Evolving robot swarm behaviors by minimizing surprise: results of simulations in 2-d on a Torus

The application of evolutionary robotics [1] to swarm robotics gives evolutionary swarm robotics [8]. The evolution or learning of multi-agent behaviors is known to be challenging [7]. Hence, new approaches still need to be explored. Examples are innovative methods to explore environment-driven, distributed evolution [2, 4]. Here, we are inspired to evolve collective behaviors following a mathematical framework by Friston et al. [3], which defines an information-theoretic analogon to thermodynamic (Helmholtz) free energy. This free energy is basically an error in the predictions that our brain makes about our environment. Evolution is related by the rationale that minimal prediction errors are achieved by limiting an agent's reactions to sensory input. This results, in turn, in better adapted behaviors: "By sampling [...] the environment selectively they restrict their exchange with it within bounds that preserve their physical integrity and allow them to last longer" [3]. The previously investigated evolution of swarm behaviors by minimizing surprisal [5, 6, 9] is subject to this study. Previous studies were limited to artificial 1-d environments, here, we report first results for 2-d. Although adding one dimension may seem a minor step, there are qualitative changes in the emergent behaviors (e.g., flocking is a collective decision with infinitely many options) and the future transition to real robots will be easier starting from 2-d.