Energetic benefits in coordinated circular swimming motion of two swimmers.

The coordinated movement of multiple swimmers is a crucial component of fish schools. Fish swimming in different formations, such as tandem, side-by-side, diamond, and phalanx, can achieve significant energetic advantages. However, the energetic benefits of nonstraight swimming behaviors, such as the collective motion of a milling pattern, are not well understood. To fill in this gap, we consider two swimmers in circular tracks, controlled by a PID approach to reach stable configurations. Our study finds that the optimal phase is affected by circumferential effects, and that substantial energy savings can result from both propulsion and turning. We also explore the radial effect in terms of energetic benefits. In a milling pattern, the inner swimmers can easily gain a certain energetic benefit (-8%), while their peers on the outside must be close enough to the inner swimmer with a proper phase to gain the energetic benefit (-14%). When the radial spacing becomes larger or is in an unmatched phase, the swimming of the outer swimmers becomes more laborious (+16%). Our results indicate that swimmers who maintain a matched phase and minimum radial effect obtain the highest energetic benefits (-26%). These findings highlight the energetic benefits of swimmers, even in a milling pattern, where the position difference dominates the extent of benefit.

Modeling three-dimensional bait ball collective motion.

Collective motion of animal groups such as fish schools and bird flocks in three-dimensional (3D) space are modeled by considering a topological (Voronoi) neighborhood. The tridimensionality of the group is quantified. Apart from the patterns of swarming, schooling, and milling, we identify a 3D bait ball around the phase transition boundary. More significantly, we find that by considering a blind angle in this topology based model, an individual interacts statistically with six to seven neighbors, consistent precisely with the previous field observations of the starling flocks. This model could be expected to enable more insightful investigation on realistic collective motion of shoals or flocks.

Fish can save energy via proprioceptive sensing.

Fish have evolved diverse and robust locomotive strategies to swim efficiently in complex fluid environments. However, we know little, if anything, about how these strategies can be achieved. Although most studies suggest that fish rely on the lateral line system to sense local flow and optimise body undulation, recent work has shown that fish are still able to gain benefits from the local flow even with the lateral line impaired. In this paper, we hypothesise that fish can save energy by extracting vortices shed from their neighbours using only simple proprioceptive sensing with the caudal fin. We tested this hypothesis on both computational and robotic fish by synthesising a central pattern generator (CPG) with feedback, proprioceptive sensing, and reinforcement learning. The CPG controller adjusts the body undulation after receiving feedback from the proprioceptive sensing signal, decoded via reinforcement learning. In our study, we consider potential proprioceptive sensing inputs to consist of low-dimensional signals (e.g. perceived forces) detected from the flow. With simulations on a computational robot and experiments on a robotic fish swimming in unknown dynamic flows, we show that the simple proprioceptive sensing is sufficient to optimise the body undulation to save energy, without any input from the lateral line. Our results reveal a new sensory-motor mechanism in schooling fish and shed new light on the strategy of control for robotic fish swimming in complex flows with high efficiency.

Spontaneous response of a self-organized fish school to a predator.

While the collective movements of fish schools evading predators in nature are complex, they can be fundamentally represented by simplified mathematical models. Here we develop a numerical model, which considers self-propelled particles subject to phenomenological behavioural rules and the hydrodynamic interactions between individuals. We introduce a predator in this model, to study the spontaneous response of a group of simulated fish to the threat. A self-organized fish school with a milling pattern is considered, which was expected to be efficient to evade the threat of predators. Four different attack tactics are adopted by the predator. We find that the simulated fish form transiently smaller structures as some prey individuals split from the main group, but eventually they will re-organize, sometimes into sub groups when the simulated predator approaches the fish school unidirectionally or take a reciprocating action. As the predator is programmed to target the centroid, the school ends in a gradually enlarging circle. For the fourth tactic, as the predator chases its nearest prey, the fish school's response varies with the predator's delay factor. Moreover, the average speed of the group and the distance between individuals have also been studied, both demonstrating that the fish school is able to respond spontaneously to the predator's invasion. We demonstrate that the currently adopted model can predict prey-predator interactions.