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<h1 id="levels-of-modularity-and-topology">Levels of modularity and topology</h1>
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<p>The brittle star can be controlled at different levels. A monolithic controller processes all inputs and outputs at
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once, whereas modular controllers divide the brains across the body, inspired by the biology of brittle stars.</p>
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<p>We define four architectures to compare:</p>
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<ol>
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<li><strong>Centralized, monolithic</strong>: A single Multi Layer Perceptron per robot that receives all observations and outputs
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all actions.</li>
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<li><strong>Fully connected arm-level</strong>: Each arm contains an MLP that processes the inputs for that arm, an MLP that processes
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the communicated inner-states, and an MLP that outputs the actions for that arm. One policy for these MLPs is shared
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across the arms. The controllers in each arm are connected to each other and form a fully connected graph. There is
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no central disk, but the controllers are fully connected.</li>
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<li><strong>Ring arm-level</strong>: Identical setup to the fully connected arm-level, but the controllers are connected in a ring
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structure. This setup is considered less centralized than the fully connected graph.</li>
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<li><strong>Segment-level</strong>: Each segment contains the three MLPs discussed above. The base segments, attached to the body,
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form a ring structure, with the remaining segments attached as extended "strings". Segments can only communicate with
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segments that are physically connected to it.</li>
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</ol>
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<h2 id="rationale">Rationale</h2>
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<p>To fairly compare decentralized modularity against centralized control, the decentralized models should not be allowed
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to contain a central organ acting as a bottleneck or coordinator. By removing the central disk in the decentralized
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models and replacing it with a ring topology, we closely approximate the biological reality of the brittle star and test
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a decentralized morphology.</p>
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<p>The fully connected graph functions as an intermediate step in between a fully centralized and a decentralized ring. We
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use it to test whether our models scale to more complex structures.</p>
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