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Reseach Article

On-Board Near Optimal Flight Trajectory Generation using Deferential Flatness

by R. Esmaelzadeh
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 89 - Number 3
Year of Publication: 2014
Authors: R. Esmaelzadeh
10.5120/15481-4219

R. Esmaelzadeh . On-Board Near Optimal Flight Trajectory Generation using Deferential Flatness. International Journal of Computer Applications. 89, 3 ( March 2014), 12-18. DOI=10.5120/15481-4219

@article{ 10.5120/15481-4219,
author = { R. Esmaelzadeh },
title = { On-Board Near Optimal Flight Trajectory Generation using Deferential Flatness },
journal = { International Journal of Computer Applications },
issue_date = { March 2014 },
volume = { 89 },
number = { 3 },
month = { March },
year = { 2014 },
issn = { 0975-8887 },
pages = { 12-18 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume89/number3/15481-4219/ },
doi = { 10.5120/15481-4219 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:08:17.395911+05:30
%A R. Esmaelzadeh
%T On-Board Near Optimal Flight Trajectory Generation using Deferential Flatness
%J International Journal of Computer Applications
%@ 0975-8887
%V 89
%N 3
%P 12-18
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

An optimal explicit guidance law that maximizes terminal velocity is developed for a reentry vehicle to a fixed target. The equations of motion are reduced with differential flatness approach and acceleration commands are related to trajectory's parameters. An optimal trajectory is determined by solving a real-coded genetic algorithm. For online trajectory generation, optimal trajectory is approximated. The approximated trajectory is compared with the pure proportional navigation, and genetic algorithm's solutions. The near optimal terminal velocity solution compares very well with these solutions. The approach robustness is examined by Monte Carlo simulation. Other advantages such as trajectory representation with minimum parameters, applicability to any reentry vehicle configuration and any control scheme, and Time-to-Go independency make this guidance approach more favorable.

References
  1. Eisler, G. R. and Hull, D. G. 1993. Guidance law for planar hypersonic descent to a point, J. of Guidance, Control, and Dynamics, V. 16, N. 2, 400-402.
  2. Eisler, G. R. and Hull, D. G. 1994. Guidance law for hypersonic descent to a point, Journal of Guidance, Control, and Dynamics, Vol. 17, No. 4, 649-54.
  3. Grä?lin, M. H. , Telaar J. , and Schottle U. M. 2004. Ascent and reentry guidance concept based on NLP-methods, Acta Astronautica, N. 55, 461-471.
  4. Shrivastava, S. K. , Bhat, M. S. , and Sinha, S. K. 1986. Closed-loop guidance of satellite launch vehicle- An overview, J. of the Institute of Engineers, N. 66, 62-76.
  5. Yakimenko, O. A. 2000. Direct method for rapid prototyping of near-optimal aircraft trajectories. J. of Guidance, Control, and Dynamics, V. 23, No. 5, 865-875.
  6. Lu, P. 1993. Inverse dynamics approach to trajectory optimization for an aerospace plane. J. of Guidance, Control and Dynamics, V. 16, No. 4, 726-731.
  7. Borri, M. , Bottasso, C. L. , and Montelaghi, F. 1997. Numerical approach to flight dynamics. J. of Guidance, Control, and Dynamics, V. 20, No. 4, 742-747.
  8. Kato, O. , Sugiura, I. 1986. An interpretation of airplane general motion and control as inverse problem. J. of Guidance, Control, and Dynamics, V. 9, No. 2, 198-204.
  9. Lane, S. H. , and Stengel, R. S. 1988. Flight control design using non-linear inverse dynamics. Automatica, V. 24, 471-483.
  10. Sentoh, E. , and Bryson, A. E. 1992. Inverse and optimal control for desired outputs. J. of Guidance, Control and Dynamics, V. 15, No. 3, 687-691.
  11. Hough, M. E. 1982. Explicit guidance along an optimal space curve. J. of Guidance, Control, and Dynamics, V. 12, No. 4, 495-504.
  12. Leng, G. 1998. Guidance algorithm design: a nonlinear inverse approach. J. of Guidance, Control, and Dynamics, V. 21, No. 5, 742-746.
  13. Lin, C. F. , and Tsai, L. L. 1987. Analytical solution of optimal trajectory-shaping guidance. J. of Guidance, Control, and Dynamics, V. 10, No. 1, 61-66.
  14. Sinha, S. K. , and Shrivastava, S. K. , 1990. Optimal explicit guidance of multistage launch vehicle along three-dimensional trajectory. J. of Guidance, Control and Dynamics, V. 13, No. 3, 394-403.
  15. Taranenko, V. T. , and Momdzhi, V. G. 1986. Direct Method of Modification in Flight Dynamic Problems, Moscow, Mashinostroenie Press (In Russian).
  16. Cameron, J. D. M. 1977. Explicit guidance equations for maneuvering re-entry vehicles. Proceedings of the IEEE Conference on Decision and Control, New York, USA: Inst. of Electrical and Electronics Engineers.
  17. Page, J. , and Rogers, R. 1977. Guidance and control of maneuvering reentry vehicles. Proceedings of the IEEE Conference on Decision and Control, New York, USA: Inst. of Electrical and Electronics Engineers.
  18. Mortazavi, M. 2000. Trajectory Determination Using Inverse Dynamics and Reentry Trajectory Optimization, PhD thesis, Moscow Aviation Institute.
  19. Esmaelzadeh R. , Naghash A. , Mortazavi M. 2008. Explicit Reentry Guidance Law Using Bezier Curves. Transactions of the Japan Society for Aeronautical and Space Sciences, N. 170, 225-230.
  20. Naghash, A. , Esmaelzadeh, R. , Mortazavi, M. , Jamilnia, R. 2008. Near Optimal Guidance Law for Descent to a Point Using Inverse Problem Approach. Aerospace Science and Technology, Vol. 12, No. 3, 241-247.
  21. Esmaelzadeh, R. , Naghash, A. , Mortazavi, M. 2008. Near optimal reentry guidance law using inverse problem approach. Journal of inverse problem in science and engineering, Vol. 16, No. 2, 187-198.
  22. Fliess M. , L´evine J. , Martin P. , Rouchon P. 1995. Flatness and defect of nonlinear systems: introduction theory and examples. Int. Journal of Control, No. 61.
  23. Zerar M. , Cazaurang F. , Zolghadri A. 2005. LPV Modeling of Atmospheric Re-entry Demonstrator for Guidance Reentry Problem. Proceedings of the 44th IEEE Conference on Decision and Control, Spain.
  24. Morio V. , Cazaurang F. , Vernis P. 2009. Flatness-based hypersonic reentry guidance of a lifting-body vehicle. Control Engineering Practice, No. 17, 588-596.
  25. Sira-Ramirez H. 1999. Soft Landing on a Planet: A Trajectory Planning Approach for the Liouvillian Model. Proceedings of the American Control Conference, USA.
  26. Sun L. G. W. , Zheng Z. 2009. Trajectory optimization for guided bombs based on differential flatness. Proceedings of the Chinese Control and Decision Conference.
  27. Neckel T. , Talbot C. , Petit N. 2003. Collocation and inversion for a reentry optimal control problem. Proceedings of the 5th International Conference on Launcher Tech.
  28. Archer, S. M. , and Sworder, D. D. 1979. Selection of the guidance variable for a re-entry vehicle. J. of Guidance, Control and Dynamics, Vol. 2, No. 2, 130-138.
  29. Judd K. B. , and McLain T. W. 2001. Spline based path planning for unmanned air vehicles. AIAA Guidance, Navigation, and Control Conf. & Exhibit, Canada.
  30. Shen Z. 2002. On-board three-dimensional constrained entry flight trajectory generation, PhD thesis, Iowa State University.
  31. Rogers, D. F. , and Adams, J. A. , 1990. Mathematical Elements for Computer Graphics, New York, McGraw-Hill, 1990.
  32. Nagatani K. , Yosuke I. , and Yutaka T. 2003. Sensor-based navigation for car-like mobile robots based on a generalized Voronoi graph. Advanced Robotics, N. 17, 385-401.
  33. Zhang J. , Raczkowsky J. , Herp A. 1994. Emulation of spline curves and its applications in robot motion control. IEEE Conf. on Fuzzy Systems, Orlando, USA, 831-836.
  34. Myong H. S. , Kyu J. L 2000. Bezier curve application in the shape optimization for transonic airfoils. the 18TH AIAA Applied Aerodynamics Conf. , USA, 884-894.
  35. Venkataraman P. 1997. Unique solution for optimal airfoil design. the 15th AIAA Applied Aerodynamics Conf. , USA, 205-215.
  36. Desideri J. A. , Peigin S. , and Timchenko S. 1999. Application of genetic algorithms to the solution of the space vehicle reentry trajectory optimization problem. INRIA Sophia Antipolice Research Report No. 3843.
  37. Rahman, T. , Zhou H. , Chen W. 2013. Bézier approximation based inverse dynamic guidance for entry glide trajectory. Control Conference (ASCC), 9th Asian.
  38. Betts, J. T. 1998. survey of numerical methods for trajectory optimization. Journal of Guidance, Control and Dynamics, Vol. 21, No. 2, 193-207.
  39. Coverstone-Carroll, V. L. , Hartmann, J. W. and Mason, W. J. 2000. Optimal multi-objective low-thrust spacecraft trajectories. Computer Methods in Applied Mechanics and Engineering, Vol. 186, 387-402. Wuerl, A. , Carin, T. and Braden, E. 2003. Genetic algorithm and calculus of variations-based trajectory optimization technique", Journal of Spacecraft and Rockets, Vol. 40, No. 6, 882-888.
  40. Yokoyama, N. , Suzuki, S. 2005. Modified genetic algorithm for constrained trajectory optimization. J. of Guidance, Control and Dynamics, V. 28, No. 1, 139-144.
  41. Deb, K. 2001. Multi-objective optimization using evolutionary algorithms, John-Wiley & Sons, Ltd. , New York.
  42. Gen, M. and Cheng, R. 2000. Genetic algorithms & engineering optimization, John Wiley & Sons Inc. , New York.
  43. Renders, J. M. and Flasse, S. P. 1996. Hybrid methods using genetic algorithms for global optimization. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 26, No. 2, 243-258.
  44. Esmaelzadeh, R. , Naghash, A. and Mortazavi, M. 2005. Hybrid trajectory optimization using genetic algorithms. Proceedings of the 1st International Conference on Modeling, Simulation and Applied Optimization, Sharjah, U. A. E.
  45. Lin, T. F. , and et al. 2003. Novel approach for maneuvering reentry vehicle design. J. of Spacecraft and Rocket, V. 40, No. 5, 605-614.
  46. Shneydor, N. A. 1998. Missile guidance and pursuit; kinematics, dynamics, and control, Chichester, Horwood Publishing Ltd.
Index Terms

Computer Science
Information Sciences

Keywords

Reentry Explicit Guidance Differential Flatness Optimal Guidance Real Genetic Algorithm.