Iterative MILP methods for vehicle-control problems

IEEE Transactions on Robotics

Volumn 21, Issue 6, 2005, Pages 1158-1167

  Earl, Matthew G ^a   D'Andrea, Raffaello ^b  

^a BAE SYSTEMS   (United States)

^b Cornell University   (United States)

Author keywords

Hybrid systems; Mathematical optimization; Mixed integer linear programming (MILP); Obstacle avoidance; Path and trajectory planning; Robot motion planning; Trajectory generation

Indexed keywords

ALGORITHMS; COLLISION AVOIDANCE; ITERATIVE METHODS; LINEAR EQUATIONS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; MOTION CONTROL; MOTION PLANNING; UNMANNED VEHICLES;

HYBRID SYSTEMS; MIXED LOGICAL DYNAMICAL SYSTEMS; MIXED-INTEGER LINEAR PROGRAMMING; PATH AND TRAJECTORY PLANNING; TRAJECTORY GENERATION;

ROBOT PROGRAMMING;

EID: 29844454811     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2005.853499     Document Type: Article

References (21)

1. S. Akella and S. Hutchinson, "Coordinating the motions of multiple robots with specified trajectories," in Proc. IEEE Int. Conf. Robot. Autom., Washington, DC, May 2002, pp. 624-631.
2. J. S. Bellingham, M. Tillerson, M. Alighanbari, and J. P. How, "Cooperative path planning for multiple UAVs in dynamic and uncertain environments," in Proc. IEEE Conf. Decision Control, Las Vegas, NV, Dec. 2002, pp. 2816-2822.
3. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, pp. 407-428, 1999.
4. D. Bertsimas and J. N. Tsitsiklis, Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997.
5. A. I. Chaudhry, K. M. Misovec, and R. D'Andrea, "Low observability path planning for an unmanned air vehicle using mixed integer linear programming," in Proc. IEEE Conf. Decision Control, Paradise Island, Bahamas, Dec. 2004, pp. 3823-3829.
6. R. D'Andrea, T. Kalmár-Nagy, P. Ganguly, and M. Babish, "The Cornell RoboCup Team," in Robot Soccer WorldCup IV, Lecture Notes in Artificial Intelligence, G. Kraetzschmar, P. Stone, and T. Balch, Eds. New York: Springer, 2001.
7. M. G. Earl and R. D'Andrea. Multi-Vehicle Cooperative Control Using Mixed Integer Linear Programming. [Online] Preprint available: http://arxiv.org/abs/cs.RO/0501092
8. M. G. Earl and R. D'Andrea, A Decomposition Approach to Multi-Vehicle Cooperative Control. [Online] Preprint available: http://arxiv.org/abs/ cs.RO/0504081
9. M. G. Earl and R. D'Andrea, "Modeling and control of a multi-agent system using mixed integer linear programming," in Proc. IEEE Conf. Decision Control, Las Vegas, NV, Dec. 2002, pp. 107-111.
10. All files for generating the plots found in this paper are available online by following the link. [Online] http://arxiv.org/abs/cs.RO/0505042 or http://control.mae.cornell.edu/earl/milp2
11. R. Fourer, D. M. Gay, and B. W. Kemighan, AMPL-A Modeling Language for Mathematical Programming. Boston, MA: Boyd & Fraser, 1993.
12. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
13. W. P. M. H. Heemels, B. De Schutter, and A. Bemporad, "Equivalence of hybrid dynamical models," Automatica, vol. 37, no. 7, pp. 1085-1091, Jul. 2001.
14. ILOG AMPL CPLEX System Version 7.0 User's Guide, 2000.
15. T. Kalmár-Nagy, R. D'Andrea, and P. Ganguly, "Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle," Robot. Auton. Syst., vol. 46, pp. 47-64, 2004.
16. J. Ousingsawat and M. E. Campbell, "Establishing optimal trajectories for multi-vehicle reconnaissance," in Proc. AIAA Guid., Navig., Control Conf., Providence, RI, 2004, [CD-ROM].
17. L. Pallottino, E. Feron, and A. Bicchi, "Conflict resolution problems for air traffic management systems solved with mixed integer programming," IEEE Trans. Intell. Transp. Syst., vol. 3, no. 1, pp. 3-11, Mar. 2002.
18. J. Peng and S. Akella, "Coordinating the motions of multiple robots with kinodynamic constraints," in Proc. IEEE Int. Conf. Robot. Autom., Taipei, Taiwan, Sep. 2003, pp. 4066-4073.
19. A. Richards, T. Schouwenaars, J. P. How, and E. Feron, "Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming," J. Guid., Control, Dynam., vol. 25, pp. 755-764, Jul.-Aug. 2002.
20. A. Richards and J. P. How, "Aircraft trajectory planning with collision avoidance using mixed integer linear programming," in Proc. Amer. Control Conf., Anchorage, AK, May 8-10, 2002, pp. 1936-1941.
21. H.P. Rothwangl, "Numerical synthesis of the time optimal nonlinear state controller via mixed integer programming", in Proc. Amer. Control Conf., Arlington,VA, Jun. 2001, pp. 3201-3205.