Robust point stabilization of underactuated mechanical systems via the extended chained form

SIAM Journal on Control and Optimization

Volumn 42, Issue 6, 2004, Pages 2172-2199

  Lizárraga, David A ^a   Aneke, Nnabdozie P I ^b   Nijmeijer, Henk ^c  

^a INSTITUTO POTOSINO DE INVESTIGACIÓN CIENTÍFICA Y TECNOLÓGICA   (Mexico)

^b FORD WERKE GMBH   (Germany)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Extended chained form; Hybrid feedback; Point stabilization; Second order chained form; Surface vessel; Underactuated manipulator

Indexed keywords

CASCADE CONTROL SYSTEMS; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING; TRAJECTORIES;

EXTENDED CHAINED FORM; HYBRID FEEDBACK; POINT STABILIZATION; SECOND-ORDER CHAINED FORM; SURFACE VESSELS; UNDERACTUATED MANIPULATORS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 10244235400     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902405571     Document Type: Article

References (32)

1. N. ANEKE, D. LIZÁRRAGA, AND H. NIJMEIJER, Homogeneous stabilization of the extended chained form system, in Proceedings of the IFAC 15th Triennial World Congress, Barcelona, Spain, 2002, paper 498.
2. M. BENNANI AND P. ROUCHON, Robust stabilization of flat and chained systems, in Proceedings of the European Control Conference, Rome, Italy, 1995, pp. 2642-2646.
3. R. BROCKETT, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, Progress in Mathematics 27, R. Brockett, R. Millman, and H. J. Sussmann, eds., Birkhäuser, Boston, 1983, pp. 181-191.
4. O. EGELAND, M. DALSMO, AND O. J. SØRDALEN, Feedback control of a nonholonomic underwater vehicle with constant desired configuration, Internat. J. Robotics Res., 15 (1996), pp. 24-35.
5. O. EGELAND, E. BERGLUND, AND O. SØRDALEN, Exponential stabilization of a nonholonomic underwater vehicle with constant desired configuration, in IEEE Conference on Robotics and Automation, 1994, pp. 20-25.
6. S. GE, Z. SUN, T. LEE, AND M. SPONG, Feedback linearization and stabilization of second-order non-holonomic chained systems, Internat. J. Control, 74 (2001), pp. 1383-1392.
7. H. HERMES, Nilpotent and high-order approximations of vector field systems, SIAM Review, 33 (1991), pp. 238-264.
8. J. IMURA, K. KOBAYASHI, AND T. YOSHIKAWA, Nonholonomic control of 3 link planar manipulator with a free joint, in IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 1435-1436.
9. M. KAWSKI, Geometric homogeneity and stabilization, in Proceedings of the IFAC Nonlinear Control Systems Design Symposium, 1995, pp. 164-169.
10. H. KHALIL, Nonlinear Systems, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 1996.
11. M.-C. LAIOU AND A. ASTOLFI, Discontinuous control of high-order generalized chained systems, Systems Control Lett., 37 (1999), pp. 309-322.
12. W. Liu, An approximation algorithm for nonholonomic systems, SIAM J. Control Optim., 35 (1997), pp. 1328-1365.
13. D. LIZÁRRAGA, P. MORIN, AND C. SAMSON, Non-Robustness of Continuous Homogeneous Stabilizers for Affine Control Systems, in Proceedings of the IEEE Conference on Decision and Control, pp. 855-860.
14. P. LUCIBELLO AND G. ORIOLO, Robust stabilization via iterative state steering with an application to chained-form systems, Automatica J. IFAC, 37 (2001), pp. 71-79.
15. N. H. MCLAMROCH, I. KOLMANOVSKY, S. CHO, AND M. REYHANOGLU, Control problems for planar motion of a rigid body with an unactuated internal degree of freedom, in Proceedings of the American Control Conference, Philadelphia, 1998, pp. 229-233.
16. R. M'CLOSKEY AND R. M. MURRAY, Nonholonomic systems and exponential convergence: Some analysis tools, in Proceedings of the IEEE Conference on Decision and Control, 1993, pp. 943-948.
17. P. MORIN AND C. SAMSON, Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics, ESAIM Control Optim. Calc. Var., 4 (1999), pp. 1-35.
18. P. MORIN, C. SAMSON, J.-B. POMET, AND Z.-P. JIANG, Time-varying feedback stabilization of the attitude of a rigid spacecraft with two controls, Systems Control Lett., 25 (1995), pp. 375-385.
19. R. R. MURRAY AND S. SASTRY, Steering Nonholonomic Systems Using Sinusoids, in Proceedings of the IEEE Conference on Decision and Control, Honolulu, HI, 1990, pp. 2097-2101.
20. W. OELEN, H. BERGHUIS, H. NIJMEIJER, AND C. CANUDAS DE WIT, Hybrid stabilizing control on a real mobile robot, IEEE Robotics & Automation Magazine, 2 (1995), pp. 16-23.
21. G. ORIOLO AND Y. NAKAMURA, Control of mechanical systems with second-order nonholonomic constraints: Underactuated manipulators, in Proceedings of the IEEE Conference on Decision and Control, Brighton, England, 1991, pp. 2398-2403.
22. M. RATHINAM AND R. M. MURRAY, Configuration flatness of Lagrangian systems underactuated by one control, SIAM J. Control Optim., 36 (1998), pp. 164-179.
23. M. REYHANOGLU, A. VAN DER SCHAFT, N. MCCLAMROCH, AND I. KOLMANOVSKY, Nonlinear control of a class of underactuated systems, in Proceedings of the IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 1682-1687.
24. M. REYHANOGLU, A. VAN DER SCHAFT, N. H. MCCLAMROCH, AND I. KOLMANOVSKY, Dynamics and Control of a Class of Underactuated Mechanical Systems, IEEE Trans. Automat. Control, 44 (1999), pp. 1663-1671.
25. S. SASTRY, Nonlinear Systems. Analysis, Stability and Control, Interdiscip. Appl. Math. 10, Springer-Verlag, Heidelberg, 1999.
26. O. SØRDALEN, Conversion of the kinematics of a car with n trailers into a chained form, in Proceedings of the IEEE Conference on Robotics and Automation, 1993, pp. 382-387.
27. H. J. SUSSMANN, Lie brackets and local controllability: A sufficient condition for scalar-input systems, SIAM J. Control and Optimization, 21 (1983), pp. 686-713.
28. A. R. TEEL, R. M. MURRAY, AND G. C. WALSH, Nonholonomic control systems: From steering to stabilization with sinusoids, Internat. J. Control, 62 (1995), pp. 849-870.
29. D. TILBURY, O. SØRDALEN, L. BUSHNELL, AND S. SASTRY, A multisteering trailer system: Conversion into chained form using dynamic feedback, IEEE Transactions on Robotics and Automation, 11 (1995), pp. 807-818.
30. K. WICHLUND, O. SØRDALEN, AND O. EGELAND, Control of vehicles with second-order nonholonomic constraints: Underactuated vechicles, in Proceedings of the European Control Conference, Rome, Italy, 1995, pp. 3086-3091.
31. G. XU AND D. WANG, Exponential stabilization of extended chained forms, in Proceedings of the American Control Conference, Chicago, IL, 2000, pp. 3259-3263.
32. T. YOSHIKAWA, K. KOBAYASHI, AND T. WATANABE, Design of a desirable trajectory and convergent control for 3-D.O.F. manipulator with a nonholonomic constraint, in Proceedings of the IEEE Conference on Robotics and Automation, San Francisco, CA, 2000, pp. 1805-810.