Research On the Dance Path of Multi-Segment Bench Dragon Based on Dynamic Spiral Curves

Abstract

The Bench Dragon is a traditional folk performance originating from southeastern China, in which performers carry a series of interconnected benches to simulate the movement of a dragon. This paper develops a mathematical motion planning model to optimize the spatial trajectory and safety of a multi-segment Bench Dragon during spiral entry. A dynamic Archimedean spiral model is constructed, and the dragon head’s position is derived by solving an ordinary differential equation. Using recursive geometric analysis, the positions and velocities of all segments are computed based on structural differences between the head and body. To detect collisions between segments, a novel method is proposed by integrating the Separating Axis Theorem (SAT) with a risk-based workspace filtering strategy, effectively identifying critical contact moments. Finally, a binary search algorithm is applied to determine the minimum spiral pitch required to avoid collisions during entry into the circular turning region. The proposed method offers a systematic solution for coordinated multi-body path planning under spatial constraints, with potential applications in large-scale performance choreography and robotics.