Artificial fish-like robot is an important branch of underwater robot research. At present, most of fish-like robot research focuses on single robot mechanism behavior, some research pays attention to the influence of the hydro-environment on robot crowds but does not reach a unified conclusion on the efficiency of fish-like robots swarm. In this work, the fish-like robots swarm is studied by numerical simulation. Four different formations, including the tandem, the phalanx, the diamond, and the rectangle are conducted by changing the spacing between fishes. The results show that at close spacing, the fish in the back can obtain a large wake from the front fish, but suffers large lateral power loss from the lateral fish. On the contrary, when the spacing is large, both the wake and pressure caused by the front and side fishes become small. In terms of the average swimming efficiency of fish swarms, we find that when the fish spacing is less than $1.25L$ (L is the length of the fish body), the tandem swarm is the best choice. When the spacing is $1.25L$ , the tandem, diamond and rectangle swarms have similar efficiency. When the spacing is larger than $1.25L$ , the rectangle swarm is more efficient than other formations. The findings will provide significant guidance for the control of fish-like robots swarm.

Autonomous Underwater Vehicle (AUV) has become a hotspot in the field of robot in recent years. As a special kind of AUV, the robotic fish can achieve better propulsion efficiency and maneuverability than traditional AUVs. Studies show that robotic fish formation can save energy and perform more complex tasks than single robotic fish, but it is difficult to maintain a stable formation because the nearby environmental condition is hard to obtain. Inspired by the lateral line system (LLS) of fish, this paper constructs a predictive model of flow velocity and a judgement model of spacing between individual platforms for robotic fish formation through monitoring sensors on robotic fish surface. The models are built by methods of polynomial fitting and neural networks based on Computational Fluid Dynamics (CFD) simulation. The results show that the flow velocity predicted by our model could reduce the error to $0.4\%$ , and the spacing judgement accuracy could reach at least 80%. The findings are useful for maintaining a stable formation and will provide significant guidance for the control of robotic fish formation and sensor installation position on the robotic fish surface.

Greedy algorithm is one of the important point selection methods in the radial basis function based mesh deformation. However, in large-scale mesh, the conventional greedy selection will generate expensive time consumption and result in performance penalties. To accelerate the computational procedure of the point selection, a block iteration with parallelization method is proposed in this paper. By the block iteration method, the computational complexities of three steps in the greedy selection are all reduced from $O\left(n^3\right)$ to $O\left(n^2\right)$ . In addition, the parallelization of two steps in the greedy selection separates boundary points into sub-cores, efficiently accelerating the procedure. Specifically, three typical models of three-dimensional undulating fish, ONERA M6 wing and three-dimensional Super-cavitating Hydrofoil are taken as the test cases to validate the proposed method and the results show that it improves 17.41 times performance compared to the conventional method.