Efficient O(n) computation of the inverse and forward dynamics algorithms

One approach to finding the inverse dynamics equations is to formulate the system dynamics and kinematics as a two-point boundary-value problem. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on inverse and forward dynamics algorithms derived from the two-point boundary-value problem establish the same level of confidence which exists for current methods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order O(n), the categorization procedure has been implemented in this work. Software packages for robot dynamics algorithms have been developed in Pascal and run on an IBM compatible computer.<>