Simulation of group motion in a discrete environment

DOI: 10.31673/2412-9070.2026.017412

Abstract

This paper presents a comprehensive approach to modeling coordinated group motion of agents in discrete environments, based on the leader–follower paradigm. The proposed agent-based framework is designed to simulate collective navigation in constrained and obstacle-rich spaces, adderssing challenges commonly encountered in autonomous robotics, multi-agent coordination, and swarm intelligence applications. A key feature of the model is the determination of an optimal trajectory for the leading agent using a wave propagation algorithm, which ensures the feasibility of collision-free paths within a discretized environment. Computational efficiency is further enhanced by constraining the search domain using a distance map to the nearest obstacles, generated through distance transform and watershed segmentation techniques. This approach highlights central navigation corridors and reduces computational overhead while preserving routing accuracy. The methodology is grounded in rigorous algorithmic design and demonstrates robustness across varying environmental configurations.
Follower agents adjust their positions relative to the leader, maintaining a minimum safe interagent distance, which ensures a stable, coordinated group configuration and realistic collective dy namics. The model effectively reproduces characteristic behaviors observed in natural and enginee red systems, including flocking, marching formations, and cooperative maneuvering of autonomous platforms. Experimental results demonstrate that the framework scales efficiently to larger agent groups and complex environments without compromising coordination or path optimality. Furthermore, the framework provides a flexible platform for integrating additional behavioral rules and adaptive strategies, thereby extending its applicability to a broad spectrum of multi-agent scenarios.
The developed methodology provides a robust basis for practical applications in autonomous navigation, crowd simulation, rescue operations, and bio-inspired swarm systems. Future work may extend the framework to dynamic obstacles, variable group sizes, and adaptive distance metrics to enhance performance in highly dynamic and uncertain environments.

Keywords: collective motion; agent-based modeling; discrete environment; wavefront algorithm; leader–follower motion; optimal path.