Dynamic Simulation of n-Axis Serial Robotic Manipulators Using a Natural Orthogonal Complement

Abstract

The concept of natural orthogonal complement is used to devise an algorithm that allows the systematic derivation of the n × n generalized inertia matrix of a general n-axis manipulator. To compute the joint accelerations from the governing equations of motion, two methods are presented, one based on the Cholesky decomposition of the generalized inertia matrix, and one based on a combination of mini mum-norm and least-squares approximations of underdeter mined and overdetermined linear algebraic systems, respec tively. Based on these methods, two corresponding algorithms for the dynamic simulation of general n-axis serial robotic manipulators are presented. The comparison of the two methods with those existing in the literature shows that the methods presented here are computationally more ef ficient. A simulation example of a well-known industrial manipulator is given.

Get full access to this article

View all access options for this article.

References

Angeles, J. , Ma, O. , and Rojas, A. , 1987. An algorithm for the inverse dynamics of general n-axis robotic manipulators using Kane's formulation of dynamic equations. Technical Report, Department of Mechanical Engineering and Robotic Mechanical Systems Laboratory—McRCIM, McGill University, Montreal.

Angeles, J. , and Lee, S. , 1987. The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement. To appear in ASME J. Applied Mechanics.

Goldenberg, A.A. 1982. Software development for simulation of a robotic-manipulator. Technical Report, Dept. of Mechanical Engineering, University of Toronto, Toronto.

Golub, G.H. , and Van Loan, C.F. 1983. Matrix computations. The Johns Hopkins University Press, Maryland.

Hartenberg, R.S. , and Denavit, J. 1964. Kinematic Synthesis of Linkages. New York: McGraw-Hill.

Huston, R.L. , and King, T.P. 1986. Dynamics of redundant robots — inverse solution . Robotica 4:263-267.

Kane, T.R. , and Levinson, D.A. 1983. The use of Kane's dynamical equations in robotics. Int. J. Robotics Res. 2(3):3-21.

Kazerounian, K. , and Gupta, K.C. 1986. Manipulator dynamics using the extended zero reference position description. IEEE J. Robotics and Automation RA-2: (4):221-224.

Lawson, L. , and Hanson, R.J. 1974. Solving List Square Problems Engelwood Cliffs: Prentice Hall.

10.

Ma, O. 1987. Dynamics of serial-type n-axis robotic manipulators. M.Eng. Thesis, Department of Mechanical Engineering, McGill University, Montreal.

11.

Singh, R.P. , and Likins, P.W. 1985. Formulation of equations of motion for systems subject to constraints. J. Applied Mechanics 52:465-470.

12.

Swartz, N.M. 1984. Arm dynamics simulation. J. Robotic Systems 1 (1):83 - 100.

13.

Walker, M.W. , and Orin D.E. , 1982. Efficient dynamic computer simulation of robotic mechanisms . J. Dynamic Sys., Meas., and Control 104:205-211.

14.

Wang, L.T. , and Ravani, B. 1985. Recursive computations of kinematic and dynamic equations for mechanical manipulators. IEEE J. Robotics and Automation RA-1(3):124-131.