根据传统文化遗产板凳龙的运动展开研究, 板凳龙表演涉及复杂的螺旋运动轨迹和多节点的协同运动, 对其建模和优化提出了极高的要求。为了深入理解其运动特点并提高安全性及观赏性, 探索了阿基米德螺旋运动轨迹的建模、碰撞检测以及优化问题的解决方案。针对复杂运动系统中的建模与求解问题, 运用中心差分法、牛顿迭代法、二分搜索法和仿真模拟技术等方法; 部分选择性创新地提出碰撞检测方法以及将约束条件转换为优化问题的模型; 采用多阶段自适应优化算法, 进一步提高了系统性能; 研究螺旋运动轨迹的数学建模、碰撞检测模型的建立和运动系统的整体性能优化; 解决了运动系统中的多重建模与求解难题。该成果不仅提供了对板凳龙运动的精确描述, 还为天体轨道设计、DNA双螺旋结构、蛋白质折叠等复杂系统的研究提供了新的思路和解决方案, 为类似动态系统的运动优化和性能提升提供了新的思路与技术支持。

This study investigates the motion characteristics of the traditional cultural heritage “Bandenglong” ( Bench Dragon) , a performance involving intricate spiral trajectories and coordinated multi-node movements, which demands high precision in modeling and optimization. To enhance safety, aesthetic performance, and operational efficiency, we propose a comprehensive framework integrating Archimedean spiral trajectory modeling, collision detection algorithms, and multi-stage dynamic path optimization. By employing numerical methods such as the central difference scheme, Newton-Raphson iteration, and binary search, alongside simulation techniques, we innovatively transform. collision constraints into optimization problems and develop a selective collision detection approach. A multi-phase adaptive optimization algorithm is introduced to dynamically adjust parameters, ensuring global optimality while addressing subproblems like spiral transition smoothing and collision avoidance. The established mathematical model accurately describes the spiral motion of the dragon’s head, body, and tail, resolving multi-scale modeling challenges in complex dynamic systems. Beyond its application to the Bandenglong, this framework offers novel insights and methodological support for diverse fields, including celestial orbital design, DNA double-helix structural analysis, and robotic path planning, thereby bridging cultural heritage preservation with modern technological advancements.