Deformable Objects: Cloth and Cables

A rigid object has six numbers for its pose. A cable or a towel has a shape that can change at every point along it, so its state has hundreds or thousands of numbers, and most of them cannot be controlled directly. Folding laundry and routing cables are still open problems in robotics for exactly this reason.

Cable segments Bending stiffness Damping

Drag the gripper to route the cable around the pegs.

A cable as a chain

This cable is a chain of point masses joined by fixed-length links, simulated with Verlet integration and repeated length corrections, a common technique called position-based dynamics. For $n$ points in 2D, the state has

$$\dim(\mathbf{x}) = 2n \text{ positions} + 2n \text{ velocities}$$

yet the robot directly controls only the one point it holds.

What to notice

Move the gripper and the motion ripples down the cable, with the far end lagging and swinging. To wrap it around a peg, you have to plan around that lag and use the pegs as helpers, much as people do. More segments make a more realistic cable but a bigger state to reason about. Robots that handle cables and cloth usually combine simulation like this with vision that tracks the shape, and increasingly with learned models.