Extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots

International Journal of Control

Volumn 79, Issue 8, 2006, Pages 895-909

  Tchoń, Krzysztof ^a   Jakubiak, Janusz ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DRIFTLESS CONTROL SYSTEM; JACOBIAN INVERSE KINEMATICS ALGORITHM; NONHOLONOMIC MOBILE ROBOTS;

ALGORITHMS; COMPUTER SIMULATION; CONTROL SYSTEMS; FUNCTIONS; MANIPULATORS; MOBILE ROBOTS;

INVERSE KINEMATICS;

EID: 33745346870     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170600708616     Document Type: Article

References (42)

1. R. Abraham, J. E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications, New York: Springer-Verlag, 1988.
2. J. Baillieul, "Kinematic programming alternatives for redundant manipulators", in Proc. 1985 IEEE Int. Conf. Robot. Automat., St. Louis, LO, 1985, pp. 818-823.
3. A.M. Bloch, Nonholonomic Mechanics and Control, New York: Springer-Verlag, 2003.
4. B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control, Berlin: Springer-Verlag, 2003.
5. R.W. Brockett, "Asymptotic stability and feedback stabilization", in Differential Geometric Control Theory, R.S. Millman, R.W. Brockelt and H.J. Sussmann, Eds, Boston: Birkhäuser, 1983, pp. 181-191.
6. R.W. Brockett, "Robotic manipulators and the product of exponentials formula", in Mathematical Theory of Networks and Systems, P. Fuhrmann, Ed., Berlin: Springer-Verlag, 1984, pp. 120-129.
7. A. Chelouah and Y. Chitour, "On the motion planning of rolling surfaces" Forum Math., 15, pp. 727-758, 2003.
8. G.S. Chirikjian and A.B. Kyalkin, Engineering Applications of Noncommutative Harmonic Analysis, Boca Raton: CRC Press, 2001.
9. Y. Chitour, "A homotopy continuation method for trajectories generation of nonholonomic systems", ESAIM: Control, Optim. Calc. Var., 12, pp. 139-168, 2006.
10. Y. Chitour and H.J. Sussmann, "Motion planning using the continuation method", in Essays on Mathematical Robotics, J. Baillieul, S.S. Sastry and H.J. Sussmann, Eds, New York: Springer-Verlag, 1998, pp. 91-125.
11. J.M. Coron, "Global asymptotic stabilization for controllable systems without drifts", Math. Control, Signals and Systetms, 5, pp. 295-315, 1992.
12. C.C. de Wit, B. Siciliano and G. Bastin, Theory of Robot Control, Berlin: Springer-Verlag, 1996.
13. P. Deuflhard, Newton Methods for Nonlinear Problems, Berlin: Springer-Verlag, 2004.
14. A.W. Divelbiss and J.T. Wen, "A path space approach to nonholonomic motion planning in the presence of obstacles", IEEE Trans. Robot. Automat., 13, pp. 443-451, 1997.
15. A.W. Divelbiss, S. Seereeram and J.T. Wen, "Kinematic path planning for robots with holonomic and nonholonomic constraints", in Essays on Mathematical Robotics, J. Baillieul, S.S. Sastry, and H.J. Sussmann, Eds, New York: Springer-Verlag, 1998, pp. 127-150.
16. I. Dulçba, Algorithms of Motion Planning for Nonholonomic Robots, Wroclaw: Wroclaw University of Technology Publisher, 1998.
17. H. Hermes, "On the synthesis of stabilizing feedback control via Lie algebraic methods", SIAM J. Contr. Optim., 18, pp. 352-361, 1980.
18. J. Jakubiak and R. Muszyński, A predicitve approach to motion planning for mobile manipulators. Technical report PRE 73, Inst. Eng. Cybernetics, Wroclaw University of Technology, Wroclaw, Poland (2004).
19. C.A. Klein, C. Chu-Jenq and S. Ahmed, "A new formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators", IEEE Trans. Robot. Automat., 11, pp. 50-55, 1995.
20. G. Lafferriere and H.J. Sussmann, "A differential geometric approach to motion planning", in Nonholonomic Motion Planning, Z. Li and J.F. Canny, Eds, Dordrecht: Kluwer Acad. Publ., 1993, pp. 233-270.
21. Z. Li and J. Canny, "Motion of two rigid bodies with rolling constraints", IEEE Trans. Robot. Automat., 6, pp. 62-72, 1990.
22. D.G. Luenberger, Optimization by Vector Space Methods, New York: J. Wiley, 1999.
23. P. Morin and C. Samson, "Feedback control of nonholonomic wheeled vehicles, a survey", Arch. Control Sci., 12, pp. 67-36, 2002.
24. P. Morin and C. Samson, "Practical stabilization of driftless systems on Lie groups: the transverse function approach", IEEE Trans. Aut. Contr., 48, pp. 1496-1508, 2003.
25. P. Morin and C. Samson, "Trajectory tracking for non-holonomic vehicles: overview and case study", in Proc. 4th Int. Workshop on Robot Motion Control RoMoCo, 2004, pp. 139-153.
26. P. Morin, J.B. Pomet, and C. Samson, "Design of homogenous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of Lie brackets in closed loop", SIAM J. Contr. Optim., 38, pp. 22-49, 1999.
27. R.M. Murray and S.S. Sastry, "Nonholonomic motion planning: steering using sinusoids", IEEE Trans. Automat. Control, 38, pp. 700-716, 1993.
28. J.B. Pomet, "Explicit design of time varying stabilization laws for a class of controllable systems without drift", Syst. Contr. Lett., 18, pp. 147-158, 1992.
29. R.G. Roberts and A.A. Maciejewski, "Nearest optimal repeatable control strategies for kinematically redundant manipulators", IEEE Trans. Robot. Automat., 8, pp. 327-337, 1992.
30. R.G. Roberts and A.A. Maciejewski, "Repeatable generalized inverse control strategies for kinematically redundant manipulators", IEEE Trans. Automat. Contr., 38, pp. 689-699, 1993.
31. C. Samson, "Control of chained systems", IEEE Trans. Automat. Control, 40, pp. 64-77, 1995.
32. T. Shamir and Y. Yomdin, "Repeatability of redundant manipulators: mathematical solution of the problem", IEEE Trans. Automat. Control, 33, pp. 1004-1009, 1988.
33. E.D. Sontag, Mathematical Control Theory, New York: Springer-Verlag, 1990.
34. E.D. Sontag, "A general approach to path planning for systems without drift", in Essays in Mathematical Robotics, J. Baillieul, S.S. Sastry, and H.J. Sussmann, Eds, New York: Springer-Verlag, 1998, pp. 151-168.
35. P. Souéres and J.D. Boissonnat, "Optimal trajectories for nonholonomic systems", in Robot Motion Planning and Control, J.P. Laumond, Ed., London: Springer-Verlag, 1998, pp. 93-167.
36. H.J. Sussmann, "New differential geometric methods in nonholonomic path finding", in Systems, Models, and Feedback, A. Isidori and T.J. Tarn, Eds, Boston: Birkhäuser, 1992, pp. 365-384.
37. K. Tchoń, "Repeatable, extended Jacobian inverse kinematics algorithm for mobile manipulators", Syst. Contr. Lett., 55, pp. 87-93, 2006.
38. K. Tchoń, "Repeatability of inverse kinematics algorithms for mobile manipulators", IEEE Trans. Autom. Control, 47, pp. 1376-1380, 2002.
39. K. Tchoń and J. Jakubiak, "Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms", Int. J. Control, 76, pp. 1387-1419, 2003.
40. K. Tchoń and J. Jakubiak, "A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators", IEEE Trans Syst., Man, Cybernet. - Part B: Cybernetics, 35, pp. 1051-1057, 2005.
41. K. Tchoń and R. Muszyński, "Instantaneous kinematics and dexterity of mobile manipulators", in Proc. 2000 IEEE Int. Conf. Robot. Automat, San Francisco, CA, 2000, pp. 2493-2498.
42. T. Ważewski, "Sur l'évaluation du domaine d'existence des functions implicites réelles ou complexes", Ann. Soc. Pol. Math., 20, pp. 81-120, 1947.