Engineering Transactions, 39, 3-4, pp. 325-349, 1991

New Computational Algorithms for a Discrete Kalman Filter in Robot Dynamics

K. Kozłowski
Robotics and Automation Laboratory, Technical University of Poznań

The equivalence between the standard Newton-Euler formulation of the equation of motion for an n-link manipulator and the inverse dynamics equations has been proved in this paper. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson­Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on the new inverse and forward dynamics algorithms derived from the two-point boundary value problem establish the same level of confidence as exists for current meth­ods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order 0(n), the categorization procedure has been implemented in this work. Software packages for both robot dynamics algorithms have been developed in Pascal and run on an IBM compatible computer. The results obtained by Rodriguez have been extended by the present author to an arbitrary manipulator with both rotational and translational joints.

Full Text: PDF


C.H.AN, C.G.ATKESON and J.M.HOLLERBACH, Model based control of a robot manipulator, MIT Press, 1988.

B.ARMSTR0NG, O.KHATIB and J.BURDICK, The explicit dynamic model and inertial parameters of the Puma 560 arm, Proc. of the 1986 Intern. Conf. on Robotics and Automation, 510-518, San Francisco 1986.

G.J.BIERMAN, Factorization methods for discrete sequential estimation, Academic Press, 1977.

H.BRANDL, R.JOHANNI AND M.OTTER, A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix, Proc. of the IFAC/IFIP/IMACS Intern. Symp. on the Theory of Robots, 365-370, Vienna. 1986.

A.E.BRYSON and Y.C.HO, Applied optimal control, Blaisdell 1969.

J.J.CRAIG, Introduction to robotics mechanics and control, Addison-Vesley Publ. Comp., 1986.

R.FEATHERSTONE, The calculation of robot dynamics using articulated-body inertias, lnt.J.Rob.Res., 2, 13-29, 1983.

A.FIJANY and A.K.BEJCZY, A class of parallel algorithms for computation of the manipulator inertia matrix, IEEE Trans. on Robotics and Automation, 5, 5, 600- 615, 1989.

M.GMIĄT AND P.MAĆKOWIAK, Application of Kalman filtering technicques in robot dynamics algorithms, M.S.Thesis [in Polish], Poznań Technical University, 1990.

J.M.HOLLERBACH, A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity, IEEE Trans.Syst., Man and Cybernet., SMC-10, 11, 730-736, 1980.

R.E.KALMAN, A new approach to linear filtering and prediction problems, ASME Trans. J. Basic Eng., vol. D, 35-45, 1960.

W.KHALIL and J.F.KLEINFINGER, Minimum operations and minimum parameters of the dynamic models of tree structure robots, IEEE J. Rob. and Aut., RA-3, 6, 517-526, 1987.

P.K.KHOSLA, Real-time control and identification of direct-drive manipulatora, Ph. D. Thesis , Carnegie-Mellon University, 1986.

K.KOZLOWSKI, Robot dynamics algorithms using Kalman filtering and smoothing techniques [in Polish], in: Tech.Rep. 89-007 written by KASIŃSKI, K.KOZŁOWSKI and M.PIŃCZAK, 21-94, Poznań Technical University, 1989.

K.KOZŁOWSKI and W.WRÓBLEWSKI, Efficient 0(n) computation of the inverse and forward dynamics algorithm [in Polish], Tech. Rep.90-004, Poznań Technical Uni­versity, 1990.

P.MAROSZ, Robot dynamics algorithms and Kalman filtering techniques [in Polish], M.S.Thesis , Poznań Technical University, 1989.

G.RODRIGUEZ, Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics, JPL Publ., 86-48, NASA, 1986.

G.RODRIGUEZ, Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics, IEEE J.Rob. and Aut., RA-3, 6, 624-639, 1987.

G.RODRIGUEZ, Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing, 6th VPI/US Symp. Control of Large Structures, VA, 45-60, Blacksburg, June 1987.

G.RODRIGUEZ and K.KREUTZ, Recursive mass matrix factorization and inversion. An operator approach to open-and closed-chain multibody dynamics, JPL. Publ., 88-11, NASA, March 15, 1988.

R.RODRIGUEZ, Spatial operator approach to flexible manipulator inverse and for­ward dynamics, Proc. of the 1990 Intern. Conf. on Robotics and Automation, 845-850, Cincinnati 1990.

M.VUSKOVIC, TING LIANG and KASI ANANTHA, Decoupled parallel recursive Newton - Euler algorithm for inverse dynamics, Proc. of the 1990 IEEE Intern. Conf. on Robotics and Automation, S-32-838, Cincinnati 1990.

M.W.WALKER and D.E.ORIN, Efficient dynamics computer simulation of robotics mechanisms, J.Dyn. Syst., Measur. and Contr., 104, 205-211, 1982.

J.WITTERBURG, Dynamics of systems of rigid bodies, R.G.Teuber, Stuttgart 1977.

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland