Mechanical Manipulation Using Reduced Models of Uncertainty

Abstract: In this paper we describe methods applicable to the modeling and control of mechanical manipulation problems, including those that experience uncertain stick/slip phenomena. Manipulation in unstructured environments often includes uncertainty arising from various environmental factors and intrinsic modeling uncertainty. This reality leads to the need for algorithms that are not sensitive to uncertainty, or at least not sensitive to the uncertainty we can neither model nor estimate. The particular contribution of this work is to point out that the use of an abstraction, in this case a kinematic reduction, not only reduces the computational complexity but additionally simplifies the representation of uncertainty in a system. Moreover, this simplified representation may be directly used in a stabilizing control law. The end result of this is two-fold. First, modeling for purposes of control is made more straight-forward by getting rid of some dependencies on low-level mechanics (in particular, the details of friction modeling). Second, the online estimation of the relevant uncertain variables is much more elegant and easily implementable than the online estimation of the full model and its associated uncertainties.