Path-planning with avoidance using nonlinear branch-and-bound optimization

Journal of Guidance, Control, and Dynamics

Volumn 32, Issue 2, 2009, Pages 384-394

  Eele, Alison ^a,b   Richards, Arthur ^a,b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b School of Medical Sciences   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

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

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

BRANCH AND BOUND METHOD;

EID: 65949095044     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.40034     Document Type: Article

References (37)

1. Pachter, M., and Chandler, P. R., "Challenges of Autonomous Control," IEEE Control Systems Magazine, Vol. 18, No. 4, 1998, pp. 92-97. doi:10.1109/37.710883
2. Perry, T. S., "In Search of the Future of Air Traffic Control," IEEE Spectrum, Vol. 34, No. 8, 1997, p. 19. doi:10.1109/6.609472
3. Reddien, G. W., "Collocation at Gauss Points as a Discretization Optimal Control," SIAM Journal on Control and Optimization, Vol. 17, No. 2, 1979, pp. 298-306. doi:10.1137/0317023
4. Latombe, J.-C., Robot Motion Planning, Kluwer Academic, Dordrecht, The Netherlands, 1991, pp. 33-37.
5. Raghunathan, A. U., Gopal, V., Subramanian, D., Biegler, L. T., and Samad, T., "Dynamic Optimization Strategies for 3D Conflict Resolution of Multiple Aircraft," Journal of Guidance, Control, and Dynamics, Vol. 27, No. 4, 2004, pp. 586-594. doi:10.2514/1.11168
6. Singh, G., and Hadaegh, F. Y., "Collision Avoidance Guidance for Formation Flying Applications," Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, AIAA Paper 2001-4088, 2001.
7. Roger, A. B., and McInnes, C. R., "Safety Constrained Free-Flyer Path Planning at the International Space Station," Journal of Guidance, Control, and Dynamics, Vol. 23, No. 6, Dec. 2000, pp. 971-979. doi:10.2514/2.4656
8. Ghosh, R., and Tomlin, C., "Maneuver Design for Multiple Aircraft Conflict Resolution," Proceedings of the American Control Conference, American Automatic Control Council, Evanston, IL, June 2000, pp. 672-676.
9. Bortoff, S. A., "Path-Planning for UAVs," Proceedings of the 2000 American Control Conference, Vol. 1, No. 6, June 2000, pp. 364-368. doi:10.1109/ACC.2000.878915
10. 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, AIAA Paper 2000-4369, 2000.
11. Bicchi, A., and Pallottino, L., "On Optimal Cooperative Conflict Resolution for Air Traffic Management Systems," IEEE Transactions On Intelligent Transportation Systems: A Publication Of The IEEE Intelligent Transportation Systems Council, Vol. 1, No. 4, 2000, pp. 221-232. doi:10.1109/6979.898228
12. 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, Vol. 1, Inst. of Electrical and Electronics Engineers, New York, 2000, pp. 845-851. doi:10.1109/CDC.2000.912875
13. Barraquand, J., Kavraki, L., Latombe, J.-C., Motwani, R., and Raghavan, P., "A Random Sampling Scheme for Path Planning," International Journal of Robotics Research, Vol. 16, No. 6, 1997, pp. 759-774. doi:10.1177/027836499701600604
14. Lee, Y. I., and Kouvaritakis, B., "Constrained Receding Horizon Predictive Control for Systems with Disturbances," International Journal of Control, Vol. 72, No. 11, 1999, pp. 1027-1032. doi:10.1080/ 002071799220579
15. Frazzoli, E., Dahleh, M., and Feron, E., "Real-Time Motion Planning for Agile Autonomous Vehicles," Proceedings of the AIAA Guidance, Navigation and Control Conference, AIAA Paper 2000-4056, Aug. 2000.
16. Chandler, P. R., Pachter, M., and Rasmussen, S., "UAV Cooperative Control," Proceedings of American Control Conference, Vol. 1, American Automatic Control Council, Evanston, IL, June 2001, pp. 50-55. doi:10.1109/ACC.2001.945512
17. Bellingham, J., Richards, A., and How, J. P., "Receding Horizon Control of Autonomous Aerial Vehicles," Proceedings of the American Control Conference, Vol. 5, American Automatic Control Council, Evanston, IL, May 2002, pp. 3741-3746. doi:10.1109/ACC.2002.1024509
18. Richards, A., Schouwenaars, T., How, J., and Feron, E., "Spacecraft Trajectory Planning with Avoidance Constraints Using Mixed-Integer Linear Programming," Journal of Guidance, Control, and Dynamics, Vol. 25, No. 4, 2002, pp. 755-764. doi:10.2514/2.4943
19. Borrelli, F., Subramanian, D., Raghunathan, A. U., and Biegler, L. T., "MILP and NLP Techniques for Centralized Trajectory Planning of Multiple Unmanned Air Vehicles," Proceedings of the 2006 American Control Conference, American Automatic Control Council, Evanston, IL, June 2006, pp. 5763-5768. doi:10.1109/ACC.2006.1657644
20. Richards, A., and How, J., "Aircraft Trajectory Planning with Collision Avoidance Using Mixed Integer Linear Programming," Proceedings of the American Control Conference, Vol. 3, American Automatic Control Council, Evanston, IL, May 2002, pp. 1936-1941. doi:10.1109/ACC.2002.1023918
21. Bertsimas, D., and Tsitsiklis, J. N., Introduction to Linear Optimization, Athena Scientific, Belmont, MA, 1997, pp. 485-490.
22. Dakin, R. J., "A Tree-Search Algorithm for Mixed Integer Programming Problems," Computer Journal, Vol. 8, No. 3, 1965, pp. 250-255. doi:10.1093/comjnl/8.3.250
23. Geoffrion, A. M., "Integer Programming by Implicit Enumeration and Balas Method," SIAM Review, Vol. 9, No. 2, 1967, pp. 178-190. doi:10.1137/1009031
24. Golomb, S. W., and Baumert, L. D., "Backtrack Programming," Journal of the Association for Computing Machinery, Vol. 12, No. 4, 1965, pp. 516-524. doi:10.1145/321296.321300
25. Glover, F., "A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem," Operations Research, Vol. 13, No. 6, 1965, pp. 879-919. doi:10.1287/opre.13.6.879
26. Balas, E., "Discrete Programming by the Filter Method," Operations Research, Vol. 15, No. 5, 1967, pp. 915-957. doi:10.1287/opre.15.5. 915
27. Lawler, E. L., and Wood, D. E., "Branch-And-Bound Methods: A Survey," Operations Research, Vol. 14, No. 4, 1966, pp. 699-719. doi:10.1287/opre.14.4.699
28. Nilsson, N. J., Problem-Solving Methods in Artificial Intelligence, McGraw, New York, 1971, pp. 43-77.
29. Ibaraki, T., "Theoretical Comparisons of Search Strategies in Branch-And-Bound Algorithms," International Journal of Parallel Programming, Vol. 5, No. 4, 1976, pp. 315-344. doi:10.1007/BF00998631
30. Benichou, M., Gauthier, J. M., Girodet, P., Hentges, G., Ribiere, G., and Vincent, O., "Experiments in Mixed-Integer Linear Programming," Mathematical Programming, Vol. 1, No. 1, 1971, pp. 76-94. doi:10.1007/BF01584074
31. Gupta, O. K., and Ravindan, A., "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, Vol. 31, No. 12, Dec. 1985, pp. 1533-1546. doi:10.1287/mnsc.31.12.1533
32. Kindt, V. T., Croce, F. D., and Esswein, C., "Revisiting Branch and Bound Search Strategies for Machine Scheduling Problems," Journal of Scheduling, Vol. 7, No. 6, 2004, pp. 429-440. doi:10.1023/B: JOSH.0000046075.73409.7d
33. Hartley, R., Linear and Nonlinear Programming, Ellis Horwood, Chichester, England, U.K., 1985, pp. 167-175.
34. Huntington, G., "Advancement and Analysis of a Guass Pseudospectral Transcription for Optimal Control Problems," Ph.D. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge, MA, May 2007.
35. Ross, M., and Fahroo, F., "Direct Trajectory Optimization by a Chebyshev Pseudospectral Method," Proceedings of the American Control Conference, Vol. 6, American Automatic Control Council, Evanston, IL, June 2000, pp. 3860-3864. doi:10.1109/ACC.2000.876945
36. 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, AIAA Paper 2007-6793, Aug. 2007.
37. Glover, F., and Tangedahl, L., "Dynamic Strategies for Branch and Bound," OMEGA: International Journal of Management Science, Vol. 4, No. 5, 1976, pp. 571-576. doi:10.1016/0305-0483(76)90007-4