UAV Swarms: Models and Effective Interfaces

  • Airlie Chapman
  • Mehran Mesbahi
Reference work entry


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 ℋ2 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 ℋ2 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.


  1. 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
  2. B. Bollobás, Modern Graph Theory (Springer, New York, 1998)CrossRefzbMATHGoogle Scholar
  3. 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
  4. 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
  5. A. Chapman, M. Mesbahi, Semi-autonomous consensus: network measures and adaptive trees. IEEE Trans. on Autom. Control 58(1), 19–31 (2013)CrossRefMathSciNetGoogle Scholar
  6. 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
  7. R. Diestel, Graph Theory (Springer, Berlin, 2000)Google Scholar
  8. 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
  9. G.E. Dullerud, F. Paganini, A Course in Robust Control Theory – A Convex Approach (Springer, New York, 2000)CrossRefGoogle Scholar
  10. D.D. Fulghum, Miniature air vehicles fly into army’s future. Aviat. Week Space Technol. 147, 37–38 (1998)Google Scholar
  11. 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
  12. A. Ghosh, S. Boyd, A. Saberi, Minimizing effective resistance of a graph. SIAM Rev. 50(1), 37–66 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. M. Mesbahi, M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (Princeton University Press, Princeton, 2010)zbMATHGoogle Scholar
  21. 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
  22. 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
  23. TJ. Mueller (ed.), Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications (AIAA, Danvers, 2001)Google Scholar
  24. 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
  25. R. Olfati-Saber, Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Auto. Control 51(3), 401–420 (2006)CrossRefMathSciNetGoogle Scholar
  26. 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
  27. D. J. Pines, F. Bohorquez, Challenges facing future micro-air-vehicle development. J. Aircr. 43(2), 290–305 (2006)CrossRefGoogle Scholar
  28. 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
  29. W. Ren, R.W. Beard, Distributed Consensus in Multi-vehicle Cooperative Control (Springer, New York, 2007)Google Scholar
  30. S. Salsa, Partial Differential Equations in Action: From Modelling to Theory. (Springer, Milan, 2008)Google Scholar
  31. L.V. Schmidt, Introduction to Aircraft Flight Dynamics (AIAA, Reston, 1998)CrossRefGoogle Scholar
  32. 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
  33. W. Shyy, Y. Lian, J. Tang, D. Viieru, H. Liu, Aerodynamics of Low Reynold Number Flyers (Cambridge University Press, Cambridge, 2007)CrossRefGoogle Scholar
  34. B. L. Stevens, F.L. Lewis, Aircraft Control and Simulation (Wiley, Chichester, 2003)Google Scholar
  35. H. G. Tanner, G.J. Pappas, V. Kumar, Leader-to-formation stability. IEEE Trans. Robot. Autom. 20(3), 443–455 (2004)CrossRefGoogle Scholar
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. D. Zelazo, M. Mesbahi, Edge agreement: graph-theoretic performance bounds and passivity analysis. IEEE Trans. Autom. Control 56(3), 544–555 (2011)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Aeronautics and AstronauticsUniversity of WashingtonSeattleUSA

Personalised recommendations