中华绒鳌蟹运动机理分析及其运动学、动力学研究
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摘要
仿生多足机器人广泛应用于灾害救援、军事侦察、深空探测、交通运输等领域，研制仿生多足机器人的灵感来源于自然界中的多足动物，这也是仿生学研究的基础。中华绒螯蟹是一种具有优秀运动能力的节肢动物，可进行长距离迁徙至河口进行繁殖或洄游，因此中华绒螯蟹不仅对复杂地面环境具有良好的适应性，而且具有多栖性，对中华绒螯蟹运动特性的研究可为仿蟹机器人的研制提供仿生原型和理论基础。此外，中华绒螯蟹还具备优秀的挖掘能力，其所使用的主要工具是两只螯，对螯结构的研究可改进触土部件的切削能力并且提高其使用寿命；对中华绒螯蟹挖掘动作的研究也可为仿生挖掘机器人的研究提供仿生学依据。
为了定量分析被试地面的不平度，研制基于激光测距仪测量地面不平度的专用装置，采集6种规格石英砂所铺设的不平地面的离散形貌样本数据，使用平均粒径作为每种规格石英砂的量度，经韦尔奇法得到每种不平地面的空间自功率谱密度函数并绘制空间自功率谱密度函数曲线。结果表明，随着石英砂平均粒径的增加，空间自功率谱密度函数曲线的峰值增加，空间自功率谱密度函数曲线与频率轴所围成的面积增加，表明不平地面所包含的能量增加。在此基础上提出了地面能量作为衡量地面不平度的一个指标，与表面不平度标准差（RMS高度）比较后表明，地面能量与RMS高度具有强相关性，说明使用地面能量定量评价地面不平度是可行的。
提出使用相互平行直线方程拟合双对数坐标系中空间自功率谱密度曲线评价地面不平度的方法。统计结果表明，随着平均粒径的增大，拟合直线方程的截距增大。由RMS高度和平均粒径相关性结论，可以得出随着拟合直线的截距增大，地面不平度越来越大，说明在双对数坐标系中对空间自功率谱密度曲线进行直线拟合，通过分析拟合直线之间的相对位置和直线截距来评估地面不平度是可靠的。
使用三维运动图像系统捕捉中华绒螯蟹平面运动图像，通过逐帧法对中华绒螯蟹的步态进行分析，结果表明中华绒螯蟹在平面上行走时使用交替四角步法，L-步足组的平均负荷因数大于R-步足组，表明L-步足组与地面相互作用产生拉力时间大于R-步足组与地面作用产生推力时间，跨步频率随平均速率的增加而增长。使用三维运动分析软件对所采集的运动图像进行解析，得到中华绒螯蟹质心运动学参数。对运动学参数分析结果表明随着中华绒螯蟹质量增加，平均速率呈非线性减小。中华绒螯蟹在平面运动时以跳跃步态为主；除跳跃步态外，中华绒螯蟹偶然使用倒立摆步态；恢复系数与其平均速率没有相关关系，且恢复系数较低。质心机械能比质量功率随着平均速率增加呈线性增长；在Heglund N C总结的质心机械能比质量功率与平均速率关系公式基础上，引入中华绒螯蟹质心总机械能比质量功率后对该公式再次进行总结。质心水平动能比质量功率和质心重力势能比质量功率分别是质心总动能比质量功率和总机械能比质量功率的主要组成部分，分别在加速和抬升中华绒螯蟹身体时起主要作用。
采集中华绒螯蟹在5种地面（包括1种平面和4种不平地面）上的运动图像，使用逐帧法对图形进行分析，结果表明随着地面不平度的增加，中华绒螯蟹的步法由交替的四角步态逐渐转变为无规律步法，L-步足组的平均负荷因数大于R-步足组的平均负荷因数，表明L-步足组与地面接触的时间大于R-步足组与地面接触的时间。L-步足组在5种地面上的平均负荷因数基本相同；而对于T-步足组，在4种不平地面上的平均负荷因数大于其在平面上的平均负荷因数。对于5种地面，L-2和L-3步足的平均负荷因数分别大于T-2和T-3步足，表明L-2和L-3步足在中华绒螯蟹运动中主要产生拉力并且用于探知其运动方向的地面环境。在不平路面运动时，中华绒螯蟹平均速率均小于其在平面运动的平均速率。个体总质量小于61.99g的中华绒螯蟹，平均速率随个体总质量的增加而减小；对于个体总质量大于61.99g的中华绒螯蟹，其运动的平均速率随个体总质量增加而增加。中华绒螯蟹在5种地面上运动时使用两种基本的机械能转换形式，即跳跃步态和倒立摆步态。其中跳跃步态为主要的机械能转换形式，中华绒螯蟹为适应复杂的地面环境偶尔使用倒立摆步态。质心水平动能决定了质心总动能的波动；质心重力势能决定了质心总机械能的波动。质心总机械能比质量功率随平均速率的增加呈线性增长，并且其质心总机械能比质量功率随陈代谢比质量功率的增加而增加，表明中华绒螯蟹运动时的机械能主要来自于新陈代谢所产生的能量。
使用形态学的方法对中华绒螯蟹的身体结构进行分析。结果表明，中华绒螯蟹身体各部分的质量、长度都随个体总质量的增加而增加。对于螯足，座节的质量最小，螯的质量最大；基节的长度最短，螯的长度最长。对于步足，指节的质量最小，长节的质量最大；基节的长度相最短，长节的长度最长。配对t检验表明中华绒螯蟹的身体结构呈双侧对称性。
建立了螯足、步足和躯干的简化物理模型，并对螯足、步足、躯干的简化模型的转动惯量进行计算。结果表明，螯足的基节转动惯量最小，螯的转动惯量最大；L-2步足和L-3步足的长节的转动惯量明显大于L-1步足和L-4步足的长节；L-2步足和L-3步足的其他节的转动惯量与L-1步足和L-4步足其他节的转动惯量基本一致。使用D-H法建立了步足摆动相和支撑相下正逆运动学方程，使用拉格朗日法建立了步足摆动相和支撑相下正逆动力学方程。
The bionic robots are widely used in safeguard health, military reconnaissance, deepspace exploration, transportation and so on. The inspiration of manufacturing new robotscomes from natural field, which is the foundation of bionic research process. Chinese mittencrab (Eriocheir sinensis Milne-Edwards), as a topic arthropod, has excellent capability oflocomotion, because they can travel from inland to seaside for reproduction or migration.Therefore, Chinese mitten crab has a well adaption to complex terrain environment andshows triphibian features. The studies of Chinese mitten crab’s habits and characteristics canoffer the bionic prototype and theory foundation to manufacturing bionic crab-like robot ormoblile platform. Moreover, Chinese mitten crab is expert in excavating hole for habitationwith its two chelas, which can offer a new insight into the design and improvement onexcavating meachinery and bionic theories for manufacturing bionic excavating robots.
In order to define the roughness of tested terrains quantitative, we used a distance lasersensor to measure the morphology of digital surfaces of six particle sizes of quartz sandpaved in the pint-sized soil bin flatly. And then the filtered data was converted with FFT fordrawing curves of space discrete power spectral density (PSD). The statistical results showedthat there were good correlations between the peak estimate of space discrete PSD, the areaof curves of space discrete PSD surrounded with frequency axis and the average particle sizeof quartz sand, which indicated that the energy terrains contained had good relationship withthe average quartz particle size of quartz sand. On the basis of average root mean-squaredheight RMS, we proposed terrain energy as a parameter for evaluating the terrain roughness.Experiments and analyzed results showed that terrain energy increased with the value ofRMS increasing. Therefore, it is reliable to use terrain energy to evaluate terrain energy.
From the power function expression of space discrete PSD, we proposed another methodto evaluate terrain roughness by fitting the curves of space discrete PSD in double logarithmcoordinate system. Results showed that with the average particle size increasing, the slopesof fitting linear equations increased. From the relationship between terrain roughness andaverage root mean-squared height RMS, we can concluded that analyzing the relative positions of fitting linears and slopes for evaluating terrain roughness was dependable.
By using a high speed3D video recording system, the video images of Chinese mittencrab moving on smooth terrain were recorded. The video images were analyzed using frameby frame method to analyze the gaits of Chinese mitten crab. The results showed thatChinese mitten crab used a metachronal wave pattern called alternating tetrapod. The dutyfactors of the rows of the leading legs were greater than those of the rows of the trailing legs,which indicated that the pulling period of the rows of the leading legs contacting with terrainwas longer than pushing period of the rows of the trailing legs. The stride frequencyincreased with the average velocity. The video images were analyzed with a3D motionanalysis system in order to obtain the kinematic parameters of the center of mass of Chinesemitten crab. The results indicated that the average velocity of Chinese mitten crab decreasedwith the mass of Chinese mitten crab increasing, and these results were consisted with ghostcrab moving on treadmill. Chinese mitten crab used a bouncing gait as the mainenergy-conserving and-releasing pattern of mechanical energy. Besides, they occasionallyused inverted pendulum gait. The percentage recovery of Chinese mitten crab was lowerthan that of ghost crab (Ocypode quadrata,55%~70%) and different from death-headcockroach (Blaberus discoidalis, the mean value is15.7%), did not vary as a function ofaverage velocity. The mass-specific rate of mechanical power increased with averagevelocity increasing linearly. On the basis of Heglund’s experimental equation, we deducedanother equation about the relationship between the mass-specific rate of total mechanicalpower and average velocity through introducing the mass-specific rate of total mechanical ofChinese mitten crab. The mass-specific rate of horizontal kinetic power was the maincomponent of the mass-specific rate of total kinetic power required to accelerate Chinesemitten crab. The mass-specific of gravitational potential power was the main component ofthe mass-specific rate of total mechanical power required to lift Chinese mitten crab.
Motion video images of Chinese mitten crab locomotion on five types of terrains(including one smooth terrain and four kinds of rough terrains) were recorded. Frame byframe analysis indicated that Chinese mitten crab used random gaits instead of thealternating tetrapod gait with the terrain roughness increasing. The duty factors of the rowsof the leading legs were greater than those of the rows of the trailing legs, which meant thatthe pulling period of the rows of the leading legs contacting with terrain was longer than thepushing period of the rows of the trailing legs. The duty factors of the rows of the leadinglegs were almost the same for all terrains, and those of the rows of the trailing legs weregreater over the four types of rough terrains than over smooth terrain. For all five kinds ofterrains, the duty factors of L-2leg and L-3leg were greater than those of T-2leg and T-3leg, which indicated L-2leg and L-3leg produced pulling force and were used to explore thesituation of terrain. When moving on four kinds of rough terrains, the average velocity ofChinese mitten crab was less than that of moving on smooth terrain. When Chinese mittencrabs over four kinds of rough terrains, with the body mass of crabs less than about61.99g,the average velocity decreased with the body mass of crabs increasing, however, with thebody mass of crabs more than about61.99g, the average velocity increased with the bodymass of crabs increased. Chinese mitten crab used two fundamental gaits to save mechanicalenergy: the inverted pendulum gait and the bouncing gait. The bouncing gait was the mainpattern of mechanical energy conservation, however, in order to adapt to complex terrains,Chinese mitten crab occasionally used inverted pendulum gait. Horizontal kinetic energywas the major component of total kinetic energy for all terrains. Thus, horizontal kineticenergy can determine the trend of undulation in total kinetic energy. Gravitational potentialenergy was the major component of total mechanical energy, which determined the trend ofthe undulation in total mechanical energy. The mass-specific rate of total mechanical powerincreased with average velocity increasing linearly. The mass-specific rates of energyconsumption increased with the mass-specific rate of total mechanical power increasing,which indicated that the mechanical energy came from the energy metabolism produced.
Besides, we investigated the structures of Chinese mitten crab with the methods ofmorphology. The statistical results indicated that the mass and length of segments of Chinesemitten crab had an increasing relationship with body mass. For chelas, the chiopodite masswas minimum and the chela mass was maximum. The basipodite length was minimum andthe chela length was maximum. For legs, the dactylopodite mass was minimum and themetropodite mass was maximum. The basipodite length was minimum and the metropoditelength was maximum. Paired t-test showed that the structure of Chinese mitten crab had asymmetrical structure.
We developed the simple physical models and calculated the moment of inertia of eachsegment of chelas, legs and trunk. The calculated results of the moment of inertia showedthat the moment of inertia of basipodite of chela was minimum and chela was maximum.The moment of inertia of metropodites of L-2leg and L-3leg was greater than that of L-1leg and L-4leg respectively and there were no prominent different between the othersegments of L-2leg and L-3leg and the other segments of L-1leg and L-4leg. By referenceto the D-H method, we deduced kinematics and inverse kinematics equations. By referenceto the Lagrange method, we deduced the dynamics and inverse dynamics equations.
为了定量分析被试地面的不平度，研制基于激光测距仪测量地面不平度的专用装置，采集6种规格石英砂所铺设的不平地面的离散形貌样本数据，使用平均粒径作为每种规格石英砂的量度，经韦尔奇法得到每种不平地面的空间自功率谱密度函数并绘制空间自功率谱密度函数曲线。结果表明，随着石英砂平均粒径的增加，空间自功率谱密度函数曲线的峰值增加，空间自功率谱密度函数曲线与频率轴所围成的面积增加，表明不平地面所包含的能量增加。在此基础上提出了地面能量作为衡量地面不平度的一个指标，与表面不平度标准差（RMS高度）比较后表明，地面能量与RMS高度具有强相关性，说明使用地面能量定量评价地面不平度是可行的。
提出使用相互平行直线方程拟合双对数坐标系中空间自功率谱密度曲线评价地面不平度的方法。统计结果表明，随着平均粒径的增大，拟合直线方程的截距增大。由RMS高度和平均粒径相关性结论，可以得出随着拟合直线的截距增大，地面不平度越来越大，说明在双对数坐标系中对空间自功率谱密度曲线进行直线拟合，通过分析拟合直线之间的相对位置和直线截距来评估地面不平度是可靠的。
使用三维运动图像系统捕捉中华绒螯蟹平面运动图像，通过逐帧法对中华绒螯蟹的步态进行分析，结果表明中华绒螯蟹在平面上行走时使用交替四角步法，L-步足组的平均负荷因数大于R-步足组，表明L-步足组与地面相互作用产生拉力时间大于R-步足组与地面作用产生推力时间，跨步频率随平均速率的增加而增长。使用三维运动分析软件对所采集的运动图像进行解析，得到中华绒螯蟹质心运动学参数。对运动学参数分析结果表明随着中华绒螯蟹质量增加，平均速率呈非线性减小。中华绒螯蟹在平面运动时以跳跃步态为主；除跳跃步态外，中华绒螯蟹偶然使用倒立摆步态；恢复系数与其平均速率没有相关关系，且恢复系数较低。质心机械能比质量功率随着平均速率增加呈线性增长；在Heglund N C总结的质心机械能比质量功率与平均速率关系公式基础上，引入中华绒螯蟹质心总机械能比质量功率后对该公式再次进行总结。质心水平动能比质量功率和质心重力势能比质量功率分别是质心总动能比质量功率和总机械能比质量功率的主要组成部分，分别在加速和抬升中华绒螯蟹身体时起主要作用。
采集中华绒螯蟹在5种地面（包括1种平面和4种不平地面）上的运动图像，使用逐帧法对图形进行分析，结果表明随着地面不平度的增加，中华绒螯蟹的步法由交替的四角步态逐渐转变为无规律步法，L-步足组的平均负荷因数大于R-步足组的平均负荷因数，表明L-步足组与地面接触的时间大于R-步足组与地面接触的时间。L-步足组在5种地面上的平均负荷因数基本相同；而对于T-步足组，在4种不平地面上的平均负荷因数大于其在平面上的平均负荷因数。对于5种地面，L-2和L-3步足的平均负荷因数分别大于T-2和T-3步足，表明L-2和L-3步足在中华绒螯蟹运动中主要产生拉力并且用于探知其运动方向的地面环境。在不平路面运动时，中华绒螯蟹平均速率均小于其在平面运动的平均速率。个体总质量小于61.99g的中华绒螯蟹，平均速率随个体总质量的增加而减小；对于个体总质量大于61.99g的中华绒螯蟹，其运动的平均速率随个体总质量增加而增加。中华绒螯蟹在5种地面上运动时使用两种基本的机械能转换形式，即跳跃步态和倒立摆步态。其中跳跃步态为主要的机械能转换形式，中华绒螯蟹为适应复杂的地面环境偶尔使用倒立摆步态。质心水平动能决定了质心总动能的波动；质心重力势能决定了质心总机械能的波动。质心总机械能比质量功率随平均速率的增加呈线性增长，并且其质心总机械能比质量功率随陈代谢比质量功率的增加而增加，表明中华绒螯蟹运动时的机械能主要来自于新陈代谢所产生的能量。
使用形态学的方法对中华绒螯蟹的身体结构进行分析。结果表明，中华绒螯蟹身体各部分的质量、长度都随个体总质量的增加而增加。对于螯足，座节的质量最小，螯的质量最大；基节的长度最短，螯的长度最长。对于步足，指节的质量最小，长节的质量最大；基节的长度相最短，长节的长度最长。配对t检验表明中华绒螯蟹的身体结构呈双侧对称性。
建立了螯足、步足和躯干的简化物理模型，并对螯足、步足、躯干的简化模型的转动惯量进行计算。结果表明，螯足的基节转动惯量最小，螯的转动惯量最大；L-2步足和L-3步足的长节的转动惯量明显大于L-1步足和L-4步足的长节；L-2步足和L-3步足的其他节的转动惯量与L-1步足和L-4步足其他节的转动惯量基本一致。使用D-H法建立了步足摆动相和支撑相下正逆运动学方程，使用拉格朗日法建立了步足摆动相和支撑相下正逆动力学方程。
The bionic robots are widely used in safeguard health, military reconnaissance, deepspace exploration, transportation and so on. The inspiration of manufacturing new robotscomes from natural field, which is the foundation of bionic research process. Chinese mittencrab (Eriocheir sinensis Milne-Edwards), as a topic arthropod, has excellent capability oflocomotion, because they can travel from inland to seaside for reproduction or migration.Therefore, Chinese mitten crab has a well adaption to complex terrain environment andshows triphibian features. The studies of Chinese mitten crab’s habits and characteristics canoffer the bionic prototype and theory foundation to manufacturing bionic crab-like robot ormoblile platform. Moreover, Chinese mitten crab is expert in excavating hole for habitationwith its two chelas, which can offer a new insight into the design and improvement onexcavating meachinery and bionic theories for manufacturing bionic excavating robots.
In order to define the roughness of tested terrains quantitative, we used a distance lasersensor to measure the morphology of digital surfaces of six particle sizes of quartz sandpaved in the pint-sized soil bin flatly. And then the filtered data was converted with FFT fordrawing curves of space discrete power spectral density (PSD). The statistical results showedthat there were good correlations between the peak estimate of space discrete PSD, the areaof curves of space discrete PSD surrounded with frequency axis and the average particle sizeof quartz sand, which indicated that the energy terrains contained had good relationship withthe average quartz particle size of quartz sand. On the basis of average root mean-squaredheight RMS, we proposed terrain energy as a parameter for evaluating the terrain roughness.Experiments and analyzed results showed that terrain energy increased with the value ofRMS increasing. Therefore, it is reliable to use terrain energy to evaluate terrain energy.
From the power function expression of space discrete PSD, we proposed another methodto evaluate terrain roughness by fitting the curves of space discrete PSD in double logarithmcoordinate system. Results showed that with the average particle size increasing, the slopesof fitting linear equations increased. From the relationship between terrain roughness andaverage root mean-squared height RMS, we can concluded that analyzing the relative positions of fitting linears and slopes for evaluating terrain roughness was dependable.
By using a high speed3D video recording system, the video images of Chinese mittencrab moving on smooth terrain were recorded. The video images were analyzed using frameby frame method to analyze the gaits of Chinese mitten crab. The results showed thatChinese mitten crab used a metachronal wave pattern called alternating tetrapod. The dutyfactors of the rows of the leading legs were greater than those of the rows of the trailing legs,which indicated that the pulling period of the rows of the leading legs contacting with terrainwas longer than pushing period of the rows of the trailing legs. The stride frequencyincreased with the average velocity. The video images were analyzed with a3D motionanalysis system in order to obtain the kinematic parameters of the center of mass of Chinesemitten crab. The results indicated that the average velocity of Chinese mitten crab decreasedwith the mass of Chinese mitten crab increasing, and these results were consisted with ghostcrab moving on treadmill. Chinese mitten crab used a bouncing gait as the mainenergy-conserving and-releasing pattern of mechanical energy. Besides, they occasionallyused inverted pendulum gait. The percentage recovery of Chinese mitten crab was lowerthan that of ghost crab (Ocypode quadrata,55%~70%) and different from death-headcockroach (Blaberus discoidalis, the mean value is15.7%), did not vary as a function ofaverage velocity. The mass-specific rate of mechanical power increased with averagevelocity increasing linearly. On the basis of Heglund’s experimental equation, we deducedanother equation about the relationship between the mass-specific rate of total mechanicalpower and average velocity through introducing the mass-specific rate of total mechanical ofChinese mitten crab. The mass-specific rate of horizontal kinetic power was the maincomponent of the mass-specific rate of total kinetic power required to accelerate Chinesemitten crab. The mass-specific of gravitational potential power was the main component ofthe mass-specific rate of total mechanical power required to lift Chinese mitten crab.
Motion video images of Chinese mitten crab locomotion on five types of terrains(including one smooth terrain and four kinds of rough terrains) were recorded. Frame byframe analysis indicated that Chinese mitten crab used random gaits instead of thealternating tetrapod gait with the terrain roughness increasing. The duty factors of the rowsof the leading legs were greater than those of the rows of the trailing legs, which meant thatthe pulling period of the rows of the leading legs contacting with terrain was longer than thepushing period of the rows of the trailing legs. The duty factors of the rows of the leadinglegs were almost the same for all terrains, and those of the rows of the trailing legs weregreater over the four types of rough terrains than over smooth terrain. For all five kinds ofterrains, the duty factors of L-2leg and L-3leg were greater than those of T-2leg and T-3leg, which indicated L-2leg and L-3leg produced pulling force and were used to explore thesituation of terrain. When moving on four kinds of rough terrains, the average velocity ofChinese mitten crab was less than that of moving on smooth terrain. When Chinese mittencrabs over four kinds of rough terrains, with the body mass of crabs less than about61.99g,the average velocity decreased with the body mass of crabs increasing, however, with thebody mass of crabs more than about61.99g, the average velocity increased with the bodymass of crabs increased. Chinese mitten crab used two fundamental gaits to save mechanicalenergy: the inverted pendulum gait and the bouncing gait. The bouncing gait was the mainpattern of mechanical energy conservation, however, in order to adapt to complex terrains,Chinese mitten crab occasionally used inverted pendulum gait. Horizontal kinetic energywas the major component of total kinetic energy for all terrains. Thus, horizontal kineticenergy can determine the trend of undulation in total kinetic energy. Gravitational potentialenergy was the major component of total mechanical energy, which determined the trend ofthe undulation in total mechanical energy. The mass-specific rate of total mechanical powerincreased with average velocity increasing linearly. The mass-specific rates of energyconsumption increased with the mass-specific rate of total mechanical power increasing,which indicated that the mechanical energy came from the energy metabolism produced.
Besides, we investigated the structures of Chinese mitten crab with the methods ofmorphology. The statistical results indicated that the mass and length of segments of Chinesemitten crab had an increasing relationship with body mass. For chelas, the chiopodite masswas minimum and the chela mass was maximum. The basipodite length was minimum andthe chela length was maximum. For legs, the dactylopodite mass was minimum and themetropodite mass was maximum. The basipodite length was minimum and the metropoditelength was maximum. Paired t-test showed that the structure of Chinese mitten crab had asymmetrical structure.
We developed the simple physical models and calculated the moment of inertia of eachsegment of chelas, legs and trunk. The calculated results of the moment of inertia showedthat the moment of inertia of basipodite of chela was minimum and chela was maximum.The moment of inertia of metropodites of L-2leg and L-3leg was greater than that of L-1leg and L-4leg respectively and there were no prominent different between the othersegments of L-2leg and L-3leg and the other segments of L-1leg and L-4leg. By referenceto the D-H method, we deduced kinematics and inverse kinematics equations. By referenceto the Lagrange method, we deduced the dynamics and inverse dynamics equations.
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