# 3-Dimensional Path Planning and Guidance using the Dubins Curve for an 3-DOF Point-mass Aircraft Model

• 오수헌 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
• 하철수 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
• 강승은 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
• 목지현 (한국항공대학교 대학원 항공우주 및 기계공학과) ;
• 고상호 (한국항공대학교 항공우주 및 기계공학과) ;
• 이용원 (리얼타임비쥬얼 기술연구소)
• 투고 : 2015.10.06
• 심사 : 2016.03.25
• 발행 : 2016.03.31

#### 초록

In this paper, we integrate three degree of freedom(3DOF) point-mass model for aircraft and three-dimensional path generation algorithms using dubins curve and nonlinear path tracking law. Through this integration, we apply the path generation algorithm to the path planning, and verify tracking performance and feasibility of using the aircraft 3DOF point-mass model for air traffic management. The accuracy of modeling 6DOF aircraft is more accurate than that of 3DOF model, but the complexity of the calculation would be raised, in turn the rate of computation is more likely to be slow due to the increase of degree of freedom. These obstacles make the 6DOF model difficult to be applied to simulation requiring real-time path planning. Therefore, the 3DOF point-mass model is also sufficient for simulation, and real-time path planning is possible because complexity can be reduced, compared to those of the 6DOF. Dubins curve used for generating the optimal path has advantage of being directly available to apply path planning. However, we use the algorithm which extends 2D path to 3D path since dubins curve handles the two dimensional path problems. Control law for the path tracking uses the nonlinear path tracking laws. Then we present these concomitant simulation results.

#### 과제정보

연구 과제 주관 기관 : 국방과학연구소

#### 참고문헌

1. D. Delahaye, S. Puechmorel, P. Tsiotras and E. Feron, " Mathematical models for aircraft trajectory design : A survey," 3rd ENRI International Workshop on ATM/CNS, Tokyo, Japan, 2013.
2. L. E. Dubins, "On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal position and tangents," American Journal of mathematics, vol. 79, pp. 497-516, 1957. https://doi.org/10.2307/2372560
3. A. M. Shkel and V. Lumelsky, "Classification of the Dubins set," Robotics and Autonomous Systems, vol. 34, pp. 179-202, 2001. https://doi.org/10.1016/S0921-8890(00)00127-5
4. M. Shanmugavel, A. Tsourdos, R. Zbikowski and B. A. White, "3D dubins sets based coordinated path planning for swarm of UAVs," AIAA-2006-6211.
5. R. Hurley, R. Lind and J. Kehoe, "A mixed local-global solution to motion planning within 3-D environments," AIAA Guidance, Navigation and Control Conference, AIAA-2009-6297, 2009.
6. H. Chitsaz and S. M. LaValle, "On time-optimal paths for the dubins airplane," 2007 IEEE Conference on Decision and Control, pp. 2379-2384, 2007.
7. R. W. Beard and T. W. McLain, "Implementing Dubins airplane paths on fixed-wing UAV," Brigham Young University, July 2013.
8. G. Ambrosino, M. Ariola, U. Ciniglio, F. Corraro, A. Pironti and M. Virgilio, "Algorithms for 3D UAV path generation and tracking," Proceedings of the 45th IEEE conference on Design and Control, pp. 5275-5280, 2006.
9. M. Hwangbo, J. Kuffner, and T. Kanade, "Efficient two-phase 3D motion planning for small fixed-wing UAVs," 2007 IEEE International Conference on Robotics an Automation, Roma, Italy, pp. 1035-1041, April 2007.
10. K. Y. Luo and A. E. Bryson "Inverse and optimal control for precision aerobatic maneuvers," Journal of Guidance, Control, and Dynamics, vol. 19, no.2, pp. 483-488, March-April 1996. https://doi.org/10.2514/3.21643
11. M. R. Anderson and A. C. Robbins, "'Formation flight as a cooperative game," AIAA Guidance, Navigation, and Control Conference and Exhibit, paper no. 98-4124, pp. 244-251, 1998.
12. T. Kinosita and F. Imado, "The application of an UAV flight simulator : The development of a new point mass model for an aircraft," SICE-ICASE, International Joint Conference 2006, pp. 4378-4383, 2006
13. J. G.H. Carretero, F. J. S. Nieto and R. R. Cordon, "Aircraft trajectory simulator using a three degrees of freedom aircraft point mass model," Air Navigation Research Group, Polytechnic University of Madrid, Madrid, Spain
14. I. W. Kim, D. H. Kim, and S. J. Yoon, "Flight trajectory generation of air traffic simulation and verification using X-Plane," Korean Society for Aeronautical and Space Sciences fall conference 2014, pp. 1434-1437, Nov 2014.
15. Eun-Mi Oh, Yeonju Eun and Dae Keun Jeon, "Development of 4-D Trajectory Modeling using BADA", Journal of the Korean Society for Aviation and Aeronautics, vol. 20, no .2, pp.1-6, Jun 2012. https://doi.org/10.12985/ksaa.2012.20.2.001
16. S. H. Park, "Autonomous aerobatic flight for fixed wing aircraft," Journal of Korean Society for Aeronautical and Space Sciences, vol. 37, no. 12, pp. 1217-1224, Dec 2009. https://doi.org/10.5139/JKSAS.2009.37.12.1217
17. S. H. Park, J. Deyst, and J. P. How, "Performance and Lyapunov stability of a nolinear path-following guidance method," Journal of Guidance, Control, and Dynamics, vol. 30, no. 6, pp. 1718-1728, Nov-Dec 2007. https://doi.org/10.2514/1.28957
18. R. C. Nelson, Flight Stability and Automatic Control, MCGraw-Hill, New York, 1989.
19. N. X. Vinh, Optimal Trajectories in Atmospheric Flight, Elsevier scientific publishing company, Amsterdam, Oxford, New York, 1981.