What is the meaning of parameter Kcfm in PGS Formulation?

[Jack2016]

I read K.Erlenben book <<Stable,Robust And Verstile>> Chapter 6 to learn the PGS in Bullet



When I see the src code in Bullet, I think the Result of the Equation is the Constraint Force Fc*deltaT = dP (delta Impulse).
But I can't understand the param 'Kcfm' in the formulation above,constraint force mixing,it's a diagonal matrix in vector form
Which paper is about 'Kcfm'?

Code: Select all

	void tbSequentialImpulseConstraintSolver::ResolveSingleConstraintRowLowerLimit(tbSolverBody& body1, tbSolverBody& body2, const tbSolverConstraint& c)
	{
		tbScalar deltaImpulse = c.m_rhs - tbScalar(c.m_appliedImpulse)*c.m_cfm;
		const tbScalar deltaVel1Dotn = c.m_contactNormal.Dot(body1.m_deltaLinearVelocity) + c.m_relpos1CrossNormal.Dot(body1.m_deltaAngularVelocity);
		const tbScalar deltaVel2Dotn = -c.m_contactNormal.Dot(body2.m_deltaLinearVelocity) + c.m_relpos2CrossNormal.Dot(body2.m_deltaAngularVelocity);

		deltaImpulse -= deltaVel1Dotn*c.m_jacDiagABInv;
		deltaImpulse -= deltaVel2Dotn*c.m_jacDiagABInv;

		const tbScalar sum = tbScalar(c.m_appliedImpulse) + deltaImpulse;
		if (sum < c.m_lowerLimit)
		{
			deltaImpulse = c.m_lowerLimit - c.m_appliedImpulse;
			c.m_appliedImpulse = c.m_lowerLimit;
		}
		else
		{
			c.m_appliedImpulse = sum;
		}

		if (body1.m_invMass > tbScalar(0.))
			body1.ApplyImpulse(c.m_contactNormal*body1.m_invMass, c.m_angularComponentA, deltaImpulse);
		if (body2.m_invMass > tbScalar(0.))
			body2.ApplyImpulse(-c.m_contactNormal*body2.m_invMass, c.m_angularComponentB, deltaImpulse);
	}

Code: Select all

tbScalar restitution = 0.f;
tbScalar positionalError = solverConstraint.m_rhs;//already filled in by getConstraintInfo2
tbScalar	velocityError = restitution - rel_vel;// * damping;
tbScalar	penetrationImpulse = positionalError*solverConstraint.m_jacDiagABInv;
tbScalar	velocityImpulse = velocityError *solverConstraint.m_jacDiagABInv;
solverConstraint.m_rhs = penetrationImpulse + velocityImpulse;
solverConstraint.m_appliedImpulse = 0.f;

In the Formulation above,I'm clear about the posErr and velocityErr,But Berror doesn't have the param 'restitution',
so what's the meaning of 'restitution' and which paper is about it.

[Dirk Gregorius]

http://box2d.org/files/GDC2011/GDC2011_ ... raints.pdf

[Jack2016]

http://box2d.org/files/GDC2011/GDC2011_ ... raints.pdf

Thanks, Drik

The Paper <<Soft Constraints>> by Erin is very helpful to me.

I also find the entire derivation about softness post by Erin https://bulletphysics.org/Bullet/phpBB3 ... f=4&t=1354

v2new = v2damaged + invM * JT * dP
J * (v2damaged + invM * JT * dP) + softness * P + softness * dP + bias = 0

(J * invM * JT + softness) * dP = -(J * v2damaged + softness * P + bias)

the softness is CFM

But I'm still not clear about the parameter 'restitution' which is about damping.
'restitution' is not in the Formula above,any one can make it clear ? thanks

[Dirk Gregorius]

This might be unrelated to the soft parameters. Normally we solve for a relative velocity of zero at a contact point or limit, but you can also imagine to solve to revert some of the approaching velocity to model bouncy contacts (e.g. a ball) or limits.

https://en.wikipedia.org/wiki/Coefficie ... estitution