Author(s)

Bohan Zhang, Yuxiao Shang, Xiaolu Lin

Corresponding Author

Bohan Zhang

Abstract

This paper focuses on the modeling, solution, and optimization of the motion of a dragon dance team along an equidistant spiral trajectory. First, a kinematic model based on the spiral equation is constructed, and formulas for the displacement, velocity, and acceleration of the dragon head and body are derived. Through numerical simulations, the motion trajectories and velocities of the dragon head, body, and tail at different time nodes are calculated, with the results presented in the form of tables and graphs. On this basis, a collision detection mechanism is proposed, using geometric relationships to determine if the dragon's benches overlap. The collision between the dragon head and the following segments of the dragon body is detected using the triangular area method. Numerical simulation results show that the first collision occurs at 412.478 seconds, making it impossible for the dragon to continue along the spiral path. Subsequently, research is conducted to optimize the model, focusing on the pitch parameter and the turnaround curve path. Using incremental search and the bisection method, the minimum pitch is determined to be 45.035 cm, enabling the dragon team to successfully follow the trajectory without collisions. The optimization of the turnaround path reveals that when the tangent distance between the spiral and arc is 427.5 cm, the dragon team achieves the optimal path. Additionally, considering the peak velocity of the dragon body, the dragon head's velocity and path parameters are optimized to limit the maximum velocity of the dragon body to within 2 m/s, ensuring smooth and controllable movement. The results of this study provide theoretical support and algorithmic tools for path planning, formation control, and collision detection in dragon dance performances. The constructed model and optimization methods can be applied to motion control and path optimization for other multi-segment rigid bodies.

Keywords

Bench Dragon, Spiral Line, Path Planning, Collision Detection, Speed Optimization, Computer Simulation