Unfortunately, the motion of a pushed object is usually unpredictable due to an uncertain distribution of support forces. With multiple contact points between the pusher and the slider, however, it is possible to find pushing directions that cause the object to remain fixed to the manipulator. These are called stable pushing directions. These stable pushing directions can be used to find pushing plans to maneuver objects among obstacles. The stable pushing directions amount to a set of nonholonomic inequality constraints.
Our focus has been on stable pushing with line contact. Given the geometry of a polygonal part, its center of mass (strictly, its center of friction), a set of pushing edges, and the friction coefficient at the pushing edges, we first calculate the set of stable pushing directions. These stable pushing plans are then used to automatically find a pushing sequence to move the object to a goal position. An example plan is shown below.