A unified geometric approach to modeling and control of constrained mechanical systems

IEEE Transactions on Robotics and Automation

Volumn 18, Issue 4, 2002, Pages 574-587

  Liu, Guanfeng ^b   Li, Zexiang ^a,b  

^a IEEE   (Hong Kong)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Asymptotic stability; Constraints; Distribution; Hybrid control; Projection; Velocity and force

Indexed keywords

HYBRID SYSTEMS; MECHANICAL CONTROL SYSTEMS; NONHOLONOMIC CONSTRAINT;

ALGORITHMS; ASYMPTOTIC STABILITY; CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; GEOMETRY; MATHEMATICAL MODELS; SYSTEM STABILITY;

CONTROL SYSTEM SYNTHESIS;

EID: 0036703669     PISSN: 1042296X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRA.2002.802207     Document Type: Article

References (41)

1. M. T. Mason, "Compliance and force control for computer controlled manipulators," IEEE Trans. Syst., Man, Cybern., vol. SMC-11, pp. 418-432, 1981.
2. M. H. Raibert and J. J. Craig, "Hybrid position/force control of manipulators," Trans. ASME J. Dynam. Syst., Meas., Contr., vol. 102, pp. 126-133, June 1981.
3. K. Sugimoto and J. Duffy, "Application of linear algebra to screw system," Mechanism Mach. Theory, vol. 17, pp. 73-83, 1985.
4. J. Duffy, "The fallacy of modern hybrid control theory that is based on orthogonal complements of twists and wrench spaces," J. Robot. Syst., vol. 7, no. 2, pp. 139-144, 1990.
5. J. Loncaric, "Geometric analysis of compliant mechanism in robotics," Ph.D. dissertation, Div. Appl. Sci., Harvard Univ., Cambridge, MA, 1985.
6. K. H. Hunt, Kinematic Geometry of Mechanisms. London, U. K.: Oxford Univ. Press, 1978.
7. R. S. Ball, A Treatise on the Theory of Screws. London, U. K.: Cambridge Univ. Press, 1990.
8. J. Duffy, Analysis of Mechanisms and Robot Manipulators. London, U. K.: E. Arnold, 1980.
9. R. Murray, Z. X. Li, and S. Sastry, A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC, 1994.
10. T. Yoshikawa, "Dynamic hybrid position/force control of robot manipulators-Description of hand constrains and calculation of joint driving force," IEEE J. Robot. Automat., vol. RA-3, Oct. 1987.
11. N. H. McClamroch and D. W. Wang, "Feedback stabilization and tracking of constrained robots," IEEE Trans. Automat. Contr., vol. 33, pp. 419-426, May 1988.
12. J. M. Selig, "Curvature in force/position control," in Proc. IEEE Int. Conf. Robotics Automation, 1998, pp. 1761-1766.
13. A. De Luca, C. Manes, and G. Ulivi, "Robust hybrid dynamic control of robot arms," in Proc. 28th Conf. Decision and Control, vol. 1989, pp. 2641-2646.
14. X. P. Yun and N. Sarkar, "Unified formulation of robotic systems with holonomic and nonholonomic constraints," IEEE Trans. Robot. Automat., vol. 14, pp. 640-650, Aug. 1998.
15. W. Blajer, "A geometric unification of constrained system dynamics," Multibody Syst. Dynam., vol. 1, pp. 3-21, 1997.
16. _____, "A geometrical interpretation and uniform matrix formulation of multibody system dynamics," Zeitschrift fuer Angewandte Mathematik und Mechanik 81, vol. 4, pp. 247-259, 2001.
17. J. J. Murray and G. H. Lovell, "Dynamic modeling of closed-chain robotic manipulators and implications for trajectory control," IEEE Trans. Robot, Automat., vol. 5, pp. 522-528, Aug. 1989.
18. Y. Nakamura and M. Ghodoussi, "Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators," IEEE Trans. Robot. Automat., vol. 5, pp. 294-302, June 1989.
19. A. Cole, J. Hauser, and S. Sastry, "Kinematics and control of a multifingered robot hand with rolling contact," IEEE Trans. Automat. Contr., vol. 34, pp. 398-404, Apr. 1989.
20. A. Cole, P. Hsu, and S. Sastry, "Dynamic control of sliding by robot hands for regrasping," IEEE Trans. Robot. Automat., vol. 8, pp. 42-52, Feb. 1992.
21. E. Paljug, X. Yun, and V. Kummar, "Control of rolling contacts in multi-arm manipulation," IEEE Trans. Robot. Automat., vol. 10, pp. 441-452, Aug. 1994.
22. N. Sarkar, X. P. Yun, and V. Kumar, "Dynamic control of 3-D rolling contacts in two-arm manipulation," IEEE Trans. Robot. Automat., vol. 13, pp. 534-376, Aug. 1997.
23. _____, "Control of contact interactions with acatastatic nonholonomic constraints," Int. J. Robot. Res., vol. 16, no. 3, pp. 357-373, 1997.
24. T. Yoshikawa, "Control algorithms for grasping and manipulation by multifingered robot hands using virtual truss model representation of internal force," in Proc. IEEE Int. Conf. Robotics and Automation, 2000, pp. 369-376.
25. X. Z. Zheng, R. Nakashima, and T. Yoshikawa, "On dynamic control of finger sliding and object motion in manipulation with multifingered hands," IEEE Trans. Robot. Automat., vol. 16, pp. 469-481, Oct. 2000.
26. J. P. Ostrowski, "Computing reduced equations for mechanical systems with constraints and symmetries," IEEE Trans. Robot. Automat., vol. 15, pp. 111-123, Feb. 1999.
27. J. P. Ostrowski and J. W. Burdick, "The geometric mechanics of undulatory robotic locomotion," Int. J. Robot. Res., vol. 17, no. 7, pp. 683-702, 1998.
28. W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry. New York: Academic, 1975.
29. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry. New York: Springer-Verlag, 1994.
30. Q. Lin and J. W. Burdick, "On well-defined kinematic metric functions," in Proc. IEEE Int. Conf. Robotics and Automation, 2000, pp. 170-177.
31. M Žefran, V. Kumar, and C. B. Croke, "On the generation of smooth three-dimensional rigid body motions," IEEE Trans. Robot. Automat., vol. 14, pp. 576-589, Aug. 1998.
32. R. M. Rosenberg, Analytical Dynamics of Discrete Systems. New York: Plenum, 1997.
33. M. Griffis, C. Crane, and J. Duffy, "Displacements that null forces," in Proc. IEEE Int. Symp. Intelligent Control, Arlington, VA, 1991, pp. 110-115.
34. J. Marsden and T. Ratiu, Introduction to Mechanics and Symmetry. New York: Springer-Verlag, 1994.
35. F. Bullo, "Nonlinear control of mechanical systems: A Riemannian geometry," Ph.D. dissertation, Dept. Contr. Dynam. Syst., CA Inst. Technol., Pasadena, CA, 1999.
36. C. Canudas, B. Siciliano, and G. Bastin, Theory of Robot Control. New York: Springer-Verlag, 1996.
37. D. Montana, "The kinematics of contact and grasp," Int. J. Robot. Res., vol. 7, no. 3, pp. 17-32, 1988.
38. Z. Li and J. Canny, "Motion of two rigid bodies with rolling constraint," IEEE Trans. Robot. Automat., vol. RA2-06, pp. 62-72, Feb. 1990.
39. S. R. Ploen and F. Park, "Coordinate-invariant algorithms for robot dynamics," IEEE Trans. Robot. Automat., vol. 15, pp. 1130-1135, Dec. 1999.
40. J. M. Selig, Geometrical Methods in Robotics. New York: Springer-Verlag, 1996.
41. J. F. O'Brien and J. T. Wen, "Redundant actuation for improving kinematic manipulability," in Proc. IEEE Int. Conf. Robotics and Automation, 1999, pp. 1520-1525.