Anyone who has worked with Position-Based Dynamics (PBD) in production will know that the constraint stiffness is heavily dependent on the number of iterations performed by the solver. Regardless of how you set the stiffness coefficients, the solver will converge to an infinitely stiff solution given enough iterations.

We have a new paper that solves this iteration count and time step dependent stiffness with a very small addition to the original algorithm. Here is the abstract:

We address the long-standing problem of iteration count and time-step dependent constraint stiffness in position-based dynamics (PBD). We introduce a simple extension to PBD that allows it to accurately and efficiently simulate arbitrary elastic and dissipative energy potentials in an implicit manner. In addition, our method provides constraint force estimates, making it applicable to a wider range of applications, such as those requiring haptic user-feedback. We compare our algorithm to more expensive non-linear solvers and find it produces visually similar results while maintaining the simplicity and robustness of the PBD method.

The method is derived from an implicit integration scheme, and produces results very close to those given by more complex Newton-based solvers, as you can see in the submission video:

I will be presenting the paper at Motion in Games (MIG) in San Francisco next month. If you're in the area you should attend, these smaller conferences are usually very nice.