Drake: Add stiction model to RigidBodyPlant

[sherm1]

Per discussion with @siyuanfeng-tri at the Utah offsite, he has an urgent need for stiction (static friction) for his foot-contact application. The current friction model isn't providing the expected behavior.

Ultimately stiction should be modeled by adding and removing a no-slip constraint. However, we can get a fair approximation now using a continuous "creep" model that limits slip velocity to below an arbitrary tolerance while generating the appropriate constraint force.

Related: #1978 (should replace discontinuous normal force model with a smooth one).

[amcastro-tri]

I can give this a try once #4033 lands. Probably worth defining now the "materials library"?

[amcastro-tri]

Excellent. @siyuanfeng-tri will provide us with a cleaner PR from #4004 for us to play with.

[siyuanfeng-tri]

4152 is that pr.

[sherm1]

@amcastro-tri, some notes on a creep stiction model:
For a compliant contact we have a normal force model Fn=Fn(x,xdot) and a tangential force model Ft=mu(v)*Fn. Here Fn and Ft are scalars, with Fn >= 0; x is penetration depth, v is slip speed. The friction model is mu(v), and we want it to look something like this:

Ignoring viscous friction for now, the parameters to this model are static and dynamic coefficients of friction mu_s and mu_d, and a "transition velocity" v_t that sets the largest "creep" velocity that is acceptable during stiction (this can be set very small at the cost of increasing stiffness). The simplest model I know of that provides this shape is the Hollars model:

// CAUTION: uv and v must be dimensionless in multiples of transition velocity.
// Const 9 flops + 1 divide = approx 25 flops.
// This calculates a composite coefficient of friction that you should use
// to scale the normal force to produce the friction force.
// Curve is similar to Stribeck above but more violent with a discontinuous
// derivative at v==1.
inline static Real hollars(Real us, Real ud, Real uv, Real v) {
    const Real mu =   std::min(v, Real(1))*(ud + 2*(us-ud)/(1+v*v))
                    + uv*v;
    return mu;
}

(code snatched from Simbody)

That's the basic idea. The Simbody code for friction in a Hertz/Hunt&Crossley contact is here.

[amcastro-tri]

Thank you @sherm1, I will study that code and I'll get back to you.

[sherm1]

P.S. Simbody actually uses a smoother function called stribeck().

[amcastro-tri]

Thank you. Do you recommend then implementing this stribeck() function instead? is it more computationally intensive than hollars()?

[sherm1]

They are both very cheap. stribeck() takes a little more code but runs faster overall (typically 10-20% faster) because its smooth profile lets larger integration step sizes be used during stiction<->sliding transitions. So I do recommend stribeck().

[RussTedrake]

fwiw -- @mposa used stribeck with some success when examining static friction experimentally on Atlas.

[amcastro-tri]

I just found out in #4232 that the problem with the Valkyrie simulation is not the contact model (which of course can be improved) but a number of collision elements not being filtered out.

[sherm1]

@SeanCurtis-TRI is working on the collision filter fix as we type.

[SeanCurtis-TRI]

Yep.

[amcastro-tri]

Delighted to review this @SeanCurtis-TRI. I just un-assigned myself as part of my triage.