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Which physics engine has most 'precise' collision detection?

Hello people,

I am currently struggling with simulating a hot wire game, controlled by a 7DOF robot arm. The arm has a metal loop thingie attached to it's wrist, and a user should be able to navigate the arm. The arm control is implemented using ros_control's effort controllers. The task requires rather precise and fast collision detection - I am aiming at a real_time_factor of 1.

Right now, the arm is showing weird behavior when the metal loop collides with the wire, ranging from the arm jittering to the metal loop passing through the wire. I guess I still have a lot of fine-tuning to do, but one important question remains:

Which of the four physics engines is most suited for this task? Currently, ODE is being used, but maybe another engine will yield better results?

Thank you for your help.