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
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
R.W. Beard, T.W. McLain, Small Unmanned Aircraft: Theory and Practice (Princeton University Press, Princeton, 2012)
S. Brunke, M.E. Campbell, Square root sigma point filtering for real-time, nonlinear estimation. J. Guid. 27(2), 314–317 (2004)
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
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
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)
J. Egbert, R.W. Beard, Low-altitude road following using strap-down cameras on miniature air vehicles. Mechatronics 21(5), 831–843 (2011)
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
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
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
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
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)
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
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
S. Karaman, E. Frazzoli, Incremental sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 June 2011
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)
F. L. Lewis, Optimal Control (Wiley, New York, 1986)
R. Mahony, T. Hamel, J.-M. Pflimlin, Nonlinear complementary filters on special orthogonal group. IEEE Trans. Autom. Control 53(5), 1203–1218 (2008)
E. A. Misawa, J.K. Hedrick, Nonlinear observers – state-of-the-art survey. Trans. ASME J. Dyn. Syst. Meas. Control 111, 344–352 (1989)
R.C. Nelson, Flight Stability and Automatic Control, 2nd edn. (McGraw-Hill, Boston, 1998)
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)
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)
W.F. Phillips, Mechanics of Flight, 2nd ed. (Wiley, Hoboken, 2010)
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
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
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)
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
B. L. Stevens, F.L. Lewis, Aircraft Control and Simulation, 2nd ed. (Wiley, Hoboken, 2003)
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
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
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)
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
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)
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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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DOI: https://doi.org/10.1007/978-90-481-9707-1_120
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