Shape formation of swarm robots based on parallel strategy

Abstract The shape formation problem has attracted significant attention due to its broad applicability in various fields such as robotics, biology, and distributed computing. The problem involves the coordination of multiple agents, such as robots, drones, or biological cells, to form a predefined geometric shape based on distributed algorithms and local communication mechanisms. Efficiently achieving the desired formation, despite variations in the number of agents, is critical for real-world applications. In response, this paper proposes a parallel strategy characterized by scalability, robustness, and adaptivity to enhance the execution efficiency of shape formation tasks. The proposed approach begins by dividing the target shape along a central axis into left and right sections. A gradient generation rule is then introduced to determine the movement order and direction for each agent. Robots located at the edge of the left or right sections initiate movement based on edge-following and positioning rules when their gradient value exceeds that of neighboring agents. These robots continue to move until they reach their target positions. The method is resilient to failures, even if some robots fail, the shape formation task can still be completed provided that there is sufficient redundancy in the robot population. An out-of-bounds monitoring mechanism is also implemented to automatically withdraw excess robots. A simulation platform with a user-friendly human-computer interaction interface is developed to test the proposed method on various shape formation tasks, including square, pentagram, and hexagram formations, with group sizes of 119, 439, and 1019 robots, respectively. Simulation results demonstrate that the proposed method achieves approximately 3.5 times the execution efficiency of traditional single-sided shape formation methods and is effective for different group sizes. Additionally, two fault tolerance experiments are conducted, simulating robot failures both inside and outside the shape, to further validate the robustness of the method.