Efficient Computation of the Generalized Inertial Tensor of Robots by Using the Gibbs- Appell Equations

In this paper, a method for computing the generalized inertial tensor of manipulator robots is described as based on the Gibbs-Appell equations. The method presents the formulation of the coefficients of the mentioned tensor by means of the Hessian of the Gibbs function. An efficient recursive algorithm is proposed, with a complexity of O(n) order, which is used to produce a program in FORTRAN. A numerical example simulates the movement of a PUMA robot. The results obtained from the simulation are compared with those obtained by using other known methods. 1. Introduction The direct dynamic problem or simulation problem of robots is a process that involves the computing of accelerations, velocities and orientations or joint positions for a manipulator, when the forces exerted by the actuators are given. The simulation problem for mechanical systems consists of two parts: the first one requires the calculation of joint accelerations from the movement equations; and the second one involves the integration of those equations. The joint accelerations can be obtained by two different approaches. In the first one a system of differential equations is proposed, obtained, and solved. In the second approach, the accelerations are calculated recursively by propagating the movement and constraint forces throughout the mechanism. The algorithms derived from the first approach have usually a computational complexity of O(n) order, mainly due to the fact that a linear system must be solved. Papers [1] and [2] are