Dirk Gregorius wrote:@Erwin/Morten: You are refering to non-linerar complementary problems. Where did we move from the LCP to the NCP? Which part is actually non-linear in the ODE/Bullet formulation?
According to Kenny, updating the low/high limits for the friction every iteration makes the problem non-linear. This is also why we cannot prove convergence of PGS anymore.
Thanks,
Erwin
Its because if some problem is to be an LCP problem, it must be on the form
w=Ax+b>=0, x>=0, w^Tx =0.
So, when we want to model the coupling between normal force magnitudes and friction force magnitudes, the only way to put that into the form of an LCP is to introduce extra variables, like Stewart and Trinkle did (they use lambda as symbol in some of the papers if I recall). When you do that, you end up with a system matrix that cannot by solved by PGS anymore. Then, someone came up with the idea of dropping the friction cone approximation from Stewart-Trinkle, and just projecting the friction forces one by one in the PGS loop. (like its done in bullet?), That showed to work out well, but it is not on the LCP form.
