Dynamics for robot control: Friction modeling and ensuring excitation during parameter identification

To accurately control any mechanism it is necessary to know the relationship between applied forces and the resultant motion. These forces may be simple to compute, as is the case for many single degree of freedom machines; or they may be quite complex. Two steps toward the accurate prediction of motion forces are presented in this thesis: an experimental investigation of friction, and a study of the sensitivity of robot inertial parameter identification methods to noise.; The friction study begins with an experimental investigation of the most basic properties required for predictive modeling: repeatability and structure. Friction is found to be surprisingly repeatable; position dependence is found, and a destabilizing effect--the Stribeck effect--is observed at low velocity. The experimental work is specific to a particular mechanism: the PUMA 560 arm; but many of the observations, particularly the study of the Stribeck effect, will extend to a broad class of machines. Using the friction model developed and an inertial model reported elsewhere, open-loop control of the PUMA robot is carried out, demonstrating the accuracy of the friction model.; When designing an identification experiment for a system described by non-linear functions, such as those of manipulator dynamics, it is necessary to consider whether the excitation is sufficient to provide an accurate estimate of the parameters in the presence of experimental noise. It is shown that the convergence rate and noise immunity of a parameter identification experiment depend directly upon the condition number of the input correlation matrix, a measure of excitation. The sensitivity of an identification experiment to unmodeled dynamics is also studied; a dimensionless measure of this sensitivity--Bias Susceptibility--is proposed and related to excitation. The issue how exciting a trajectory may be is addressed, and a method is presented to maximize the excitation. Two identification experiments reported in the literature are studied; analysis of these experiments shows that intuitively selected trajectories may provide poor excitation and that considerable improvement results from employing the optimization to maximize excitation.