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 (e.g., joint speeds) and configuration (e.g., closeto-singularity) 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 robotic manipulator (5DOF 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 realsystem 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 the mobile robots (multiple iRobots).It is shown that one can rely on less demanding RMT-based formulation and yet meets the acceptable accuracy.