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摘要: 随着我国冰雪运动的蓬勃发展和2022年北京冬季奥运会的成功申办，冰雪运动生物力学和冰雪机器人的研究越来越受关注.首先，介绍冰雪环境下摩擦力学的基本理论，进一步，对比不同变量对摩擦系数的影响；其次，讨论冰雪运动中空气阻力的成因，并分析潜在的减阻机制；再次，介绍研究中常用的测量手段和不同维度的建模方法，阐明各类手段和方法的优缺点；最后，回顾冰雪机器人的研究进展，分析冰雪机器人研究领域的技术挑战，展望冰雪机器人未来的研究思路.Abstract: With the flourishing development of China's ice and snow sports and the successful bidding of the Beijing's 2022 Olympic Winter Games, the research on ice and snow sport biomechanics as well as ice and snow robots plays an increasingly important role. First of all, we introduce the basic theories of friction mechanics in ice and snow environments. Further, the influence of different variables on the friction coefficient is compared. Secondly, we discuss contributing factors of aerodynamic drag in snow and ice, and analyze the potential drag reduction mechanism. Thirdly, the measurement methods typically involved in the research as well as the modeling methods with different dimensions are introduced, and the relative merits are clarified. Finally, we review the research progress of ice and snow robots, analyze the key technical challenges in the field, and offer the ideas of future development of related robots.1) 本文责任编委 孙富春
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图 2 基于IMU和GNSS测量的数据融合积分算法框图
Fig. 2 Block diagram of sensor fusion integration algorithm for IMU and GNSS measurements
图 6 日本金泽大学研制的滑雪机器人三维结构图
Fig. 6 3D structure diagram of skiing robot developed by Kanazawa University in Japan
图 7 斯洛文尼亚约瑟夫斯蒂芬研究所研制的三关节滑雪机器人
Fig. 7 Three-joint skiing robot developed by Jožef Stephen Institute in Slovenia
图 8 加拿大曼尼托巴大学研制的滑冰和滑雪机器人
Fig. 8 Skating and skiing robots developed by the University of Manitoba in Canada
表 1 不同变量对摩擦系数的影响
Table 1 Influence of different parameters on the friction coefficient
符号 变量含义 与摩擦系数的关系 潜在原因及说明 文献 $T$ 温度(Temperature) $-7$至$-2$ ℃下取得最小摩擦系数, 超出范围摩擦系数均呈增大趋势 温度过低时, 接触面为固–固摩擦, 呈现干摩擦性质; 温度接近熔点及以上时, 液态膜厚度明显增加, 接触面的毛细管桥引入附加阻力 [23-26] $v_s$ 滑动速度(Sliding velocity) 速度越快, 摩擦系数越小 高速相对于低速产生更多热量, 提升接触面的润滑效果 [22, 25-26] $A_c$ 表观接触面积(Apparent area of contact) 接触面积越大, 摩擦系数也越大 接触面较小时, 单位面积摩擦释放的热量越大, 有效提升润滑效果, 反之面积越大, 接触点越分散, 润滑效果越差 [16, 22] $R_a$ 表面粗糙度(Roughness) 表面越粗糙, 摩擦系数越大 增加表面的粗糙度导致在滑动运动期间增加实际接触面积和更多的互锁接触点, 最终增加磨损率和总摩擦 [28-29] $R_w$ 润湿性(Wettability) 亲水性材料易于润湿表面, 摩擦系数高, 接近熔点处尤甚 不具备支撑作用的冰雪颗粒易于通过毛细管桥与亲水材料相连, 毛细管力引入附加阻力 [27] $R_H$ 相对湿度(Relative humidity) 相对湿度在滑动初始阶段影响较大, 相对湿度越大摩擦系数越小 湿度越高, 接触面润滑效果越好, 摩擦力越小, 目前相对湿度的研究较少, 需要更多实验数据来支撑 [30] $\lambda$ 热导率(Thermal conductivity) 良好的热导体摩擦系数更高 导热率高意味着接触面获得的热量变少, 不利于液态膜厚度增加 [30] 
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表 2 应力转换器和压力鞋垫系统优缺点对比
Table 2 Comparison of force transducers and pressure insole systems
优点 缺点 应力转换器 能够测量三维力和力矩; 测量的力较为准确, 可被认定为标准值 较重(约0.5 kg$\, \sim\, $1.0 kg); 改变滑雪设备的特性(刚度和高度) 压力鞋垫系统 尺寸小, 适合野外使用; 对运动员干扰小 只能测量足部与鞋垫垂直方向的压力; 测量精度目前仍有待验证
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表 3 几种典型的数学建模方法
Table 3 Several typical mathematical modeling methods
文献 维度 场景 研究目标 体段数 实验数据 建模方法 Kawai等(2004)[82] 3 滑雪 基于计算机图形学开发一个新的滑雪控制模型, 用于模拟滑雪者重心与地面的相对运动, 以及滑雪运动员对雪板的作用力 15 基于视频数据的二维运动数据 计算机辅助3D人体建模; 多体系统仿真 Holmberg等(2008)[85] 3 滑雪 越野滑雪双极推撑滑行技术的生物力学分析, 用于和相关文献中的数据进行对比 64刚体, 464肌肉 基于视频数据的二维运动数据; 手杖对地面作用力 右侧上半身和手杖的三维逆向动力学; 带约束的牛顿–欧拉方程; 未考虑地面与雪板的作用力 Chen等(2009)[79] 2 滑雪 考虑地面作用力和空气阻力的二维滑雪模型 4 人工设定的仿真数据 基于牛顿–欧拉方程的二维逆动力学模型; 雪–地作用力用基于库伦摩擦力的刚性离散点接触模型来描述 Oberegger等(2010)[88] 3 滑雪 三维多体滑雪者模型来模拟连续转弯 7 基于三台同步相机分析获得滑雪者和滑雪板上标记的3D坐标 带约束的牛顿–欧拉方程; 运动路径作为约束给出, 并不依赖于模型与环境的交互; 引入非完整平衡条件 Rudakov等(2010)[78] 1 滑雪 特殊障碍赛中滑雪轨迹的优化 2 经验数据和仿真数据 多项式拟合质心轨迹, 最小化方法优化参数 Fintelman等(2011)[81] 2 滑冰 提出简单的直线速度滑冰模型以模拟和优化速度滑冰的生物力学 3 商用局部位置测量(Local position measurement, LPM)系统; DAQ力采集系统; 高速相机系统用于同步上述两者 只考虑了二维运动, 包括空气阻力、冰鞋库伦摩擦力; 两种约束:垂直方向上的完整约束、横向上的非完整约束 Bruzzo等(2016)[89] 3 滑雪 越野滑雪三维多体动力学模型, 对单个推进阶段建模, 以获得运动中设计的动力学参数 3 16个相机的运动捕捉系统, 采样频率达1 000 Hz; 配备力传感器的雪板; 视觉速度指示器指导运动员动作 多体系统动力学建模 Kruk等(2017)[90] 2 滑冰 直道速度滑冰运动生物力学模拟 3 配备力传感器的冰鞋; 20个相机组成的动作捕捉系统 基于全局优化逆运动学估计每个身体段的重心
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