Research on Dragon Dance Formation Modeling and Collision Detection Based on Spiral Motion Model

In dragon dance performances, precise control of formations and collision avoidance are crucial for enhancing performance quality and safety. In recent years, mathematical modeling and computational algorithms have become key research directions for optimizing dragon dance formations. This study proposes a modeling approach based on the Archimedean spiral to analyze the dynamic behavior of the "bench dragon" (a specific type of dragon in the formation) along complex paths. By numerically solving the differential equations and geometric constraints using the forward Euler method, the spatial distribution of the segments of the "bench dragon" is obtained, and its dynamic evolution is simulated through time-stepping discretization. The results indicate that the distance between the "bench dragon" and the origin gradually decreases. Within the first 300 seconds, the distance of the dragon head decreases by 3.8027 meters, and that of the dragon tail decreases by 2.4486 meters, with more significant changes occurring in the segments closer to the head. To prevent collisions, the minimum safe distance between the segments is maintained above 0.8 meters, and the maximum position deviation between the dragon head and tail is reduced to 1.3%. However, the inward spiral contraction characteristic of the Archimedean spiral may increase the risk of trajectory overlap or collision in the central region of the spiral. This study provides significant theoretical support and practical reference for the dynamic optimization of multi-segment flexible systems.