Lyapunov and Minimum-Time Path Planning for Drones

详细信息    查看全文

• 作者：Thibault Maillot (1)
  Ugo Boscain (2) (3)
  Jean-Paul Gauthier (1) (3)
  Ulysse Serres (4)
  
  1. Universit茅 de Toulon ; LSIS ; UMR CNRS 7296 ; B.P 20132 ; 83957 ; La Garde Cedex ; France
  2. CNRS ; Centre de Math茅matiques Appliqu茅es - Ecole Polytechnique (CMAP) ; UMR CNRS 7641 ; Route de Saclay ; 91128 ; Palaiseau Cedex ; France
  3. INRIA GECO Project ; La Garde Cedex ; France
  4. Universit茅 Claude Bernard Lyon 1 ; LAGEP ; UMR CNRS 5007 ; 43 bd du 11 novembre 1918 ; 69100 ; Villeurbanne ; France
  
• 关键词：Optimal control ; Path planning ; Aircraft navigation ; Unmanned aerial vehicles ; Rigid ; body dynamics ; Under ; actuated systems ; Nonlinear control ; Trajectory tracking ; 93D15 ; 49J15 ; 34H05
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：21
• 期：1
• 页码：47-80
• 全文大小：3,276 KB
• 参考文献：1. Agrachev A A, Sachkov YL. Control theory from the geometric viewpoint, Vol. 87. Encyclopaedia of mathematical sciences. Control theory and optimization, II. Berlin: Springer; 2004.
  2. Agrachev A A, Sigalotti M. On the local structure of optimal trajectories in R ³. SIAM J Control Optim. 2003;42(2):513鈥?31. electronic. 10.1137/S0363012902409246" target="_blank" title="It opens in new window">CrossRef
  3. Ajami A, Maillot T, Boizot N, Balmat J-F, Gauthier J-P. Simulation of a uav ground control station. In: Proceedings of the 9th international conference of modeling and simulation, MOSIM鈥?2, 2012. Bordeaux, France, 6鈥? June.
  4. Ariyur K, Fregene K. Autonomous tracking of a ground vehicle by a UAV. In: American control conference; 2008. p. 669 鈥?71.
  5. Bertuccelli L, Wu A, How J. Robust adaptive Markov decision processes: planning with model uncertainty. IEEE Control Syst. 2012;32(5):96鈥?09. 10.1109/MCS.2012.2205478" target="_blank" title="It opens in new window">CrossRef
  6. Besan莽on G (ed). Nonlinear observers and applications, Vol. 363. Lecture notes in control and information sciences. Papers from the 28th international summer school on control held in Grenoble, September 2007. Berlin: Springer; 2007.
  7. Bhatia A, Graziano M, Karaman S, Naldi R, Frazzoli E. Dubins trajectory tracking using commercial off-the-shelf autopilots. In: AIAA guidance, navigation, and control conference. Honolulu, Hawaii; 2008.
  8. Boissonnat J-D, Cerezo A, Leblond J. Shortest paths of bounded curvature in the plane. In: Proceedings 1992 IEEE international conference on robotics and automation; 1992. vol. 3, p. 2315鈥?320.
  9. Boizot N, Gauthier J. Motion planning for kinematic systems. IEEE Trans Autom Control. 2013;58(6):1430鈥?442. 10.1109/TAC.2012.2232376" target="_blank" title="It opens in new window">CrossRef
  10. Bonnard B, Jurdjevic V, Kupka I, Sallet G. Transitivity of families of invariant vector fields on the semidirect products of Lie groups. Trans Amer Math Soc. 1982;271(2):525鈥?35. 10.1090/S0002-9947-1982-0654849-4" target="_blank" title="It opens in new window">CrossRef
  11. Boscain U, Chitour Y. Time-optimal synthesis for left-invariant control systems on / S / O(3). SIAM J Control Optim. 2005;44(1):111鈥?39 . (electronic). 10.1137/S0363012904441532" target="_blank" title="It opens in new window">CrossRef
  12. Boscain U, Piccoli B. Extremal synthesis for generic planar systems. J Dyn Control Syst. 2001;7(2):209鈥?58. 10.1023/A:1013003204923" target="_blank" title="It opens in new window">CrossRef
  13. Boscain U, Piccoli B. Optimal syntheses for control systems on 2-D manifolds, Vol. 43. Math茅matiques and applications. Berlin: Springer; 2004.
  14. Bressan A, Piccoli B. A generic classification of time-optimal planar stabilizing feedbacks. SIAM J Control Optim. 1998;36(1):12鈥?2. (electronic). 10.1137/S0363012995291117" target="_blank" title="It opens in new window">CrossRef
  15. Bui X-N, Boissonnat J-d, Soueres P, Laumond J-P. Shortest path synthesis for Dubins non-holonomic robot. In: 1994 IEEE international conference on robotics and automation, Proceedings;1994. vol. 1 p. 2鈥?.
  16. Bui X-N, Soueres P, Boissonnat J-D, Laumond J-P. The shortest path synthesis for non-holonomic robots moving forwards. Rapport de recherche RR-2153. Nice: INRIA; 1994.
  17. Bullo F, Lewis A D. Geometric control of mechanical systems, Vol. 49. Texts in Applied Mathematics. Modeling, analysis, and design for simple mechanical control systems. New York: Springer; 2005.
  18. Campolo D, Schenato L, Guglielmelli E, Sastry S. A Lyapunov-based approach for the control of biomimetic robotic systems with periodic forcing inputs. In: Proceedings of 16th IFAC World congress on automatic control (IFAC05); 2005.
  19. Chen H, Chang K, Agate CS. Tracking with UAV using tangent-plus-Lyapunov vector field guidance. In: 12th International conference on information fusion. FUSION 鈥?9; 2009. p. 363鈥?72.
  20. Chitour Y, Sigalotti M. Dubins鈥?problem on surfaces. I. Nonnegative curvature. J Geom Anal. 2005;15(4):565鈥?87. 10.1007/BF02922245" target="_blank" title="It opens in new window">CrossRef
  21. Chitsaz H, LaValle S. Time-optimal paths for a Dubins airplane. In: 46th IEEE conference on decision and control; 2007. p. 2379鈥?384.
  22. Cichella V, Kaminer I, Dobrokhodov V, Xargay E, Hovakimyan N, Pascoal A. Geometric 3D path-following control for a fixed-wing UAV on SO(3). In: AIAA guidance, navigation, and control conference. American Institute of Aeronautics and Astronautics, 2013/05/02; 2011.
  23. Dimarogonas D V, Loizou S G, Kyriakopoulos K J, Zavlanos M M. A feedback stabilization and collision avoidance scheme for multiple independent non-point agents. Automatica 2006;42(2):229鈥?43. 10.1016/j.automatica.2005.09.019" target="_blank" title="It opens in new window">CrossRef
  24. Ding X, Rahmani A, Egerstedt M. Multi-UAV convoy protection: an optimal approach to path planning and coordination. IEEE Trans Robot. 2010;26(2):256鈥?68. 10.1109/TRO.2010.2042325" target="_blank" title="It opens in new window">CrossRef
  25. Dubins L E. On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Amer J Math. 1957; 79:497鈥?16. 10.2307/2372560" target="_blank" title="It opens in new window">CrossRef
  26. Frew E, Lawrence D, Dixon C, Elston J, Pisano W. Lyapunov guidance vector fields for unmanned aircraft applications. In: American Control Conference. ACC鈥?7; 2007. p. 371鈥?76.
  27. Frew E, McGee T, Kim Z, Xiao X, Jackson S, Morimoto M, Rathinam S, Padial J, Sengupta R. Vision-based road-following using a small autonomous aircraft. In: Aerospace conference. Proceedings. 2004 IEEE; 2004. vol. 5, p. 3006鈥?015.
  28. Frew E W, Lawrence DA, Morris S. Coordinated standoff tracking of moving targets using Lyapunov guidance vector fields. J Guid Control Dyn. 2008;31(2):290鈥?06. 2013/02/21. 10.2514/1.30507" target="_blank" title="It opens in new window">CrossRef
  29. Gauthier J-P, Kupka I. Deterministic observation theory and applications. Cambridge: Cambridge University Press; 2001. 10.1017/CBO9780511546648" target="_blank" title="It opens in new window">CrossRef
  30. Gauthier J-P, Zakalyukin V. On the one-step-bracket-generating motion planning problem. J Dyn Control Syst. 2005;11(2):215鈥?35. 10.1007/s10883-005-4171-0" target="_blank" title="It opens in new window">CrossRef
  31. Goerzen C, Kong Z, Mettler B. A survey of motion planning algorithms from the perspective of autonomous UAV guidance. J Intell Robot Syst. 2010;57(1鈥?):65鈥?00. 10.1007/s10846-009-9383-1" target="_blank" title="It opens in new window">CrossRef
  32. Hua M-D, Hamel T, Morin P, Samson C. A control approach for thrust-propelled underactuated vehicles and its application to VTOL drones. IEEE Trans Autom Control 2009;54(8):1837鈥?853. 10.1109/TAC.2009.2024569" target="_blank" title="It opens in new window">CrossRef
  33. Kokkeby K L, Lutter R P, Munoz M L, Cathey F W, Hilliard J D, Olson T L. System and methods for autonomous tracking and surveillance, Vol. 06;2009.
  34. LaSalle J. Stability theory for ordinary differential equations. J Diff Equ. 1968;4(1):57鈥?5. 10.1016/0022-0396(68)90048-X" target="_blank" title="It opens in new window">CrossRef
  35. Laumond J-P (ed). Robot motion planning and control, Vol. 229. Lecture notes in control and information sciences. London: Springer; 1998. http://www.laas.fr/~jpl/book.html.
  36. Lawrence D, Frew E, Pisano W. Lyapunov vector fields for autonomous UAV flight control. In: AIAA guidance, navigation and control conference and exhibit. American Institute of Aeronautics and Astronautics, 2013/02/21;2007.
  37. Lee J, Huang R, Vaughn A, Xiao X, Hedrick J K, Zennaro M, Sengupta R. Strategies of path-planning for a UAV to track a ground vehicle. AINS Conference; 2003.
  38. Park S, Deyst J, How JP. A new nonlinear guidance logic for trajectory tracking. In: AIAA guidance, navigation, and control conference and exhibit. American Institute of Aeronautics and Astronautics; 2004.
  39. Piccoli B. Classification of generic singularities for the planar time-optimal synthesis. SIAM J Control Optim. 1996;34(6):1914鈥?946. 10.1137/S0363012993256149" target="_blank" title="It opens in new window">CrossRef
  40. Piccoli B, Sussmann H J. Regular synthesis and sufficiency conditions for optimality. SIAM J Control Optim. 2000;39(2):359鈥?10. (electronic). 10.1137/S0363012999322031" target="_blank" title="It opens in new window">CrossRef
  41. Pr茅vost C G, Desbiens A, Gagnon D, Hodouin E. UAV optimal cooperative target tracking and collision avoidance of moving objects, Vol. 17. In: Chung M, Jin, Misra, Pradeep, editors. The International Federation of Automatic Control; 2008, pp. 5724鈥?729.
  42. Rafi F, Khan S, Shafiq K, Shah M. Autonomous target following by unmanned aerial vehicles. Unmanned Syst Tech VIII. 2006;6230(1):623010. 10.1117/12.667356" target="_blank" title="It opens in new window">CrossRef
  43. Sachkov Y. Control theory on lie groups. J Math Sci. 2009;156:381鈥?39. 10.1007/s10958-008-9275-0" target="_blank" title="It opens in new window">CrossRef
  44. Sch盲ttler H. On the local structure of time-optimal bang-bang trajectories in / R ³. SIAM J Control Optim. 1988;26(1):186鈥?04. 10.1137/0326012" target="_blank" title="It opens in new window">CrossRef
  45. Sebesta K, Boizot N. A real-time adaptive high-gain EKF, applied to a quadcopter inertial navigation system. IEEE Trans Indus Elec. 2014;61(1):495鈥?03. 10.1109/TIE.2013.2253063" target="_blank" title="It opens in new window">CrossRef
  46. Sigalotti M, Chitour Y. Dubins鈥?problem on surfaces. II. Nonpositive curvature. SIAM J Control Optims 2006;45(2):457鈥?82. (electronic). 10.1137/040619739" target="_blank" title="It opens in new window">CrossRef
  47. Sou猫res P, Balluchi A, Bicchi A. Optimal feedback control for route tracking with a bounded-curvature vehicle. Int J Control. 2001;74(10):1009鈥?019. 10.1080/00207170110052211" target="_blank" title="It opens in new window">CrossRef
  48. Sussmann H J. Regular synthesis for time-optimal control of single-input real analytic systems in the plane. SIAM J Control Optim. 1987;25(5):1145鈥?162. 10.1137/0325062" target="_blank" title="It opens in new window">CrossRef
  49. Theodorakopoulos P, Lacroix S. A strategy for tracking a ground target with a UAV. In: IEEE/RSJ international conference on intelligent robots and systems. IROS; 2008. p. 1254鈥?259.
  50. Walsh G, Montgomery R, Sastry S. Optimal path planning on matrix lie groups. In: Proceedings of the 33rd IEEE conference on decision and control 1994. vol. 2, p. 1258鈥?263.
  51. Xargay E, Dobrokhodov V, Kaminer I, Pascoal A, Hovakimyan N, Cao C. Time-critical cooperative control of multiple autonomous vehicles: robust distributed strategies for path-following control and time-coordination over dynamic communications networks. IEEE Control Syst. 2012;32(5):49鈥?3. 10.1109/MCS.2012.2205477" target="_blank" title="It opens in new window">CrossRef
  52. Zhu S, Wang D, Low C. Ground target tracking using UAV with input constraints. J Intell Robot Syst. 2013;69:417鈥?29. 10.1007/s10846-012-9737-y" target="_blank" title="It opens in new window">CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

In this paper, we study the problem of controlling an unmanned aerial vehicle (UAV) to provide a target supervision and/or to provide convoy protection to ground vehicles. We first present a control strategy based upon a Lyapunov-LaSalle stabilization method to provide supervision of a stationary target. The UAV is expected to join a predesigned admissible circular trajectory around the target which is itself a fixed point in the space. Our strategy is presented for both high altitude long endurance (HALE) and medium altitude long endurance (MALE) types of UAVs. A UAV flying at a constant altitude (HALE type) is modeled as a Dubins vehicle (i.e., a planar vehicle with constrained turning radiusand constant forward velocity). For a UAV that might change its altitude (MALE type), we use the general kinematic model of a rigid body evolving in \(\mathbb {R}^{3}\) . Both control strategies presented are smooth, and unlike what is usually proposed in the literature, these strategies asymptotically track a circular trajectory of exact minimum turning radius. We also present the time-optimal control synthesis for tracking a circle by a Dubins vehicle. This optimal strategy is very rich, although much simpler than the point-to-point time-optimal strategy studied in the 1990s. Finally, we propose control strategies to provide supervision of a moving target, which are based upon theprevious ones.