Nonprehensile Manipulation: Pushing

Robots do not always need to grasp. Pushing, sliding, and tipping, called nonprehensile manipulation, can move objects that are too big, too flat, or too awkward to pick up. The catch is that the object's motion depends on exactly where and in which direction it is pushed, and on how friction is spread under it.

Push point offset from the center Steer the pusher to keep the box on course

The quasi-static push

Pushed slowly, a box slides with friction spread over its base. A push through the center of friction moves it straight. A push offset by $d$ also makes it turn. A common approximation, the ellipsoidal limit surface, relates the push force $\mathbf{F}$ and the torque it makes to the box's motion:

$$\mathbf{v} \propto \mathbf{F}, \qquad \omega \propto \frac{d\,\lVert\mathbf{F}\rVert}{c^2}$$

where $c$ is a length set by the box's size and how its weight is spread.

What to notice

Push dead center and the box slides straight to the goal. Push off-center and it turns away from the contact, drifting off course more and more. Turn on steering and the pusher moves sideways to keep its contact behind the box's center relative to the goal, which corrects the drift: this is the basic idea of push planning. Pushing is used to clear clutter, to line objects up for grasping, and by mobile robots that move carts.