A symbolic analysis of the minimum dynamic parameters for the closed-chain manipulator using computer algebra software

Abstract This paper presents a symbolic analysis method of the minimum set of dynamic parameters for general closed-chain manipulator by means of the computer algebra software. A key step is to determine fundamental functions that are necessary and sufficient to express the coefficient matrix of dynamic parameters. The linear independence of column vectors of the matrix is tested using the fundamental functions. The paper also discusses a sufficient condition in which the dynamics of the closed-chain mechanism is equivalent to that of the serial-link mechanism. To illustrate the merits of the new method, minimum sets of dynamic parameters of three closed-chain mechanisms are examined using the computer algebra software called “Maple V.”

[1]  Wisama Khalil,et al.  A direct determination of minimum inertial parameters of robots , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[2]  Koichi Osuka,et al.  Base parameters of manipulator dynamic models , 1990, IEEE Trans. Robotics Autom..

[3]  Haruhisa Kawasaki,et al.  Parameter Identification of Mechanical Manipulators , 1986 .

[4]  Hirokazu Mayeda,et al.  Base parameters of dynamic models for general open loop kinematic chains , 1991 .

[5]  Koichi Osuka,et al.  Adaptive Control for Nonlinear Mechanical Systems , 1986 .

[6]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[7]  Fouad Bennis,et al.  Calculation of the base inertial parameters of closed-loops robots , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[8]  Yoshihiko Nakamura,et al.  Principal base parameters of open and closed kinematic chains , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[9]  Bruce W. Char,et al.  Maple V Library Reference Manual , 1992, Springer New York.

[10]  W. Khalil,et al.  The use of the generalized links to determine the minimum inertial parameters of robots , 1990, J. Field Robotics.

[11]  Yuan F. Zheng,et al.  Computation of input generalized forces for robots with closed kinematic chain mechanisms , 1985, IEEE J. Robotics Autom..

[12]  Haruhisa Kawasaki,et al.  Minimum dynamics parameters of tree structure robot models , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[13]  Yoshihiko Nakamura,et al.  Dynamics Computation of Parallel Mechanisms , 1992 .

[14]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[15]  Fouad Bennis,et al.  Minimum inertial parameters of robots with parallelogram closed loops , 1991, IEEE Trans. Syst. Man Cybern..

[16]  Yoshihiko Nakamura,et al.  Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators , 1989, IEEE Trans. Robotics Autom..

[17]  Christopher G. Atkeson,et al.  Estimation of Inertial Parameters of Manipulator Loads and Links , 1986 .

[18]  Haruhisa Kawasaki,et al.  MINIMUM DYNAMICS PARAMETERS OF ROBOT MODELS , 1991 .

[19]  Koichi Osuka,et al.  A New Identification Method for Serial Manipulator Arms , 1984 .

[20]  Haruhisa Kawasaki,et al.  An Efficient Computational Algorithm for Adaptive Manipulator Control , 1993 .