基于动态搜索的 “板凳龙” 运动状态及路线研究  

Analysis of Motion States and Route Planning of the"Bench Dragon"Based on Dynamic Search

作　　者：游天明 陈诺严 陈静怡 高晓沨 YOU Tianming;CHEN Nuoyan;CHEN Jingyi;GAO Xiaofeng(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China;School of Electronic Information and Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;SJTU ParisTech Elite Institute of Technology,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学数学科学学院,上海200240 [2]上海交通大学电子信息与电气工程学院,上海200240 [3]上海交通大学巴黎卓越工程师学院,上海200240

出　　处：《数学建模及其应用》2025年第1期33-41,共9页Mathematical Modeling and Its Applications

摘　　要：本文研究了“板凳龙”表演中盘入、调头和盘出的运动状态及行进路线.针对盘入过程,在极坐标系中建立位置与速度模型,通过几何关系递推求解各把手位置函数,并对其求导得到速度函数;在此基础上,提出了一种结合变步长搜索与二分搜索的碰撞检测方法,精确计算首次碰撞时间.针对调头过程,建立了最短螺距的单目标优化模型,利用碰撞检测模型,结合粒子群算法求解调头前保证不发生碰撞的最小螺距;通过几何推导证明调头曲线长度为常数,将调头路径划分为4段曲线,分别求解出其参数方程,并将位置与速度模型扩展应用于调头与盘出过程.针对盘出过程,分析各把手的最大速度,通过比例关系推导出龙头的最大行进速度.This paper analyses the marching route and motion states of the"bench dragon"performance,including three key phases:spiraling inward,turning,and spiraling outward.A model of position and velocity motions is established in polar coordinates based on geometry relationships.A method combining the binary search and adaptive step size search algorithm is proposed to detect collisions and calculate the exact timing of the first collision.A single-objective optimization model,integrated with a particle swarm optimization algorithm is employed to determine the minimum pitch.Through mathematical proof,it is demonstrated that the length of the turning curve remains constant,and the motion model is extended to encompass the entire performance process regarding the different curve equations.Another single-objective optimization model is developed to obtain the maximum speed of the bench dragon′s head.

关 键 词：板凳龙 等距螺线 动态搜索 粒子群算法 单目标优化 

分 类 号：O29[理学—应用数学]