Abstract
The problem of managing swarms of UAVs consists of multi-agent collection (i.e., distributed robust data fusion and interpretation) and multi-agent coordination (i.e., distributed robust platform and sensor monitoring and control). These two processes should be feedback-connected in order to improve the over-all quality of data be collected on suitable targets. This paper summarizes work proposed by Lockheed Martin Tactical Systems (LMTS) of Eagan MN and its subcontractor Scientific Systems Co., Inc. (SSCI) of Woburn MA, under contract F49620-01-C-0031 of the AFOSR Cooperative Control Theme 2. LMTS and SSCI have proposed to (1) develop a mathematical programming framework for hybrid systems analysis and synthesis, (2) develop a computational hybrid control paradigm, (3) develop transition-aware anytime algorithms for time-bounded synthesis, and (4) develop suitable modeling and cooperative control of UAV swarms for a SEAD-type mission. Regarding multi-agent collection, LMTS and SSCI will (4) develop new theoretical approaches for integrating multiplatform, multisensor, multitarget sensor management into hybrid systems theory; (5) investigate real-time nonlinear filtering for detecting and tracking low-observable targets; (6) develop new approaches to distributed, robust data fusion; and (7) develop a language for Multi-Agent Coordination broad enough to encompass Bayesian, Dempster-Shafer, and fuzzy-logic inference. The basis of our approach is twofold: (a) a novel hybrid-systems control architecture that integrates the best of the current approaches; and (b) a new foundation for multisensor-multitarget problems called “finite-set statistics.” Our approach integrates theoretically rigorous statistics (hybrid control, point process theory) with potential practicability (computational hybrid control, computational nonlinear filtering).
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References
D.J. Ballantyne, H.Y. Chan, and M.A. Kouritzin, “A novel branching particle method for tracking”, SPIE Proc, 4048: 277–287, 2000.
M. Bardin, “Multidimensional Point Processes and Random Closed Sets”, J. Applied Prob., 21: 173–178, 1984.
Y. Bar-Shalom and X.-R. Li, Estimation and Tracking: Principles, Techniques, and Software, Artech House, 1993.
R. W. Beard and F. Y. Hadaegh, “Constellation templates: An approach to autonomous formation flying”, World Automation Congress, pages 177.1–177.6, Anchorage, Alaska, May 1998.
R. W. Beard, J. Lawton, and F. Y Hadaegh, “A feedback architecture for formation control”, Proc. Amer. Control Confi, pp. 4087–4091, Chicago, IL., June 2000.
A. Bemporad and M. Morari, “Control of systems integrating logic, dynamics and constraints”, Automatica, 35, 1999.
V.E. Beneš, “Exact finite-dimensional filters for certain diffusions with nonlinear drift”, Stochastics, 5: 65–92, 1981.
R.E. Bethel and G.J. Paras, “A PDF multitarget-tracker”, IEEE Trans AES, 30: 386–403, 1994.
P.J. Bickel and D. A. Feedman, “Some asymptotic theory for the bootstrap”, Annals of Statistics, 9: 1196–1217, 1981.
V. Borkar, V. Chandru and S. Mitter, “Mathematical programming embeddings of logic”, Preprint, 2000.
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, 1994.
M. Branicky, Studies in Hybrid Systems: Modeling, Analysis and Control, Ph.D dissertation, MIT, June, 1995.
T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, MIT Press, 1990.
D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer-Verlag, 1988.
F. Daum, “Exact finite dimensional nonlinear filters for continuous time processes with discrete time measurements”, in Proc. IEEE Conf. Dec. and Contr., pp. 16–22, 1984.
N. Elia and B. Brandin, “Verification of an automotive active leveler”, Proc. American Cont. Conf, pp. 2476–2480, 1999.
M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Linéarisation par bouclage dynamique et transformations de lie-bäcklun”, D.R. Acad. Sci. Paris, t. 317, Serie I, pp. 981–986, 1993
W. Gangbo and R.J. McCann, “Shape recognition via Wasserstein Distance”, Quarterly of Applied Math., Vol LVIII No. 4: 705–737, 2000.
M. Gelbrich, “On a formula for the L 2 Wasserstein Metric between measures on Euclidean and Hilbert Spaces”, Math. Nachr., 147: 185–203, 1990.
CR. Givens and R.M. Shortt, “A class of Wasserstein Metrics for probability distributions”, Michigan Math. J., 31: 231–240, 1984.
LR. Goodman, R.P.S. Mahler, and H.T. Nguyen, Mathematics of Data Fusion, Kluwer Academic Publishers, 1997.
Y.C. Ho and R.C.K. Lee, “A Bayesian approach to problems in stochastic estimation and control”, IEEE Trans. AC, AC-9: 333–339, 1964.
H.J. Hooker, Logic-based methods for optimization: Combining optimization and constraint satisfaction, Wiley, 2000.
A.H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970.
V. Kapila, A. G. Sparks, J. M. Buffington, and Q. Yan, “Spacecraft formation flying: Dynamics and control”, J. Guidance, Control, and Dynamics, 23:561–564, 2000.
V. Klee and C. Witzgall, “Facets and vertices of transportation poly–topes”, Mathematics of the Decision Sciences, Part I, American Mathematical Society, pp. 257–282, 1968.
M.A. Kouritzin, “On exact filters for continuous signals with discrete observations”, IEEE Trans. Auto. Control, 43: 709–71, 1998.
R. Kruse, E. Schwencke, and J. Heinsohn, Uncertainty and Vagueness in Knowledge-Based Systems, Springer-Verlag, 1991.
J. Lawton, Multiple Spacecraft Elementary Formation Maneuvers, PhD thesis, Brigham Young University, Provo, UT 84602, 2000.
J. Lawton, B. Young, and R. Beard, “A decentralized approach to elementary formation maneuvers”, IEEE Trans. Robotics and Automation, to appear.
E. Levina and P. Bickel, “The Earth Mover’s Distance is the Mallow’s Distance: Some Insights From Statistics”, Proc. IEEE 8th Int’l Conf. on Computer Vision, Vol. II: 251–256, July 9–12 2001.
M.A. Lewis and K.-H. Tan, “High precision formation control of mobile robots using virtual structures”, Autonomous Robots, 4: 387–403, 1997.
S.–M. Li, J. D. Boskovic, and R. K. Mehra, “Globally stable automatic formation flight control in two dimensions”, 2007 AIAA Guidance, Navigation, and Control Conf., 2001.
J. Lygeros, C. Tomlin, S. Sastry, “Controller for reachability specifications for hybrid systems”, Automatica, March 1999.
R. Mahler, “Approximate multi–sensor, multi–target detection, tracking, and target identification using a multitarget first–order moment statistic”, submitted to IEEE Trans. AES, 2001.
R. Mahler, An Introduction to Multisource–Multitarget Statistics and Its Applications, Lockheed Martin Technical Monograph, 104 pages, 2000.
R. Mahler (2001) “Multitarget moments and their application to multi–target tracking”, Proc. Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar–Shalom, May 17, 2001, Naval Postgraduate School, Monterey CA, pp. 134–166, ISBN 0–9648–3124–4
R. Mahler (1996) “Representing Rules as Random Sets, I: Statistical Correlations Between Rules”, Information Sciences, Vol. 88, pp. 47–68
R. Mahler (1996) “Representing Rules as Random Sets, II: Iterated Rules”, Int’ Jour. Intelligent Sys., Vol. 11, pp. 583–610
R. Mahler, “Random set theory for target tracking and identification”, in D.L. Hall and J. Llinas (eds.), Handbook of Multisensor Data Fusion, CRC Press, Boca Raton FL, pp. 14–1 to 14–133, 2001.
R. Mahler, “A theoretical foundation for the Stein–Winter ‘Probability Hypothesis Density (PHD)’ multitarget tracking approach”, Proc. 2000 MSS Nat’l Symp. on Sensor and Data Fusion, Vol. I (Unclassified), San Antonio TX, Infrared Information Analysis Center, pp. 99–118, 2000.
G. Mathéron, Random Sets and Integral Geometry, J. Wiley, 1975.
C.R. McInnes, “Autonomous ring formation for a planar constellation of satellites”, J. of Guidance, Control and Dynamics, 18: 1215–1217, 1995.
T. McLain and R. Beard, “Cooperative rendezvous of multiple unmanned air vehicles”, Proc. AIAA Guidance, Navigation and Control Confi, Denver, CO, August 2000.
J.E. Moyal, “The general theory of stochastic population processes”, Acta Mathematica, 108: 1–31, 1962.
S. Musick, K. Kastella, and R. Mahler, “A practical implementation of joint multitarget probabilities”, SPIE Proc, 3374: 26–37, 1998.
N. Portenko, H. Salehi, and A. Skorokhod, “On optimal filtering of multi–target tracking systems based on point processes observations”, Random Operators and Stochastic Equations, 1: 1–34, 1997.
A. W. Proud, M. Pachter, and J. J. D’Azzo, “Close formation flight control”, AIAA Guidance, Navigation, and Control Confi, pp. 1231–1246, Portland, OR, August 1999.
B.D. Ripley, “Locally finite random sets: foundations for point process theory”, Annals of Prob., 4: 983–994, 1976.
P. Rouchon, M. Fliess, J. Lévine, and Ph. Martin, “Flatness, motion planning and trailer systems”, Proc. IEEE Control and Decision Confi, pp. 2700–2705, 1993.
O. Shakernia, G. Pappas and S. Sastry, “Decidable controller synthesis for classes of linear systems”, Hybrid Systems, 1999.
S. Sheikholeslam and C. A. Desoer, “Control of interconnected nonlinear dynamical systems: The platoon problem”, IEEE Trans. Auto. Control, 37: 806–810, 1992.
D.L. Snyder and M.I. Miller, Random Point Processes in Time and Space, Second Edition, Springer, 1991.
H.W. Sorenson, “Recursive estimation for nonlinear dynamic systems”, in J.C. Spall, editor, Bayesian Analysis of Statisical Time Series and Dynamic Models, Marcel Dekker, 1988.
H.W. Sorenson and D.L. Alspach, “Recursive Bayesian Estimation Using Gaussian Sums”, Automatica, 7: 465–479, 1971.
A. Srivastava, M.I. Miller, and U. Grenander, “Jump–diffusion processes for object tracking and direction finding”, Proc. 29th Allerton Confi on Communication, Control, and Computing, U. of Illinois Urbana, pp. 563–570, 1991.
C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, 1989.
L.D. Stone, CA. Barlow, and T.L. Corwin, Bayesian Multiple Target Tracking, Artech House, 1999.
D. Stoyan, W.S. Kendall, and J. Meche, Stochastic Geometry audits Applications, Second Edition, John Wiley & Sons, 1995.
X. Yun, G. Alptekin, and O. Albayrak, “Line and circle formation of distributed physical mobile robots”, J. Robotic Systems, 14: 63–76, 1997.
E.L. Wahspress, Iterative Solution of Elliptic Systems and Application to the Neutron Diffusion Equations of Reactor Physics, Prentice–Hall, 1966.
P. K. C. Wang and F. Y. Hadaegh, “Coordination and control of multiple microspacecraft moving in formation”, J. Astronautical Sciences, 44: 315–355, 1996.
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Mahler, R., Prasanth, R. (2003). Technologies Leading to Unified Multi-Agent Collection and Coordination. In: Butenko, S., Murphey, R., Pardalos, P.M. (eds) Cooperative Control: Models, Applications and Algorithms. Cooperative Systems, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3758-5_11
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