I've asked a few similar questions over the past 8 months or so with no real joy, so I am going make the question more general.

I have an Android game which is OpenGL ES 2.0. within it I have the following Game Loop:

My loop works on a fixed time step principle (dt = 1 / ticksPerSecond)

loops=0;

    while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip){

        updateLogic(dt);
        nextGameTick+=skipTicks;
        timeCorrection += (1000d/ticksPerSecond) % 1;
        nextGameTick+=timeCorrection;
        timeCorrection %=1;
        loops++;

    }

    render();   

My intergration works like this:

sprite.posX+=sprite.xVel*dt;
sprite.posXDrawAt=sprite.posX*width;

Now, everything works pretty much as I would like. I can specify that I would like an object to move across a certain distance (screen width say) in 2.5 seconds and it will do just that. Also because of the frame skipping that I allow in my game loop, I can do this on pretty much any device and it will always take 2.5 seconds.

Problem

However, the problem is that when a render frame skips, the graphic stutter. It's extremely annoying. If I remove the ability to skip frames, then everything is smooth as you like, but will run at different speeds on different devices. So it's not an option.

I'm still not sure why the frame skips, but I would like to point out that this is Nothing to do with poor performance, I've taken the code right back to 1 tiny sprite and no logic (apart from the logic required to move the sprite) and I still get skipped frames. And this is on a Google Nexus 10 tablet (and as mentioned above, I need frame skipping to keep the speed consistent across devices anyway).

So, the only other option I have is to use interpolation (or extrapolation), I've read every article there is out there but none have really helped me to understand how it works and all of my attempted implementations have failed.

Using one method I was able to get things moving smoothly but it was unworkable because it messed up my collision. I can foresee the same issue with any similar method because the interpolation is passed to (and acted upon within) the rendering method - at render time. So if Collision corrects position (character now standing right next to wall), then the renderer can alter it's position and draw it in the wall.

So I'm really confused. People have said that you should never alter an object's position from within the rendering method, but all of the examples online show this.

So I'm asking for a push in the right direction, please do not link to the popular game loop articles (deWitters, Fix your timestep, etc) as I've read these multiple times. I'm not asking anyone to write my code for me. Just explain please in simple terms how Interpolation actually works with some examples. I will then go and try to integrate any ideas into my code and will ask more specific questions if need-be further down the line. (I'm sure this is a problem many people struggle with).