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In this article, we propose bionic swarm control based on second-order communication topology (SOCT) inspired by the migration of birds, which solves the difficulty in constructing communication topologies and high-computational complexity in controlling large-scale swarm systems. To realize bionic swarm control, there are three problems supposed to be solved. First, the adjacency matrix and the Laplacian matrix in traditional methods cannot be applied to SOCT directly, which should be redesigned. Second, sub-swarm systems formed based on 2-order communication topology (2-OCT) and independently distributed with each other also need to be put forward to reduce computational complexity. At last, the followers in 1-order communication topology (1-OCT) are set as the leaders of sub-swarm systems in 2-OCT. As a result, coupling in large-scale swarm systems would be reduced. The bionic swarm controller is designed through the backstepping method. In this case, the stability of bionic swarm controller is proven by the designed Lyapunov function. The simulations show the efficiency of the designed bionic swarm controller. And the tracking-containment control based on SOCT with 42 swarm members is realized.

In this article, an expert system-based multiagent deep deterministic policy gradient (ESB-MADDPG) is proposed to realize the decision making for swarm robots. Multiagent deep deterministic policy gradient (MADDPG) is a multiagent reinforcement learning algorithm proposed to utilize a centralized critic within the actor–critic learning framework, which can reduce policy gradient variance. However, it is difficult to apply traditional MADDPG to swarm robots directly as it is time consuming during the path planning, rendering it necessary to propose a faster method to gather the trajectories. Besides, the trajectories obtained by the MADDPG are continuous by straight lines, which is not smooth and will be difficult for the swarm robots to track. This article aims to solve these problems by closing the above gaps. First, the ESB-MADDPG method is proposed to improve the training speed. The smooth processing of the trajectory is designed in the ESB-MADDPG. Furthermore, the expert system also provides us with many trained offline trajectories, which avoid the retraining each time we use the swarm robots. Considering the gathered trajectories, the model predictive control (MPC) algorithm is introduced to realize the optimal tracking of the offline trajectories. Simulation results show that combining ESB-MADDPG and MPC can realize swarm robot decision making efficiently.

In this article, we propose a complex continuous action iterated dilemma (CAID) with an incremental dynamic approach to overcome the limitations of traditional methods. In traditional CAID, the number of players was fixed. Consequently, when new players joined, computing resources were wasted due to repeated refreshes during the dynamic update process. To address these issues, we first propose a CAID model with an incremental dynamic approach. This model reflects the dynamic changes in the number of players, aligning more closely with real-world scenarios. Second, we propose an incremental updating method to prevent unnecessary refreshes of the original players’ states. When the number of players, denoted as $N$ , increases, we update and expand the evolutionary dynamic model using incremental information. This allows for an incremental connection between the original and new players. We use a weighted adjacency matrix to represent the relationships among players. The incremental updating method then updates the state matrix and the adjacency matrix. Furthermore, an analysis based on the designed Lyapunov function is proposed to prove the convergence of the CAID with incremental dynamic. The simulation results reveal the effectiveness of our proposed method.