New Computational Algorithms for a Discrete Kalman Filter in Robot Dynamics - Kozłowski, K. (Engineering Transactions, 1991)
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.