Contact-Rich Assembly: Peg in Hole

Inserting a peg into a hole is the classic assembly task. If the hole is even a fraction of a millimeter off, a stiff, position-controlled robot jams the peg against the edge, and forces shoot up. A compliant robot, one that gives way sideways, lets the chamfer slide the peg into place, the way a person does without thinking.

Control Hole offset from the expected spot Sideways stiffness (compliant)

Why compliance helps

The robot pushes down. When the peg touches the chamfer, a slanted edge at angle $\phi$, the contact pushes back along the chamfer's normal, which has a sideways part. A compliant robot with sideways stiffness $k$ moves sideways under that force:

$$F_{\text{side}} = F_{\text{down}}\tan\phi \qquad \Delta x = \frac{F_{\text{side}}}{k}$$

A stiff robot has huge $k$, so it barely moves sideways, and the force builds until the peg jams or something breaks. Passive devices called remote center compliance wrists were invented to do this mechanically.

What to notice

With no offset both methods slide right in. Add a few millimeters of offset and stiff control slams into the chamfer edge, so the force plot spikes and the peg stops. Compliant control drifts sideways along the chamfer and drops in with small forces. A very soft setting also works but wobbles more. If the hole is off by more than the chamfer's width, the peg lands on the flat top, there is no sideways push to follow, and even the compliant robot jams. Modern robots get this compliance in software, through impedance control, or by learning insertion policies.