Single-objective optimization model based on spiral motion in bench dancing dragon

The Bench Dragon dance is a traditional folk cultural activity in Zhejiang and Fujian, China, representing a unique form of collective behavior. A successful performance requires precise path planning and speed control to ensure safety and aesthetic appeal. This study develops a single-objective optimization model based on spiral motion to address these challenges. Using geometric analysis, velocity decomposition, vector analysis, traversal search, and dichotomous search, we derive and prove various geometric relationships. The model provides optimal motion parameters, including positions and velocities of the dragon dance team, and investigates the trends of speed changes and potential collisions. Results indicate that the speed difference between the dragon's head and tail remains minimal (0.0035 m/s), ensuring a stable and coordinated performance. The study concludes that maintaining a consistent speed profile is crucial for reducing the risk of accidents and enhancing the visual impact of the dance. This research not only offers practical guidance for Bench Dragon performances but also introduces a novel quantitative approach for analyzing traditional cultural activities, highlighting the potential for mathematical modeling to preserve and enhance cultural heritage.