Oblique coordinate control for advanced motion control applied to micro-macro bilateral control

Abstract-A controller for oblique coordinates is proposed in this paper. In an oblique coordinate, certain vector is expressed by two forms. One is a covariant vector, the other is contravariant vector. Usually, position is described by a contravariant vector, and force is given by a covariant vector. In order to realize hybrid control in a oblique coordinate, position and force should be unified into same vectors. These vectors are synthesized by a metric tensor, and a novel hybrid controller for oblique coordinate is obtained. The dynamic properties are given by "task mass matrix". By this method, whatever tasks given by position and force would be decoupled. Micro-macro bilateral is considered as an example of the oblique coordinate control. It was confirmed by some simulations and an experiment.