Minimal dynamic: Characterization of tree-like multibody systems

The dynamic model of tree-like multibody systems is linear with respect to the parameters of mass distribution for instance when barycentric parameters are used. Thus, assuming that the parameters related to the kinematics are perfectly known, these quantities can be estimated through linear regression techniques. The necessary data are obtained by measuring the joint forces and/or torques and the resulting motion given in terms of positions, velocities and accelerations. An alternative method uses measurements of the reaction forces and torques applied to the bedplate. The linearity of the dynamic and reaction models with respect to the barycentric quantities does not however imply that the latter constitute the minimum set of parameters characterizing the mass distribution of the system. In other words, some barycentric parameters may disappear from the models or may be redundant in the sense that they appear only via linear combinations. In the first case they are not identifiable, while in the second case the linear regression technique leads to estimated values which are correct for the combinations but can be erroneous for the individual parameters. The various options taken to derive the dynamic and reaction models by use of the ROBOTRAN programme are briefly reviewed. Then the rules leading to the minimal parametrization are presented and illustrated by means of a practical example related to a robot calibration problem.