The team went through numerous iterations in the analytic-synthetic loop.
At the most basic level, the robotic fish embodied behaviours that are typically seen in social interactions between pairs of fish but the system was open loop – i.e. the robot was not directly responding to the live fish’s behaviour. In a second iteration they closed the loop because it was obvious that it is not only important for the robot to show typical social behaviour but to show it at the right time. Once the closed loop system was implemented, the team was capable of letting the robot embody social responses from the literature including the well-cited Couzin-model. This model includes repulsive (close-range) and attraction (longer range) interactions. Interestingly neither this nor any of the other published interactive algorithms were capable of providing the robot with behaviour that made a real connection with the live fish. For this they needed to include recruitment behaviour in the robot – i.e. if the robot gets isolated from the live fish it will return to it. This additional behaviour was highly successful in bringing about a social connection between robot and live fish (Maxeiner et al. 2023 BB). When they looked at the literature, they realised that this recruitment behaviour was indeed described in real fish in the original publication of Reebs 2000 which was used as inspiration for many collective behaviour fish models. But the team didn’t just rediscover this recruitment behaviour because they now better understand its importance in social interactions.

Apart from fish behavioral studies, the team conducted simulation studies in which simple neural networks with varying available temporal information about a partner were evolved to a) imitate a pre-recorded fish’s behavior in a pair scenario and b) to produce fish-like behavior in general. This proved to be an effective tool for discovering post-hoc whether a fish was socially anticipating without needing to use experimental manipulation.

Robot-robot simulation studies were conducted to explore the potential for social coordination and mutual entrainment to emerge from intrinsic motivations, possibly scaffolding and thus facilitating anticipation as suggested by the literature. Results were inconclusive, as social coordination was shown to emerge, but did not always aid the predictions.

In addition, another methodological study tested a new type of Hidden Markov Model as a generative and analytical tool in modeling a “we-space” envisioned in the literature. The model achieved high testing accuracies and gave indirect support to the notion of a we-centric space in these fish’s interactions.