Title: Matrix-Based Characterization of the Motion and Wrench Uncertainties in Robotic Manipulators,
Abstract: Characterization of the uncertainty in robotic manipulators is the focus of
this paper. Based on the random matrix theory (RMT), we propose uncertainty
characterization schemes in which the uncertainty is modeled at the macro
(system) level. This is different from the traditional approaches that model
the uncertainty in the parametric space of micro (state) level. We show that
perturbing the system matrices rather than the state of the system provides
unique advantages especially for robotic manipulators. First, it requires only
limited statistical information that becomes effective when dealing with
complex systems where detailed information on their variability is not
available. Second, the RMT-based models are aware of the system state and
configuration that are significant factors affecting the level of uncertainty
in system behavior. In this study, in addition to the motion uncertainty
analysis that was first proposed in our earlier work, we also develop an
RMT-based model for the quantification of the static wrench uncertainty in
multi-agent cooperative systems. This model is aimed to be an alternative to
the elaborate parametric formulation when only rough bounds are available on
the system parameters. We discuss that how RMT-based model becomes advantageous
when the complexity of the system increases. We perform experimental studies on
a KUKA youBot arm to demonstrate the superiority of the RMT-based motion
uncertainty models. We show that how these models outperform the traditional
models built upon Gaussianity assumption in capturing real-system uncertainty
and providing accurate bounds on the state estimation errors. In addition, to
experimentally support our wrench uncertainty quantification model, we study
the behavior of a cooperative system of mobile robots. It is shown that one can
rely on less demanding RMT-based formulation and yet meets the acceptable
accuracy.