V-REP, the Virtual Robot Experimentation Platform, is a 3D robot simulator, with integrated development environment, based on a distributed control architecture. Its default physics engine is Bullet, but ODE is also supported (for a same simulation, the user can switch from one to the other physics engine with a single click).
Here the latest demo video: http://www.youtube.com/watch?v=7due-XHlGG4
And here the latest simulation: http://www.youtube.com/watch?v=HiFlb8EB4Z4
(the robot control in that simulation requires less than 200 lines of code)
V-REP is free for students and can be downloaded here: http://www.v-rep.eu
The embedded physics engines are just a small part of V-REP. V-REP also supports inverse/forward kinematics for any type of mechanism (can work hand-in-hand with the physics engines), collision detection, minimum distance calculation, proximity sensors, camera-like sensors with image processing, path planning, surface cutting simulation, graphing, custom user interfaces, etc.
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Here again, a big thanks for such a great Physics engine that is Bullet (Credit is of course also given in the V-REP application package).