Differential Dynamics Modeling and Simulation Analysis of Multi-Agent Cooperative Motion

With the widespread application of multi-agent systems (MASs) in fields such as drone formations, autonomous driving, and robotic swarms, achieving efficient collaboration and stable motion among agents has become a key research focus. This study begins by describing the vertices of agents relative to the formation centroid to enable collision avoidance and formation shape tracking control. Using the Lyapunov direct method, a heat-equation-based collective dynamics model for multi-agent systems is established, providing stability criteria for the model and a leader-follower algorithm. The model enables the transformation from continuous multi-agent systems to discrete systems, completing the cooperative motion of real multi-agent systems. Simulation analysis verifies the effectiveness of the proposed model and control strategy. In a typical simulation scenario, follower agents achieve consensus with leader agents within approximately 10 seconds, with the number of path nodes reduced to just six, zero obstacle collisions, and a computation time of only 49.6 seconds. The proposed control method significantly enhances the cooperative efficiency and motion stability of multi-agent systems under limited information exchange and complex environmental conditions, offering robust theoretical support for the collaborative control of future intelligent systems.