Turtlebot spinning in place + not going straight when speeding up simulation

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It appears that you're speeding up gazebo to the point that the physics simulation is no longer converging to an accurate result. This can happen when the granularity of the simulation gets too great or the number of iterations for the solver are inadequate.

In general it's expected that if you speed up the physics that the accuracy drops. I suspect that this is something that can be tuned to run at the speeds you want w/o drifting turns. But to get more advice on this I'd recommend asking on http://answers.gazebosim.org/questions/ since this really is an issue releated to simulation. They can probably help you tune the parameters for the model. As you've noticed this is related to both the robot model as well as the world model and how much computational time it takes for both.