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Implementing Dubins Airplane Paths on Fixed-Wing UAVs*

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Handbook of Unmanned Aerial Vehicles

Abstract

A well-known path-planning technique for mobile robots or planar aerial vehicles is to use Dubins paths, which are minimum-distance paths between two configurations subject to the constraints of the Dubins car model. An extension of this method to a three-dimensional Dubins airplane model has recently been proposed. This chapter builds on that work showing a complete architecture for implementing Dubins airplane paths on small fixed-wing UAVs. The existing Dubins airplane model is modified to be more consistent with the kinematics of a fixed-wing aircraft. The chapter then shows how a recently proposed vector-field method can be used to design a guidance law that causes the Dubins airplane model to follow straight-line and helical paths. Dubins airplane paths are more complicated than Dubins car paths because of the altitude component. Based on the difference between the altitude of the start and end configurations, Dubins airplane paths can be classified as low, medium, or high altitude gain. While for medium and high altitude gain there are many different Dubins airplane paths, this chapter proposes selecting the path that maximizes the average altitude throughout the maneuver. The proposed architecture is implemented on a six degree-of-freedom Matlab/Simulink simulation of an Aerosonde UAV, and results from this simulation demonstrate the effectiveness of the technique.

*Contributed Chapter to the Springer Handbook for Unmanned Aerial Vehicles

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References

  • R. Anderson, D. Milutinovic, A stochastic approach to Dubins feedback control for target tracking. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco, Sept 2011

    Google Scholar 

  • A. Balluchi, A. Bicchi, A. Balestrino, G. Casalino, Path tracking control for Dubins cars, in Proceedings of the International Conference on Robotics and Automation, Minneapolis, 1996, pp. 3123–3128

    Chapter  Google Scholar 

  • R.W. Beard, T.W. McLain, Small Unmanned Aircraft: Theory and Practice (Princeton University Press, Princeton, 2012)

    Google Scholar 

  • S. Brunke, M.E. Campbell, Square root sigma point filtering for real-time, nonlinear estimation. J. Guid. 27(2), 314–317 (2004)

    Article  Google Scholar 

  • H. Chitsaz, S.M. LaValle, Time-optimal paths for a Dubins airplane, in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Dec 2007, pp. 2379–2384

    Google Scholar 

  • R.V. Cowlagi, P. Tsiotras, Shortest distance problems in graphs using history-dependent transition costs with application to kinodynamic path planning, in Proceedings of the American Control Conference, St. Louis, June 2009, pp. 414–419

    Google Scholar 

  • L.E. Dubins, On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  • J. Egbert, R.W. Beard, Low-altitude road following using strap-down cameras on miniature air vehicles. Mechatronics 21(5), 831–843 (2011)

    Article  Google Scholar 

  • J. Elston, E.W. Frew, Hierarchical distributed control for search and track by heterogeneous aerial robot network, in Proceedings of the International Conference on Robotics and Automation, Pasadena, May 2008, pp. 170–175

    Google Scholar 

  • J. Elston, B. Argrow, A. Houston, E. Frew, Design and validation of a system for targeted observations of tornadic supercells using unmanned aircraft, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and System, Taipei, Oct 2010, pp. 101–106E

    Google Scholar 

  • E. Frew, T. McGee, Z. Kim, X. Xiao, S. Jackson, M. Morimoto, S. Rathinam, J. Padial, R. Sengupta, Vision-based road-following using a small autonomous aircraft, in 2004 IEEE Aerospace Conference Proceedings, Big Sky, Mar 2004, vol. 5, pp. 3006–3015

    Google Scholar 

  • E. W. Frew, C. Dixon, J. Elston, M. Stachura, Active sensing by unmanned aircraft systems in realistic communications environments, in Proceedings of the IFAC Workshop on Networked Robotics, Golden, Oct 2009

    Google Scholar 

  • V.M. Gonçalves, L.C.A. Pimenta, C.A. Maia, B.C.O. Durtra, G.A.S. Pereira, Vector fields for robot navigation along time-varying curves in n-dimensions. IEEE Trans. Robot. 26(4), 647–659 (2010)

    Article  Google Scholar 

  • C. Hanson, J. Richardson, A. Girard, Path planning of a Dubins vehicle for sequential target observation with ranged sensors, in Proceedings of the American Control Conference, San Francisco, June 2011, pp. 1698–1703

    Google Scholar 

  • S. Hosak, D. Ghose, Optimal geometrical path in 3D with curvature constraint, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 113–118, Taipei, Oct 2010

    Google Scholar 

  • S. Karaman, E. Frazzoli, Incremental sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 June 2011

    Article  Google Scholar 

  • D. A. Lawrence, E.W. Frew, W.J. Pisano, Lyapunov vector fields for autonomous unmanned aircraft flight control. AIAA J. Guid. Control Dyn. 31, 1220–12229 (2008)

    Google Scholar 

  • F. L. Lewis, Optimal Control (Wiley, New York, 1986)

    MATH  Google Scholar 

  • R. Mahony, T. Hamel, J.-M. Pflimlin, Nonlinear complementary filters on special orthogonal group. IEEE Trans. Autom. Control 53(5), 1203–1218 (2008)

    Article  MathSciNet  Google Scholar 

  • E. A. Misawa, J.K. Hedrick, Nonlinear observers – state-of-the-art survey. Trans. ASME J. Dyn. Syst. Meas. Control 111, 344–352 (1989)

    Article  MATH  Google Scholar 

  • R.C. Nelson, Flight Stability and Automatic Control, 2nd edn. (McGraw-Hill, Boston, 1998)

    Google Scholar 

  • D.R. Nelson, D.B. Barber, T.W. McLain, R.W. Beard, Vector field path following for miniature air vehicles. IEEE Trans. Robot. 37(3), 519–529, (2007)

    Article  Google Scholar 

  • S. Park, J. Deyst, J.P. How, Performance and Lyapunov stability of a nonlinear path-following guidance method. AIAA J. Guid. Control Dyn. 30(6), 1718–1728 (2007)

    Article  Google Scholar 

  • W.F. Phillips, Mechanics of Flight, 2nd ed. (Wiley, Hoboken, 2010)

    Google Scholar 

  • A. Rahmani, X.C. Ding, M. Egerstedt, Optimal motion primitives for multi-UAV convoy protection, in Proceedings of the International Conference on Robotics and Automation, Anchorage, May 2010, pp. 4469–4474

    Google Scholar 

  • S. Rathinam, Z. Kim, A. Soghikian, R. Sengupta, Vision based following of locally linear structure using an unmanned aerial vehicle, in Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, Seville, Dec 2005, pp. 6085–6090

    Chapter  Google Scholar 

  • T. Shima, S. Rasmussen, D. Gross, Assigning micro UAVs to task tours in an urban terrain. IEEE Trans. Control Syst. Technol. 15(4), 601–612 (2007)

    Article  Google Scholar 

  • S.C. Spry, A.R. Girard, J.K. Hedrick, Convoy protection using multiple unmanned aerial vehicles: organization and coordination, in Proceedings of the American Control Conference, Portland, June 2005, pp. 3524–3529

    Google Scholar 

  • B. L. Stevens, F.L. Lewis, Aircraft Control and Simulation, 2nd ed. (Wiley, Hoboken, 2003)

    Google Scholar 

  • P.B. Sujit, J.M. George, R.W. Beard, Multiple UAV coalition formation, in Proceedings of the American Control Conference, Seattle, June 2007, pp. 2010–2015

    Google Scholar 

  • G. Yang, V. Kapila, Optimal path planning for unmanned air vehicles with kinematic and tactical constraints, in Proceedings of the IEEE Conference on Decision and Control, Las Vegas, 2002, pp. 1301–1306

    Google Scholar 

  • T.R. Yechout, S.L. Morris, D.E. Bossert, W.F. Hallgren, Introduction to Aircraft Flight Mechanics. AIAA Education Series (American Institute of Aeronautics and Astronautics, Reston, 2003)

    Google Scholar 

  • C. Yong, E.J. Barth, Real-time dynamic path planning for Dubins’ nonholonomic robot, in Proceedings of the IEEE Conference on Decision and Control, San Diego, Dec 2006, pp. 2418–2423

    Chapter  Google Scholar 

  • H. Yu, R.W. Beard, A vision-based collision avoidance technique for micro air vehicles using local-level frame mapping and path planning. Auton. Robots 34(1–2), 93–109 (2013)

    Article  Google Scholar 

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Correspondence to Randal W. Beard or Timothy W. McLain .

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Owen, M., Beard, R.W., McLain, T.W. (2015). Implementing Dubins Airplane Paths on Fixed-Wing UAVs*. In: Valavanis, K., Vachtsevanos, G. (eds) Handbook of Unmanned Aerial Vehicles. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9707-1_120

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