Optimal coordinated motions of multiple agents moving on a plane

SIAM Journal on Control and Optimization

Volumn 42, Issue 2, 2003, Pages 637-668

  Hu, Jianghai ^a   Prandini, Maria ^b   Sastry, Shankar ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Braids; Calculus of variation with constraints; Convex optimization; Cooperative motion planning

Indexed keywords

BRAIDS; CALCULUS OF VARIATION WITH CONSTRAINTS; CONVEX OPTIMIZATION; COOPERATIVE MOTION PLANNING;

AIR TRAFFIC CONTROL; ALGORITHMS; CONSTRAINT THEORY; MANEUVERABILITY; MATHEMATICAL MODELS; MOTION PLANNING; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; QUADRATIC PROGRAMMING; VARIATIONAL TECHNIQUES;

MULTI AGENT SYSTEMS;

EID: 1942445417     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901387562     Document Type: Article

References (40)

1. A. ABRAMS, Configuration Spaces and Braid Groups of Graphs, Ph.D. thesis, University of California, Berkeley, CA, 2000.
2. F. ALBRECHT AND I. BERG, Geodesics in Euclidean space with analytic obstacle, Proc. Amer. Math. Soc., 113 (1991), pp. 201-207.
3. V. I. ARNOLD, K. VOGTMANN, AND A. WEINSTEIN, Mathematical Methods of Classical Mechanics, 2nd ed., Springer-Verlag, New York, 1989.
4. B. ARONOV, M. DE BERG, A. VAN DER STAPFEN, P. SVESTKA, AND J. VLEUGELS, Motion planning for multiple robots, Discrete Comput. Geom., 22 (1999), pp. 502-525.
5. A. BICCHI AND L. PALLOTTINO, On optimal cooperative conflict resolution for air traffic management systems, IEEE Trans. Intelligent Transport. Systems, 1 (2000), pp. 221-231.
6. J. BIRMAN, Braids, Links, and Mapping Class Groups, Princeton University Press, Princeton, NJ, 1974.
7. J. P. DESAI AND V. KUMAR, Nonholonomic motion planning for multiple mobile manipulators, in Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 4, IEEE Press, Piscataway, NJ, 1997, pp. 3409-3414.
8. M. P. DO CARMO, Riemannian Geometry, Birkhäuser, Boston, MA, 1992.
9. M. ERDMANN AND T. LOZANO-PEREZ, On multiple moving objects (motion planning), Algorithmica, 2 (1987), pp. 477-521.
10. E. FRAZZOLI, Z.-H. MAO, J.-H. OH, AND E. FERON, Resolution of conflicts involving many aircraft via semidefinite programming, J. Guidance Control Dynam., 24 (2001), pp. 79-86.
11. K. FUJIMURA, Motion Planning in Dynamic Environments, Springer-Verlag, Tokyo, 1991.
12. J. Hu, A Study of Conflict Detection and Resolution in Free Flight, Master's thesis, University of California, Berkeley, CA, 1999.
13. J. Hu, M. PRANDINI, K. H. JOHANSSON, AND S. SASTRY, Hybrid geodesies as optimal solutions to the collision-free motion planning problem, in Hybrid Systems: Computation and Control. 4th International Workshop (HSCC01), Rome, Italy, 2001, Lecture Notes in Comput. Sci. 2034, M. Domenica, D. Benedetto, and A. Sangiovanni-Vincentelli, eds., Springer-Verlag, Berlin, pp. 305-318.
14. J. Hu, M. PRANDINI, AND S. SASTRY, Optimal maneuver for multiple aircraft conflict resolution: A braid point of view, in Proceedings of the 39th IEEE International Conference on Decision and Control, Vol. 4, IEEE Press, Piscataway, NJ, 2000, pp. 4164-4169.
15. J. Hu, M. PRANDINI, AND S. SASTRY, Optimal coordinated maneuvers for three dimensional aircraft conflict resolution, J. Guidance Control Dynam., 25 (2002), pp. 888-900.
16. J. Hu AND S. SASTRY, Optimal collision avoidance and formation switching on Riemannian manifolds, in Proceedings of the 40th IEEE International Conference on Decision and Control, Vol. 2, IEEE Press, Piscataway, NJ, 2001, pp. 1071-1076.
17. J. Hu AND S. SASTRY, Hybrid Geodesic Flows on Manifolds with Boundary, University of California, Berkeley, CA, manuscript.
18. Y. K. HWANG AND N. AHUJA, Gross motion planning, ACM Comput. Surveys, 24 (1992), pp. 219-291.
19. A. INSELBERG AND B. DIMSDALE, Multidimensional lines II: Proximity and applications, SIAM J. Appl. Math., 54 (1994), pp. 578-596.
20. J. JOST, Riemannian Geometry and Geometric Analysis, 2nd ed., Springer-Verlag, Berlin, 1998.
21. W.-S. KOON AND J. E. MARSDEN, Optimal control for holonomic and nonholonomic mechanical systems with symmetry and Lagrangian reduction, SIAM J. Control Optima, 35 (1997), pp. 901-929.
22. P. S. KRISHNAPRASAD, Eulerian many-body problems, in Dynamics and Control of Multibody Systems (Brunswick, ME, 1988), AMS, Providence, RI, 1989, pp. 187-208.
23. J. KUCHAR AND L. C. YANG, Survey of conflict detection and resolution modeling method's, IEEE Trans. Intelligent Transport. Systems, 1 (2000), pp. 179-189.
24. J. LATOMBE, Robot Motion Planning, Kluwer Academic Publishers, Boston, MA, 1991.
25. S. LAVALLE AND S. HUTCHINSON, Optimal motion planning for multiple robots having independent goals, IEEE Trans. Robotics Automation, 14 (1998), pp. 912-925.
26. J. E. MARSDEN AND T. S. RATIU, Introduction to Mechanics and Symmetry, 2nd ed., Springer-Verlag, New York, 1999.
27. C. D. MEDIO AND G. ORIOLO, Robot obstacle avoidance using vortex fields, in Advances in Robot Kinematics, S. Stifter and J. Lenarcic, eds., Springer-Verlag, Vienna, 1991, pp. 227-235.
28. F. MEDIONI, N. DURAND, AND J. M. ALLIOT, Air traffic conflict resolution by genetic algorithms, in Artificial Evolution, European Conference (AE '95), Springer-Verlag, Berlin, 1995, pp. 370-383.
29. P. MENON, G. SWERIDUK, AND B. SRIDHAR, Optimal strategies for free-flight air traffic conflict resolution, J. Guidance Control Dynam., 22 (1999), pp. 202-211.
30. A. MIELE, T. WANG, C. CHAO, AND J. DABNEY, Optimal control of a ship for collision avoidance maneuvers, J. Optim. Theory Appl., 103 (1999), pp. 495-519.
31. J. W. MILNOR, Morse Theory, Princeton University Press, Princeton, NJ, 1963.
32. S. MORGAN, The Mathematical Theory of Knots and Braids: An Introduction, North-Holland, Amsterdam, 1991.
33. K. MURASUGI AND B. I. KURPITA, A Study of Braids, Kluwer Academic Publishers, Boston, MA, 1999.
34. M. PRANDINI, J. HU, J. LYGBROS, AND S. SASTRY, A probabilistic approach to aircraft conflict detection, IEEE Trans. Intelligent Transport. Systems, 1 (2000), pp. 199-220.
35. RADIO TECHNICAL COMMISSION FOR AERONAUTICS, Minimum Aviation System Performance Standards for Automatic Dependent Surveillance-Broadcast (ADS-B), Technical report, RTCA-186, Draft 4.0, RTCA, Inc., Washington, DC, 1997.
36. E. RIMON AND D. KODITSCHEK, Exact robot navigation using artificial potential functions, IEEE Trans. Robotics Automation, 8 (1993), pp. 501-519.
37. M. RUDE, Collision avoidance by using space-time representations of motion processes, Autonomous Robots, 4 (1997), pp. 101-119.
38. M. SHARIR AND S. SIFRONY, Coordinated motion planning for two independent robots, Ann. Math. Artificial Intelligence, 3 (1991), pp. 107-130.
39. C. TOMLIN, Hybrid Control of Air Traffic Management Systems, Ph.D. thesis, University of California, Berkeley, CA, 1998.
40. C. TOMLIN, G. PAPPAS, AND S. SASTRY, Conflict resolution for air traffic management: A study in multi-agent hybrid systems, IEEE Trans. Automat. Control, 43 (1998), pp. 509-521.