How do I fix objects "popping" or jittering in physics engine?

Question

I've got a simple physics engine that solves collisions by simply correcting the position of overlapping bodies (just circles for now) directly, as opposed to just changing the velocity or applying an impulse. Velocity is only changed after impacts are already resolved, or during the integration part.

I've had the problem that in heaps of objects the top objects apply too much pressure (this exists implicitly, there's no pressure modelling in the algorithm) on the objects at the bottom of the heap, which results in them getting pushed through floors, etc.

I wanted to fix this by sorting the objects by their y-coordinate, so the collisions are resolved bottom-up. But now, the engine shows weird popping behavior for objects which should actually be at rest (see gif)

Without just giving you the source code - what could this be?

Answer 1

One solution I have found when using position correcting is to have a few iterations and vary the strength with each iteration.

doPhysics();

int num_iterations = 5;
for(int iteration=0; iteration<num_iterations; ++iteration)
{
    float strength = float(iteration+1)/num_iterations;
    correctPositions(strength);
}

So the first iteration has a strength of 1/num_iterations and the last has a strength of 1. This makes my simulations smoother and more stable than simply using the same number of iterations with a fixed strength.

Answer 2

Your problem lies in the fact that you have no "resting" state for your bodies. Any physics system has an amount of energy, be that kinetic, thermal, and so on. In reality, solid object deform slightly, and tranform some kinetic energy into heat, though it is hardly measurable. It's also worth noting that in reality there is no such thing as a completely solid object. Even dense materials, like diamond, have space in between the atoms, giving the atomic structure room to flex, and absorb kinetic energy.

To make this relevant, resting bodies are in a state where the only forces in effect is the "normal force", which is to say, the force that prevents bodies from floating through each other. The magnitude of that normal force, is proportional to the density of the objects, and how far they have penetrated each other.

Physics engines call this value "slop".

Here's the trick: Calculate the slop, and correct the position of the bodies, and apply the normal force, based on the relative velocity of the two bodies. during the update of the bodies themselves, calculate the kinetic energy of each body. If it is below a minimum value, then put the body to sleep, until a force of sufficient magnitude is applied to it. (usually twice the minimum value).

Answer 3

Why not add a "sticky" surface to them and have them stick to a resting position gradually and when another object hits it it transfers some energy into it causing it to move but the sticky surface will cause it to lose some of this energy and stop in a resting position. the gif looks like it has no friction to it.