The Calculation of Robot Dynamics Using Articulated-Body Inertias

This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to open-loop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulated-body inertias, which represent the inertia properties of collections of rigid bodies connected together by joints allowing constrained relative motion between the bodies. A new, matrix-based notation is introduced to represent articulated-body inertias and other spatial quantities. This notation is used to develop the algorithm, and results in a compact representation of the equations. The new algorithm has a computational requirement that varies linearly with the number of joints, and its efficiency is compared with other published algorithms.

[1]  J. D. Everett.  A Treatise on the Theory of Screws , 1901, Nature.

[2]  L. Brand.  Vector and tensor analysis , 1947 .

[3]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[4]  F. Dimentberg.  The screw calculus and its applications in mechanics , 1968 .

[5]  A. T. Yang.  Inertia Force Analysis of Spatial Mechanisms , 1971 .

[6]  M. Vukobratovic,et al.  Dynamics of articulated open-chain active mechanisms , 1976 .

[7]  M. Vukobratović,et al.  Computer method for dynamic model construction of active articulated mechanisms using kinetostatic approach , 1978 .

[8]  J Rooney.  A Comparison of Representations of General Spatial Screw Displacement , 1978 .

[9]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[10]  R. Huston,et al.  Dynamics of Multirigid-Body Systems , 1978 .

[11]  David E. Orin,et al.  Kinematic and kinetic analysis of open-chain linkages utilizing Newton-Euler methods , 1979 .

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

[13]  John M. Hollerbach,et al.  A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[15]  William M. Silver.  On the Equivalence of Lagrangian and Newton-Euler Dynamics for Manipulators , 1982 .