# Comparing Direct and Indirect Representations for Environment-Specific Robot Component Design

## TL;DR

This paper compares direct and indirect voxel-based representations for designing hexapod robot legs, demonstrating that indirect methods enable better exploration and improved environment-specific performance in simulation.

## Contribution

It introduces a comparative analysis of Bezier spline and CPPN-NEAT representations for robot leg morphology, highlighting the advantages of indirect encoding in design exploration.

## Key findings

- Indirect representation leads to higher fitness in design optimization.
- Post-processing strategies affect the feasibility of generated leg designs.
- Results support the hypothesis that indirect methods enhance design space exploration.

## Abstract

We compare two representations used to define the morphology of legs for a hexapod robot, which are subsequently 3D printed. A leg morphology occupies a set of voxels in a voxel grid. One method, a direct representation, uses a collection of Bezier splines. The second, an indirect method, utilises CPPN-NEAT. In our first experiment, we investigate two strategies to post-process the CPPN output and ensure leg length constraints are met. The first uses an adaptive threshold on the output neuron, the second, previously reported in the literature, scales the largest generated artefact to our desired length. In our second experiment, we build on our past work that evolves the tibia of a hexapod to provide environment-specific performance benefits. We compare the performance of our direct and indirect legs across three distinct environments, represented in a high-fidelity simulator. Results are significant and support our hypothesis that the indirect representation allows for further exploration of the design space leading to improved fitness.