String Instabilities in Formation Flight: Limitations Due to Integral Constraints

[+] Author and Article Information
P. Seiler

University of Illinois, Urbana-Champaign

A. Pant

Tata Research Development and Design Center

J. K. Hedrick

University of California, Berkeley

J. Dyn. Sys., Meas., Control 126(4), 873-879 (Mar 11, 2005) (7 pages) doi:10.1115/1.1858444 History: Received June 23, 2003; Revised January 22, 2004; Online March 11, 2005
Copyright © 2004 by ASME
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Hummel,  D., 1995, “Formation Flight as an Energy-Savings Mechanism,” Israel J. Zoology,41, pp. 261–278.
Lissaman,  P. B. S., and Shollenberger,  C. A., 1970, “Formation Flight of Birds,” Science, 168, pp. 1003–1005.
Richardson, C., and Schoultz, M., 1991, “Formation Flight System Design Concept,” Proc. of IEEE/AIAA 10th Digital Avionics Systems Conference, IEEE, New York, pp. 18–25.
Pachter,  M., D’Azzo,  J. J., and Dargan,  J. L., 1994, “Automatic Formation Flight Control,” J. Guid. Control Dyn., 17(6), pp. 1380–1383.
Chichka, D. F., and Speyer, J. L., 1998, “Solar-Powered, Formation-Enhanced Aerial Vehicle Systems for Sustained Endurance,” Proc. of American Control Conference, IEEE, Philadelphia, pages 684–688.
Chichka, D. F., Speyer, J. L., and Park, C. G., 1999, “Peak-Seeking Control With Application to Formation Flight,” IEEE Conference on Decision and Control, IEEE, New York, pp. 2463–2470.
Seiler, P., Pant, A., and Hedrick, J. K., 1999, “Preliminary Investigation of Mesh Stability for Linear Systems,” Proc. of ASME: DSC Div., ASME, New York, Vol. 67, pp. 359–364.
Mehra, R. K., Boskovic, J. D., and Li, S., 2000, “Autonomous Formation Flying of Multiple UCAVs Under Communication Failure,” Position Locations and Navigation Symposium, IEEE, New York, pp. 371–378.
Giulietti,  F., Pollini,  L., and Innocenti,  M., 2000, “Autonomous Formation Flight,” IEEE Control Syst. Mag., 20(6), pp. 34–44.
Pachter,  M., D’Azzo,  J. J., and Proud,  A. W., 2001, “Tight Formation Flight Control,” J. Guid. Control Dyn., 24(2), pp. 246–254.
Chichka,  D. F., and Speyer,  J. L., “Peak-Seeking Control for Drag Reduction in Formation Flight,” J. Guid. Control Dyn., (submitted).
Fowler, J. M., and D’Andrea, R., 2002, “Distributed Control of Close Formation Flight,” Proc. of 41st IEEE Conference on Decision and Control, IEEE, New York, pp. 2972–2977.
Banda, S., Doyle, J., Murray, R., Paduano, J., Speyer, J., and Stein, G., 1997, “Research Needs in Dynamics and Control for Uninhabited Aerial Vehicles,” Panel Report, http://www.cds.caltech.edu/murray/notes/uav-nov97.html
Swaroop,  D., and Hedrick,  J. K., 1996, “String Stability of Interconnected Systems,” IEEE Trans. Autom. Control, 41(4), pp. 349–356.
Swaroop,  D., and Hedrick,  J. K., 1999, “Constant Spacing Strategies for Platooning in Automated Highway Systems,” ASME J. Dyn. Syst., Meas., Control, 121, pp. 462–470.
Tanner, H., and Pappas, G. J., 2002, “Formation Input-to-State Stability,” Proc. of 15th IFAC World Congress, July.
Skogestad, S., and Postlethwaite, I., 1996, Multivariable Feedback Control: Analysis and Design, Wiley, New York, pp. 127–137.
Middleton, R. H., and Goodwin, G. C., 1990, “Digital Control and Estimation: A Unified Approach,” Prentice Hall, Englewood Cliffs, NJ, pp. 423–433.
Looze, D. P., and Freudenberg, J. S., 1996, “Tradeoffs and Limitations in Feedback Systems,” The Control Handbook, W. S. Levine, ed., CRC Press, Boca Raton, Chap. 31, pp. 537–549.
Chen, J., 1998, “On Logarithmic Complementary Sensitivity Integrals for MIMO Systems,” Proc. of American Control Conference, IEEE, Philadelphia, pp. 3529–3530.
Chen,  J., 2000, “Logarithmic Integrals, Interpolation Bounds, and Performance Limitations in MIMO Feedback Systems,” IEEE Trans. Autom. Control, 45(6), pp. 1098–1115.
Boyd,  S., and Desoer,  C. A., 1985, “Subharmonic Functions and Performance Bounds on Linear Time-Invariant Feedback Systems,” IMA J. Math. Control Inf., 2, pp. 153–170.
Royden, H. L., 1988, Real Analysis, MacMillan, London, p. 87.
Shim, H., 2000, “Hierarchical Flight Control System Synthesis for Rotorcraft-Based Unmanned Aerial Vehicles,” Ph.D. thesis, University of California at Berkeley.
Mettler,  B., Tischler,  M. B., and Kanade,  T., 2002, “System Identification Modeling of a Small-Scale Unmanned Rotorcraft for Flight Control Design,” J. Am. Helicopter Soc., Vol. 47, pp. 50–63.
Seiler, P., 2001, “Coordinated Control of Unmanned Aerial Vehicles,” Ph.D. thesis, University of California, Berkeley.


Grahic Jump Location
Feedback block diagram for helicopter and controller
Grahic Jump Location
Time domain plots of reference tracking: Left: Control effort: Cyclic longitudinal input [δlon(t)]. Right: Reference [xd(t)] and Helicopter [x(t)] trajectories in the x direction.
Grahic Jump Location
Plots of ρ[T(jω)] vs ω. Peak is ρ[T(jω)]=1.77 achieved at ω0=1.15 rads/s. The eigenvector that achieves the spectral radius is (−0.08+0.32i;0.94;0.01−0.01i;0)T.
Grahic Jump Location
Time domain plots of predecessor following control law: Left: Cyclic longitudinal control input δlon(t) for vehicles 1,[[ellipsis]],4; Right: spacing errors in the x direction for vehicles 1,[[ellipsis]],4
Grahic Jump Location
Block diagram for tight formation flight



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