docs: Modularity

docs/design/controllers.md

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+# Levels of modularity and topology
+
+The brittle star can be controlled at different levels. A monolithic controller processes all inputs and outputs at
+once, whereas modular controllers divide the brains across the body, inspired by the biology of brittle stars.
+
+We define four architectures to compare:
+
+1. **Centralized, monolithic**: A single Multi Layer Perceptron per robot that receives all observations and outputs
+all actions.
+2. **Fully connected arm-level**: Each arm contains an MLP that processes the inputs for that arm, an MLP that processes
+the communicated inner-states, and an MLP that outputs the actions for that arm. One policy for these MLPs is shared
+across the arms. The controllers in each arm are connected to each other and form a fully connected graph. There is no
+central disk, but the controllers are fully connected.
+3. **Ring arm-level**: Identical setup to the fully connected arm-level, but the controllers are connected in a ring
+structure. This setup is considered less centralised than the fully connected graph.
+4. **Segment-level**: Each segment contains the three MLPs discussed above. The base segments, attached to the body,
+form a ring structure, with the remaining segments attached as extended "strings". Segments can only communicate with
+segments that are physically connected to it.
+
+## Rationale
+
+To fairly compare decentralized modularity against centralized control, the decentralized models should not be allowed
+to contain a central organ acting as a bottleneck or coordinator. By removing the central disk in the decentralized
+models and replacing it with a ring topology, we closely approximate the biological reality of the brittle star and test
+a decentralized morphology. 
+
+The fully connected graph functions as an intermediate step in between a fully centralised and a decentralised ring. We
+use it to test if the scaling of our models to more complex structures.