Multi vehicle avoidance using nonlinear branch and bound optimisation

AIAA Guidance, Navigation, and Control Conference and Exhibit

Volumn , Issue , 2009, Pages

  Eele, Alison ^a   Richards, Arthur ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AIR NAVIGATION; AIR TRAFFIC CONTROL; ANTENNAS; INTEGER PROGRAMMING; MOTION PLANNING; OPTIMAL SYSTEMS; ROBOT PROGRAMMING; ROBOTS; VEHICLES;

BRANCH-AND-BOUND APPROACHES; INITIAL SOLUTION; MIXED-INTEGER LINEAR PROGRAMMING; NON-LINEAR DYNAMICS MODEL; NONCONVEX PROBLEM; OPTIMAL SOLUTIONS; OPTIMAL TRAJECTORIES; ROBOT PATH-PLANNING;

BRANCH AND BOUND METHOD;

EID: 78049245959     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2009-5780     Document Type: Conference Paper

References (31)

1. Eele, A. and Richards, A., "Path-Planning with Avoidance using Nonlinear Branch-and-Bound Optimisation," Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, No. AIAA-2007-6793, Hilton Head, South Carolina, August 2007.
2. Eele, A. and Richards, A., "Path-Planning with Avoidance Using Nonlinear Branch-and-Bound Optimisation," Journal of Guidance, Control and Dynamics, Vol. To Appear, 2009.
3. Pachter, M. and Chandler, P. R., "Challenges of Autonomous Control," IEEE Control Systems Magazine, Vol. 18, No. 4, 1998, pp. 92-97.
4. Perry, T. S., "In Search of the Future of Air Traffic Control," IEEE Spectrum, Vol. 34, No. 8, 1997, pp. 19.
5. Reddien, G. W., "Collocation at Gauss Points as a Discretization in Optimal Control," SIAM Journal on Control and Optimization, Vol. 17, No. 2, 1979, pp. 298-306.
6. Latombe, J.-C., Robot Motion Planning, Kluwer Academic Publishers, 3300 AA Dordrecht The Netherlands, 1991.
7. Rahmani, A., Kosuge, K., t Tsukamaki, and Mesbahi, M., "Multiple UAV Deconfliction via Navigation Functions," Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, August 2008.
8. Rimon, E. and Koditschek, D. E., "Exact Robot Navigation using Artificial Potential Fields," IEEE Transactions on Robotics and Automation, Vol. 8, No. 5, 1992, pp. 501-518.
9. Raghunathan, A. U., Gopal, V., Subramanian, D., Biegler, L. T., and Samad, T., "Dynamic Optimization Strategies for 3D Conflict Resolution of Multiple Aircraft," AIAA Journal of Guidance, Control and Dynamics, Vol. 27, No. 4, 2004, pp. 586-594.
10. Singh, G. and Hadaegh, F. Y., "Collision Avoidance Guidance for Formation Flying Applications," Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, No. AIAA 2001-4088, Montreal, Canada, 2001.
11. Roger, A. B. and McInnes, C. R., "Safety Constrained Free-Flyer Path Planning at the International Space Station," AIAA Journal of Guidance, Control and Dynamics, Vol. 23, No. 6, December 2000, pp. 971-979.
12. Ghosh, R. and Tomlin, C., "Maneuver Design for Multiple Aircraft Conflict Resolution," Proceedings of the American Control Conference, Chicago, Illinois, June 2000, pp. 672-676.
13. Bortoff, S. A., "Path-Planning for UAVs," Proceedings of American Control Conference, Chicago, Illinois, June 2000, pp. 364-368.
14. McLain, T. W. and Beard, R. W., "Trajectory Planning for Coordinated Rendezvous of Unmanned Air Vehicles," Proceedings of the AIAA Guidance, Navigation and Control Conference, No. AIAA-2000-4369, 2000.
15. Bicchi, A. and Pallottino, L., "On Optimal Cooperative Conflict Resolution for Air Traffic Management Systems," IEEE Transactions on Intelligent Transporation Systems, Vol. 1, No. 4, 2000, pp. 221-232.
16. Milam, M. B., Mushambi, K., and Murray, R. M., "A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems," Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers, New York, 2000, pp. 845-851.
17. Richards, A., Schouwenaars, T., How, J., and Feron, E., "Spacecraft Trajectory Planning with Avoidance Constraints Using Mixed-Integer Linear Programming," AIAA Journal of Guidance, Control, and Dynamics, Vol. 25, No. 4, 2002, pp. 755-764.
18. Borrelli, F., Subramanian, D., Raghunathan, A. U., and Biegler, L. T., "MILP and NLP Technniques for Centralized Trajectory Planning of Multiple Unmanned Air Vehicles," Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, June 2006, pp. 5763-5768.
19. Richards, A. and How, J., "Aircraft Trajectory Planning with Collision Avoidance using Mixed Integer Linear Programming," Proceedings of the American Control Conference, Vol. 3, Anchorage, Alaska, May 2002, pp. 1936-1941.
20. Frazzoli, E., Mao, Z. H., Oh, J. H., and Feron, E., "Resolution of Conflicts Involving Many Aircraft via Semidefinite Programming," AIAA Journal of Guidance, Control and Dynamics, Vol. 24, No. 1, 2001, pp. 79-86.
21. Hu, J., Pradini, M., and Sastry, S., "Optimal Coordinated Maneuvers for Three Dimensional Aircraft Conflict Resolution," AIAA Journal of Guidance, Control and Dynamics, Vol. 25, 2002, pp. 888-900.
22. Bertsimas, D. and Tsitsiklis, J. N., Introduction to Linear Optimization, Athena Scientific, Belmont, Massachusetts, 1997.
23. Dakin, R. J., "A tree-search algorithm for mixed integer programming problems," The Computer Journal, Vol. 8, No. 3, 1965, pp. 250-255.
24. Lawler, E. L. and Wood, D. E., "Branch-And-Bound Methods: A Survey," Operations Research, Vol. 14, No. 4, 1966, pp. 699-719.
25. Huntington, G., Advancement and Analysis of a Guass Pseudospectral Transcription for Optimal Control Problems, Ph.D. thesis, Department of Aeronautics and Astronautics, Massachusetts Institue of Technology, Cambridge, Massachusetts, May 2007, 2007.
26. Ross, M. and Fahroo, F., "Direct Trajectory Optimization by a Chebyshev Pseudospectral Method," Proceedings of the American Control Conference, Vol. 6, Chicago, Illinois, June 2000, pp. 3860-3864. (Pubitemid 32027776)
27. Eele, A. and Richards, A., "Comparison of Branching Strategies for Path-Planning with Avoidance using Nonlinear Branch-and-Bound," Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu, Hawaii, August 2008.
28. MATLAB Website, http://www.mathworksl.com/, Visited July 2007.
29. SNOPT Website, http://www.sbsi-sol-optimize.com/asp/sol-product-snopt. htm, Visited June 2008.
30. AMPL Website, http://www.ampl.com/, Visited July 2007.
31. ILOG CPLEX Website, http://www.ilog.com/products/cplex/, visited July 2007.