Comments on "Direct calculation of minimum set of inertial parameters of serial robots"

The paper presented by Gautier and Khalil [1] gives a direct and efficient method to calculate most of the minimum inertial parameters of serial robots. Some parameters concerning the translational links between the first rotational joints which are not parallel need particular calculation, partial results concerning the case where these links are either perpendicular or parallel are given in the paper [1]. This correspondence presents a direct solution to this particular case, such that all the minimum inertial parameters can be obtained directly without calculating the energy or the dynamic model of any link. ICalculation of the minimum inertial parameters The minimum inertial parameters can be calculated from the standard inertial parameters by eliminating the parameters which have no effect on the dynamic model and those which can be regrouped to some others. The expression of the total energy (potential +kinetic) which is linear in the inertial parameters can be used to determine these parameters, it can be seen that the energy of the robot is given as: H = ∑ j=1 n hj Xj (1) where: Xj represent the standard inertial parameters of link j, and hj contains the coefficients of the inertial parameters in the energy expression. It can be seen that [1]: Xj = [ ] XXj XYj XZj YYj YZj ZZj mXj mYj mZj mj hj = [ ] hXXj hXYj hXZj hYYj hYZj hZZj hmXj hmYj hmZj hmj The expressions of the elements of hj, can be found in [2]. Based on relation (1) the following results can be given: aAn inertial parameter Xi has no effect on the dynamic model if: