民俗活动“板凳龙”行进状态建模与路径优化研究

Research on State Modeling and Path Optimization of the Folk Activity “Bench Dragon”

  • 摘要: 针对民俗活动“板凳龙”的行进状态建模与路径优化问题,提出一种基于平面几何分析和运动学约束的递推建模方法:首先构建把手位置和速度递推模型,进而建立考虑碰撞约束的调头路径长度优化模型。基于递推模型求解各时刻把手运动参数后,通过几何关系分析与坐标系变换方法,建立碰撞时间估计模型,依据路径不相交、不发生碰撞与龙头不逆行确定模型的约束条件,并设计多重搜索算法实现碰撞时刻的精确判定。在给定螺距与调头空间下,使用遗传算法计算得“板凳龙”的近似最短调头路径为11.7915 m。计算结果表明:当优化路径下要求各把手速度不大于2 m/s时,需约束龙头速度不大于0.9670 m/s,该结果为安全控制提供量化依据。

     

    Abstract: Aiming at the modeling of movement states and path optimization for the folk activity “Bench Dragon”, this study proposes a recursive modeling method based on planar geometric analysis and kinematic constraints: First, establish recursive models for handle positions and velocities, then develop a U-turn path length optimization model incorporating collision constraints. After solving motion parameters of handles at each time step through the recursive model, a collision time estimation model is constructed via geometric relationship analysis and coordinate system transformation. The constraints of the model are determined based on path non-intersection, collision avoidance, and non-reverse movement of the dragon head. A multi-search algorithm is designed to achieve precise determination of collision timings. Under the given helix pitch and U-turn space constraints, the approximate shortest U-turn path for the “bench dragon” calculated using a genetic algorithm is 11.7915 meters. Computed results demonstrate that when the optimized path requires the speed of each handle to not exceed 2 m/s, the dragon head speed must be constrained to no more than 0.9670 m/s. This outcome provides a quantitative basis for safety control measures.

     

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