Quasi-static analysis of planar sliding using friction patches

Flat objects lying on a surface are hard to grasp, but could be manipulated by sliding along the surface in a non-prehensile manner. This strategy is commonly employed by humans as pre-manipulation, for example to bring a cell phone to the edge of a table to pick it up. To endow robots with a similar capability, we introduce a mathematical model of planar sliding by means of a soft finger. The model reveals various aspects of interaction through frictional contacts, which can be used for planning and control. Specifically, using a quasi-static analysis we are able to derive a hybrid dynamical system to predict the motion of the object and the interaction forces. The conditions for which the object sticks to the friction patch, pivots, or completely slides against it are obtained. It is possible to find fixed points of the system and the path taken by the object to reach such configurations. Theoretical as well as comprehensive experimental results are presented.