**(2), 290–305 (2006)CrossRefGoogle Scholar - A. Rahmani, M. Ji, M. Mesbahi, M. Egerstedt, Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J. Control Optim.
**48**(1), 162–186 (2009)CrossRefzbMATHMathSciNetGoogle Scholar - W. Ren, R.W. Beard,
*Distributed Consensus in Multi-vehicle Cooperative Control*(Springer, New York, 2007)Google Scholar - S. Salsa,
*Partial Differential Equations in Action: From Modelling to Theory.*(Springer, Milan, 2008)Google Scholar - L.V. Schmidt,
*Introduction to Aircraft Flight Dynamics*(AIAA, Reston, 1998)CrossRefGoogle Scholar - W. Shyy, Y. Lian, J. Tang, H. Liu, P. Trizila, B. Stanford, L. Bernal, C. Cesnik, P. Friedmann, P. Ifju, Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications, in
*46th AIAA Aerospace Sciences Meeting and Exhibit*, Reno, vol. 24, no. 4, 2008, pp. 1–33Google Scholar - W. Shyy, Y. Lian, J. Tang, D. Viieru, H. Liu,
*Aerodynamics of Low Reynold Number Flyers*(Cambridge University Press, Cambridge, 2007)CrossRefGoogle Scholar - B. L. Stevens, F.L. Lewis,
*Aircraft Control and Simulation*(Wiley, Chichester, 2003)Google Scholar - H. G. Tanner, G.J. Pappas, V. Kumar, Leader-to-formation stability. IEEE Trans. Robot. Autom.
**20**(3), 443–455 (2004)CrossRefGoogle Scholar - G. Tyson, A.T. Lindsay, S. Simpson, D. Hutchison, Improving wireless sensor network resilience with the INTERSECTION framework, in
*Proceedings of the 2nd International Conference on Mobile Lightweight Wireless Systems*,*Critical Information Infrastructure Protection*, Barcelona, 2010Google Scholar - E. R. Ulrich, D.J. Pines, J.S. Humbert, Pitch and heave control of robotic Samara micro air vehicles. J. Aircr.
**47**(4), 1290–1299 (2010)CrossRefGoogle Scholar - Y. Wan, S. Roy, A. Saberi, Network design problems for controlling virus spread, in
*Proceedings of the 46th IEEE Conference on Decision and Control*, New Orleans, 2007, pp. 3925–3932Google Scholar - Z. Wu, R. Wang, The consensus in multi-agent system with speed-optimized network. Int. J. Modern Phys. B
**23**(10), 2339–2348 (2009)CrossRefzbMATHGoogle Scholar - C.-D. Yang, W.-H. Liu, P.-W. Chang, H.-J. Weng, Decoupling control for hovering flight vehicle with parameter uncertainties, in
*AIAA Guidance*,*Navigation*,*and Control Conference and Exhibit*, Keystone, no. 1, 2006, pp. 1–13.Google Scholar - D. Zelazo, M. Mesbahi, Edge agreement: graph-theoretic performance bounds and passivity analysis. IEEE Trans. Autom. Control
**56**(3), 544–555 (2011)CrossRefMathSciNetGoogle Scholar