Feedback encoding for efficient symbolic control of dynamical systems

IEEE Transactions on Automatic Control

Volumn 51, Issue 6, 2006, Pages 987-1002

  Bicchi, Antonio ^a   Marigo, Alessia ^b   Piccoli, Benedetto ^b  

^a UNIVERSITY OF PISA   (Italy)

^b CNR   (Italy)

Author keywords

Hybrid logic dynamical systems; Specification complexity; Symbolic control

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONTROL SYSTEMS; ENCODING (SYMBOLS); OPTIMIZATION; POLYNOMIAL APPROXIMATION;

DYNAMICAL SYSTEMS; HYBRID LOGIC; SPECIFICATION COMPLEXITY; SYMBOLIC CONTROL;

FEEDBACK CONTROL;

EID: 33745700839     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.876947     Document Type: Article

References (34)

1. M. J. van Nieuwstadt and R. M. Murray, "Real time trajectory generation for differentially flat systems," Int. J. Robust Nonlinear Control, vol. 8, no. 11, pp. 995-1020, 1998.
2. F. Bullo and K. M. Lynch, "Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems," IEEE Trans. Robot. Automat., vol. 17, no. 4, pp. 402-412, Jul. 2001.
3. E. Frazzoli, M. A. Dahleh, and E. Feron, "Real-time motion planning for agile autonomous vehicles," in Proc. AlAA Guidance, Navigation, and Control Conf. Exhibit, Aug. 2000, pp. 1-11.
4. E. Frazzoli, M. A. Dahleh, and E. Feron, "Maneuver-based motion planning for nonlinear systems with symmetries," IEEE Trans. Robot., vol. 21, no. 6, pp. 1077-1091, Dec. 2005.
5. P. Tabuada and G. J. Pappas, "Hierarchical trajectory generation for a class of nonlinear systems," Automatica, vol. 41, no. 4, pp. 701-708, 2005.
6. M. Okada and Y. Nakamura, "Polynomial design of dynamics-based information processing system," in Control Prob. Robot., A. Bicchi, H. Christensen, and D. Prattichizzo, Eds. New York: Springer-Verlag, 2003, pp. 91-104.
7. V. Manikonda, P. S. Krishnaprasad, and J. Hendler, "A motion description language and hybrid architecture for motion planning with non-holonomic robots," in Proc. Int. Conf. Robotics and Automation, 1995, pp. 2021-2028.
8. M. Egerstedt, "Motion description languages for multimodal control in robotics," in Control Prob. Robot., A. Bicchi, H. Christensen, and D. Prattichizzo, Eds. New York: Springer-Verlag, 2003, pp. 75-89.
9. R. Brockett, "On the computer control of movement," in Proc. IEEE Conf. Robotics and Automation, Apr. 1988, pp. 534-540.
10. P. Tabuada and G. J. Pappas, "Bisimilar control affine systems," Syst. Control Lett., vol. 52, no. 1, pp. 49-58, 2004.
11. P. Tabuada, Hybrid Systems: Computation and Control. New York: Springer-Verlag, 2005, vol. 3414, Lecture Notes in Computer Science, pp. 640-654.
12. M. Egerstedt and R. W. Brockett, "Feedback can reduce the specification complexity of motor programs," IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 213-223, Feb. 2003.
13. Y. Anzai, "A note on reachability of discrete-time quantized control systems," IEEE Trans. Autom. Control, vol. AC- 19, no. 5, pp. 575-577, May 1974.
14. Y. Chitour and B. Piccoli, "Controllability for discrete systems with a finite control set," Math. Control Signals Syst., vol. 14, no. 2, pp. 173-193, 2001.
15. A. Bicchi, A. Marigo, and B. Piccoli, "On the reachability of quantized control systems," IEEE Trans. Autom. Control, vol. 47, no. 4, pp. 546-563, Apr. 2002.
16. M. Fliess, J. Lévine, P. Martin, and P. Rouchon, "Flatness and defect of nonlinear systems: Introductory theory and examples," Int. J. Control, vol. 61, pp. 1327-1361, 1995.
17. S.M. LaValle, Planning Algorithms. Cambbridge, U.K.: Cambridge Univ. Press, 2006 [Online]. Available: http://msl.cs.uiuc.edu/planning/
18. G. Heinzinger, P. Jacobs, J. Canny, and B. Paden, "Time-optimal trajectories for a robot manipulator: A provably good approximation algorithm," in Proc. IEEE Int. Conf. Robotics and Automation, 1990, pp. 150-156.
19. B. R. Donald and P. G. Xavier, "Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators," Algorithmica, vol. 14, no. 6, pp. 480-530, 1995.
20. S. M. LaValle and J. J. Kuffner, "Randomized kinodynamic planning," Int. J. Robot. Res., vol. 20, no. 5, pp. 378-400, 2001.
21. A. Schrijver, Theory of Linear and Integer Programming. New York: Wiley, 1986.
22. L.A. Wolsey, Integer Programming. New York: Wiley, 1998.
23. R. K. Guy, Unsolved Problems in Number Theory. New York: Springer-Verlag, 1994.
24. A. Marigo, "Optimal input sets for time minimality in quantized control systems," Math. Control Signal Syst., vol. 18, no. 2, pp. 101-146, 2006.
25. A. V. Sarichev and H. Nijmeier, "Extremal controls for chained systems," J. Dyna. Control Syst., vol. 2, pp. 503-527, 1996.
26. A. W. Divelbiss and J. Wen, "Nonholonomic path planning with inequality constraints," in Proc. IEEE Int. Conf. on Decision and Control, 1993, pp. 2712-2717.
27. D. Tilbury, R. M. Murray, and S. S. Sastry, "Trajectory generation for then traile problem using goursat normal form," IEEE Trans. Autom. Control, vol. 40, no. 5, pp. 802-819, May 1995.
28. P. Rouchon, M. Fliess, J. Lévine, and P. Martin, "Flatness, motion planning, and trailer systems," in Proc. IEEE Int. Conf. Decision and Control, 1993, pp. 2700-2705.
29. O. J. Sordalen, "Conversion of the kinematics of a car with n trailers into a chained form," in Proc. IEEE Int. Conf. Robotics and Automation, 1993, pp. 382-387.
30. M. Kawski, "Nilpotent lie algebras of vectorfields," J. für die Reine Angewandte Mathematik, vol. 388, pp. 1-17, 1988.
31. B. Charlet, J. Levine, and R. Marino, "Sufficient conditions for dynamic state feedback linearization," SIAM J. Control, vol. 29, no. 1, pp. 38-57, 1991.
32. E. Aranda-Bricaire, C. H. Moog, and J-B. Pomet, "A linear algebraic framework for dynamic feedback linearization," IEEE Trans. Autom. Control, vol. 40, no. 1, pp. 127-132, Jan. 1995.
33. E. Sontag, "Control of systems without drift via generic loops," IEEE Trans. Autom. Control, vol. 40, no. 7, pp. 1210-1219, Jul. 1995.
34. A. De Luca and G. Oriolo, "Trajectory planning and control for planar robots with passive last joint," Int. J. Robot. Res., vol. 21, no. 5-6, pp. 575-590, 2002.