Similarity and Invariance in Scaled Bilateral Telemanipulation

Abstract

This paper addresses the issue of dynamic similarity and intensive property invariance in scaled bilateral manipulation, and offers a design methodology based on these considerations. The methodology incorporates dimensional analysis techniques to define a set of necessary and sufficient conditions to preserve the dynamic similarity of any physical environment. These techniques are utilized to demonstrate that any combination of kinematic and force scaling in a bilateral manipulator control structure will preserve the dynamic similarity of any physical environment. Any combination of kinematic and force scaling, however, will not in general maintain intensive property invariance between the original and scaled physical environments, and thus will result in lost information. As such, the dimensional analysis methods are further utilized to form the basis of a constrained optimization problem that enables selection of a force scaling factor that minimizes the intensive distortion of the environment. The proposed formulation is applicable to any physical environment, including those that are nonlinear and contain multiple degrees of freedom. Further, the formulation does not require an exact environmental model, provided the parameters that influence the environment are known. The proposed techniques are particularly relevant to bilateral manipulation of a microscopic environment (i.e., macro-micro bilateral manipulation), since such environments are difficult to model exactly and are largely influenced by nonlinear effects.