# Simplified and Abstracted Geometry for Forward Dynamics

*Draft*

## Contents |

## Abstract

## Introduction

- simplifications and abstractions for geometric data are needed for simulations
- such simulation are useful, and will be more useful in the future
- they have been investigated in the computer graphics field
- forward dynamics and CAD data pose specific challenges distinct from those of graphics
- simplification and abstraction in this context thus needs specific attention: metrics, methods, empirical studies

The need for simulation and abstraction of robot and mechanism geometry arises out of the large size of CAD data and the computational cost of simulations involving them. Typical tessellations for CAD data viewing, inside CAD programs, results in a very high number of triangles, more than can be effectively simulated with current hardware. Even with hardware advances, it will always be advantageous in some situations to cull away data that is ultimately irrelevent to answering a posed technical problem. For example, in an adversarial situation, the agent who uses the smallest sufficient set of data to arrive at an answer will dominate in a competition due to its increased search horizon. The motivation for simplification and abstraction then exists, but just how to simplify or abstract is a question that to our knowledge has not been addressed in the area of forward dynamics simulation incorperating geometric data.

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 that hit contact points appropriately, this might be acceptable 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 dynamics 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.

## Background

## Example Problem

## Approach

## Empirical Results

## Conclusions

## References

Milling Machine Simplification(PDF)