Simplified and Abstracted Geometry for Forward Dynamics

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Geometric simplification has played an important role in the computer graphics field by allowing believable viewing of scenes too complex for timely computation. However, the approaches used in computer graphics for geometric simplification have as their goal the realistic portrayal of a scene to a viewer, not the similarity between the simplified or abstracted system and the physical ground truth. In physical simulations, the model does not need to look like the original. If a robot's legs can be abstracted as a pair of oval wheels or rotating meshes that hit contact points appropriately, this might be acceptabel for a physical simulation. However, it would be completely inappropriate for a graphical system. This offers a freedom of abstraction and simplification that does not exist in the graphics world. However, other constraints apply: in rigid-body simulations of robots and complex mechanisms, geometry plays a key role in determining where the contact points, and thus collision joints, occur; different simplification methods will lead to different simulated results. The choice of simplification method can be the determining factor of whether a simulation is accurate enough.


Example Problem


Empirical Results



Model Simplification(PDF)

Adaptive Dynamics(PDF)

Milling Machine Simplification(PDF)

Geometric Model Simplification for CAD(PDF)