Abstract
This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.
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References
Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. American Journal of Mathematics 79, 497–516 (1957)
Reeds, J.A., Shepp, L.A.: Optimal paths for a car that goes both forwards and backwards. Pacific Journal of Mathematics 145, 367–393 (1990)
Boissonnat, J.D., Cerezo, A., Leblond, J.: Shortest paths of bounded curvature constraints. Journal of Intelligent and Robotic Systems 11(1-2), 5–20 (1994)
Hota, S., Ghose, D.: Optimal path planning for a miniature air vehicle using a modified Dubins method. In: UKIERI Workshop on Robust Control of Smart Autonomous Unmanned Air Vehicle, IISc, Bangalore, August 22-23, pp. 64–71 (2008)
Hota, S., Ghose, D.: A modified Dubins method for optimal path planning of a miniature air vehicle converging to a straight line path. In: Proc. of the American Control Conference, St. Louis, Missouri, USA, June 10-12, pp. 2397–2402 (2009)
Hota, S., Ghose, D.: Optimal rectilinear path convergence of a Miniature Air Vehicle using Pontryagin’s Maximum Principle. In: Proc. of the International Conference and Exhibition on Aerospace Engineering, IISc, Bangalore, India, May 19-22 (2009)
McGee, T., Spry, S., Hedrick, K.: Optimal path planning in a constant wind with a bounded turning rate. In: Proc. of the AIAA Guidance, Navigation and Control Conference and Exhibit, San Francisco, CA (August 2005)
Nelson, D.R., Barber, D.B., Mclain, T.W., Beard, R.W.: Vector field path following for miniature air vehicle. IEEE Trans. on Robotics 23(3) (June 2007)
Chitsaz, H., LaValle, S.M.: Time-optimal paths for a Dubins airplane. In: Proc. of the 46th IEEE Conf. on Decision and Control, New Orleans, LA, USA, December 12-14 (2007)
Ambrosino, G., Ariola, M., Ciniglio, U., Corraro, F., Lellis, E.D., Pironti, A.: Path generation and tracking in 3-D for UAVs. IEEE Trans. on Control Systems Technology 17(4) (July 2009)
Shanmugavel, M., Tsourdos, A., Zbikowski, R., White, B.A.: 3D Dubins sets based coordinated path planning for swarm of UAVs. In: AIAA Guidance, Navigation, and Control Conf. and Exhibit, Keystone, Colorado, August 21 - 24 (2006)
Sussmann, H.J.: Shortest 3-dimensional paths with a prescribed curvature bound. In: 34th IEEE Conf. on Decision and Control, New Orleans, pp. 3306–3312 (1995)
Bestaoui, Y., Dicheva, S.: 3D flight plan for an autonomous aircraft. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, January 4 - 7 (2010)
Shanmugavel, M., Tsourdos, A., Zbikowski, R., White, B.A.: 3D path planning for multiple UAVs using Pythagorean Hodograph curves. In: AIAA Guidance, Navigation and Control Conf. and Exhibit, Hilton Head, South Carolina, August 20 - 23 (2007)
Betts, J.T.: Practical methods for optimal control using nonlinear programming. The Society for Industrial and Applied Mathematics, Philadelphia (2001)
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Hota, S., Ghose, D. (2010). Rectilinear Path Following in 3D Space. In: Vadakkepat, P., et al. Trends in Intelligent Robotics. FIRA 2010. Communications in Computer and Information Science, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15810-0_27
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DOI: https://doi.org/10.1007/978-3-642-15810-0_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15809-4
Online ISBN: 978-3-642-15810-0
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