Multirate haptic simulation achieved by coupling finite element meshes through Norton equivalents

This paper introduces a methodology to simulate the dynamics of deformable viscoelastic 3D bodies in real-time for haptic interaction. The method is based upon a finite element approach. The central idea in this scheme is to reduce the computation required in regions which are to the periphery of the region of interaction between the virtual haptic device and the virtual body. This is accomplished by implementing a multilayer finite element mesh. The top layer, or parent, consists of a coarse mesh of the entire body; child meshes represent sub-regions of the coarse mesh, but have a much finer resolution. By using equivalent impedances to relate the two meshes, it is possible to decouple the coarse and fine regions; this enables the system to not only to have different resolutions in different regions, but also allows the parent and child meshes to be updated at different frequencies. The multilayer mesh also addresses numerical integration issues.