Table 1 Theoretical and robotics implementations of the main control mechanisms in our model, and their respective control parameter (s)
Characteristic of the MCD dynamics | Theoretical control mechanism | Robotic control mechanism |
|---|---|---|
Attraction/repulsion with respect to the origin | Symmetric part of the dynamical matrix \(\mathbb {V}\) | Forward speed in the Braitenberg control mechanism |
Control parameter: \(M\), \(\rho \) | Control parameter: \(\alpha \), \(\rho \) | |
Rotation around the origin | Anti-symmetric part of the dynamical matrix \(\mathbb {V}\) | Heading correction in the Braitenberg control mechanism |
Control parameter: \(\omega \), \(\rho \) | Control parameter: \(\beta \), \(\rho \) | |
Attraction to the limit cycle | \(U'[H,t]\) term in the symmetric part of the dynamical matrix \(\mathbb {V}\) Control parameter: \(\rho \) | Transmission of \(N_\rho (t-1)\) to/from neighbors, and filtering step of \(N_\rho (t)\) |
Control parameter: \(\rho \), majority window size | ||
Repartition on the limit cycle | Noise sources \(dW(t)\). Control parameter: \(\sigma \) | Robotics noise sources (motors imprecisions, communications errors, environmental noise, etc.). Avoidance mechanism. |