本科生畢業(yè)設(shè)計(jì) (論文)
外 文 翻 譯
原 文 標(biāo) 題
Influence of construction mass distribution on the walking robot's gait stability
Synthesis
譯 文 標(biāo) 題
施工質(zhì)量分布對(duì)步行機(jī)器人步態(tài)穩(wěn)定性的影響
作者所在系別
機(jī)電工程學(xué)院
作者所在專(zhuān)業(yè)
機(jī)械設(shè)計(jì)制造及其自動(dòng)化
作者所在班級(jí)
作 者 姓 名
作 者 學(xué) 號(hào)
指導(dǎo)教師姓名
指導(dǎo)教師職稱(chēng)
完 成 時(shí) 間
譯文標(biāo)題
施工質(zhì)量分布對(duì)步行機(jī)器人步態(tài)穩(wěn)定性的影響
原文標(biāo)題
Influence of construction mass distribution on the walking robot's gait stability
作 者
H.W.Muller
譯 名
哈維穆勒
國(guó) 籍
美國(guó)
原文出處
Journal of Mechanism Design,1981,Vol.103.No.1-4
譯文：
摘要：本研究的目的是找出步行機(jī)的施工參數(shù)與其穩(wěn)定性之間的聯(lián)系。此外，本文展示了重要的質(zhì)量分布對(duì)于正確設(shè)計(jì)的步態(tài)生成算法。這項(xiàng)研究是基于在Matlab Simulink開(kāi)發(fā)的六邊形雙壓電機(jī)器人的仿真模型。分析了機(jī)器人的腿和軀干之間的可變百分比質(zhì)量分布。
基于結(jié)果，我們可以得出結(jié)論，行走機(jī)器人的腿和軀干的重量之間的比例對(duì)大多數(shù)步行參數(shù)，如步幅長(zhǎng)度和速度，穩(wěn)定姿勢(shì)的機(jī)器，控制方法和移動(dòng)性有很大影響。 它對(duì)質(zhì)心位置也有巨大的影響，這是行走機(jī)器人的靜態(tài)和動(dòng)態(tài)穩(wěn)定性的關(guān)鍵問(wèn)題。 因此，在整個(gè)設(shè)計(jì)和編程過(guò)程中應(yīng)考慮步行機(jī)器人的質(zhì)量分布。
關(guān)鍵詞：六邊形雙壓機(jī)器人; 昆蟲(chóng); 質(zhì)量分布; 質(zhì)心; 步態(tài)穩(wěn)定性
1. 介紹
由身體的重量分布百分比限定的質(zhì)心位置影響所設(shè)計(jì)的機(jī)器的多個(gè)參數(shù)。 首先，它負(fù)責(zé)確保其在工作期間和靜止時(shí)的穩(wěn)定性。 它還對(duì)運(yùn)動(dòng)學(xué)參數(shù)和動(dòng)態(tài)參數(shù)具有主要影響，尤其包括運(yùn)動(dòng)中產(chǎn)生的慣性效應(yīng)。 這使得重量分布分析成為設(shè)計(jì)過(guò)程的重要部分，特別是在設(shè)計(jì)機(jī)器人，操縱器和處理設(shè)備時(shí)。
關(guān)于機(jī)器人的質(zhì)心位置的研究起源于人和動(dòng)物的運(yùn)動(dòng)的生物力學(xué)分析。 這樣的生物模型可以成功地用于機(jī)器工程。 當(dāng)代機(jī)器人的主要部分基于上述生物模型。 其中最重要的群體是步行機(jī)器人，其移動(dòng)類(lèi)似于大多數(shù)動(dòng)物使用步態(tài)循環(huán)組成的步驟[1]。
在當(dāng)前對(duì)質(zhì)心（c.o.m.）位置的研究中，重點(diǎn)在于確保機(jī)器人的靜態(tài)穩(wěn)定性。 當(dāng)c.o.m.時(shí)機(jī)器人被認(rèn)為是靜態(tài)穩(wěn)定的。 投影落在支撐多邊形內(nèi)。 支撐多邊形由所有接觸點(diǎn)定義，在多支腿機(jī)器人的情況下是支撐階段中機(jī)器人腿的尖端[1-3]。 在雙腿（雙足）機(jī)器人的情況下，動(dòng)態(tài)穩(wěn)定性是分析的因素，并且當(dāng)作用在質(zhì)心上的力矩在運(yùn)動(dòng)期間平衡時(shí)，機(jī)器人被認(rèn)為是動(dòng)態(tài)穩(wěn)定的。
在大多數(shù)研究中，作者考慮c.o.m. 相對(duì)于機(jī)器人姿勢(shì)的位置[4]。 在大多數(shù)情況下忽略由機(jī)器人設(shè)計(jì)限定的結(jié)構(gòu)特性的影響。 它主要被認(rèn)為是關(guān)于雙足機(jī)器人的研究，其重量分布是身體平衡的關(guān)鍵問(wèn)題[5]。 本研究的重點(diǎn)是重量分布對(duì)步行機(jī)的靜態(tài)穩(wěn)定性的影響，基于六邊形雙晶機(jī)器人。 第2節(jié)提供了分析設(shè)計(jì)的簡(jiǎn)要描述，包括原型的重量百分比分布。 第3節(jié)描述了本研究中使用的研究方法，第4節(jié)給出了他們獲得的結(jié)果
2. 六邊形雙壓機(jī)器人
六邊形雙晶機(jī)器人可以從六到四腿構(gòu)型（或相反方向）變換，而不需要改變。 由此，機(jī)器人可以在崎嶇的地形中以相對(duì)高的速度移動(dòng)，同時(shí)在站立和行走期間保持其操縱功能。 機(jī)器人主體（圖1）由三個(gè)主干段組成：前段KP，中間段KM和后段KT。 每個(gè)段配備有一對(duì)三連桿腿，命名為NL2，NP2，NL3，NP3（僅運(yùn)動(dòng)）和NP1和NL1（運(yùn)動(dòng)和操縱能力）。 作為一個(gè)特殊的特點(diǎn)，機(jī)器人配備了一個(gè)可擴(kuò)展的重量，可以控制c.o.m. 運(yùn)動(dòng)期間的位置[6]。
圖 1.六邊形雙壓機(jī)器人示意圖，顯示了原型的重量分布百分比KP-前主干節(jié)段，KM-中間主干節(jié)段，KT-后主干節(jié)段，1P-單軸接頭，2P-雙軸接頭，WM-可擴(kuò)展配重組件， NP1（NL1） - 右（左）前肢與操縱和運(yùn)動(dòng)功能，NP2（NL2） - 右（左）肢具有運(yùn)動(dòng)功能，NP3（NL3） - 右（左）后肢具有運(yùn)動(dòng)功能。
分析的行走機(jī)器人的原型組件的重量在表1中給出。可以在此基礎(chǔ)上計(jì)算總體重的百分比。 腿 - 軀干重量比為38.8％至61.2％。 軀干部分以及連接到它們的肢體的重量以總體重的百分比表示為24.4％/ 38.8％/ 36.8％（KP / KM / KT）
表1.六邊形雙壓機(jī)器人的段的重量
3. 研究方法
本文報(bào)告的研究是使用在軟件程序Matlab Simulink中開(kāi)發(fā)的仿真模型進(jìn)行的。 仿真模型是在六元四元雙機(jī)器人的數(shù)學(xué)模型的基礎(chǔ)上開(kāi)發(fā)的，是先前研究的派生分析。 選擇來(lái)量化機(jī)器人的靜態(tài)穩(wěn)定性的參數(shù)是縱向穩(wěn)定裕度（LSM）。 它被定義為距離c.o.m的最小距離。 投影和支撐多邊形邊緣平行于機(jī)器的c.o.m速度矢量測(cè)量[7]。
在該研究下進(jìn)行了兩個(gè)分析。 第一個(gè)是調(diào)查肢體的重量相對(duì)于機(jī)器人的總重量和機(jī)器人的靜態(tài)穩(wěn)定性之間的關(guān)系。 針對(duì)所分析的六邊形雙壓電機(jī)器人的三個(gè)選定姿勢(shì)檢查五個(gè)肢體重量比。 比率從30％到70％相差10％。 為了執(zhí)行分析的目的，必須假定身體段之間具有恒定的比率。 選擇最接近實(shí)際結(jié)構(gòu)的比率，前部分占總重量的20％，剩余重量在中間和后部分之間平均分配（每個(gè)40％）。 注意，在這些分析中，段的重量不包括附接到它們的肢體的重量。
第二項(xiàng)研究的目的是檢查機(jī)器人部分中幾個(gè)重量分布對(duì)其靜態(tài)穩(wěn)定性的影響。 選擇五個(gè)重量分布模式，質(zhì)心位于軀干前段（40％/ 30％/ 30％），雙軸關(guān)節(jié)（40％/ 40％/ 20％），軀干中段 （20％/ 40％/ 40％）和軀干后段（20％/ 30％/ 50％）上的平均值（30％/ 40％/ 30％）。 以與研究No.1相同的方式進(jìn)行分析，即通過(guò)讀取用于相同的三個(gè)機(jī)器人姿勢(shì)和每個(gè)預(yù)定義的重量分布配置的模擬模型中的質(zhì)心位置，隨后確定 在站立階段的縱向穩(wěn)定裕度。 在這些分析中，假定所有模擬200克單腿重量包括肢體重量。 假定的體重為3000g。
考慮三種特征姿勢(shì)，如圖1所示。 姿勢(shì)No.1（圖2a）表示機(jī)器人在三腳架步態(tài)中行走，其中三個(gè)腿（NL1，NP2，NL3）處于向前擺動(dòng)（轉(zhuǎn)移）階段，而其余的腿（NP1，NL2，NP3） 相。 在姿勢(shì)No.2（圖2b）中，失去靜態(tài)穩(wěn)定性的最大風(fēng)險(xiǎn)。 在該姿勢(shì)中，右腿的后腿和中腿處于站立期，而其他腿處于搖擺階段。 在兩種姿勢(shì)中，六邊形雙態(tài)機(jī)器人處于六足（即主要）配置。 姿勢(shì)No.3表示其中機(jī)器人支撐在腿NP2，NP3和NL3上的替代配置（四路）。 在四通道結(jié)構(gòu)中，軀干的前段向上傾斜90度的角度。
圖2.表示六邊形雙壓機(jī)器人的分析姿態(tài)的象形圖：a）六足機(jī)配置中的三角架步態(tài)，b）六足機(jī)構(gòu)配置中的最低穩(wěn)定性情況，c）四足配置。
4. 研究結(jié)果
在站立階段期間肢體的重量相對(duì)于機(jī)器人的總重量和機(jī)器人的穩(wěn)定性之間的關(guān)系在圖1的圖表中呈現(xiàn)。從曲線可以看出，對(duì)于三腳架步態(tài)，肢體的重量相對(duì)于機(jī)器人的總重量的變化對(duì)LSM值幾乎沒(méi)有影響。軀干和四肢之間的平均重量分布提供了最大的穩(wěn)定性。對(duì)于姿勢(shì)2和姿勢(shì)3，LSM值隨著肢體相對(duì)于軀干重量的增加的重量而減小。它是一個(gè)或多或少的線性關(guān)系。姿勢(shì)2中的肢體的低重量將姿勢(shì)穩(wěn)定性的損失改變?yōu)闃O限穩(wěn)定性條件。因此，對(duì)于小肢體權(quán)重，廣義坐標(biāo)配置對(duì)c.o.m的變化幾乎沒(méi)有影響。位置。在姿勢(shì)編號(hào)3中提升軀干產(chǎn)生較高的LSM值。 65％的值被認(rèn)為是肢體的極限重量，在該極限重量下機(jī)器人不能再在替代QUADRUPED配置中操作。
圖3.相對(duì)于機(jī)器人的總重量的肢體的重量對(duì)于三種不同姿勢(shì)的LSM值。
圖1中的條形圖。 下面的圖4表示六邊形雙晶機(jī)器人的段之間的重量分布對(duì)其靜態(tài)穩(wěn)定性的影響。 虛線表示穩(wěn)定性極限。 從圖中可以看出，在這種情況下，三腳架步態(tài)特征總是具有大的穩(wěn)定性余量。 對(duì)于剩余的姿勢(shì)，只有當(dāng)c.o.m. 位于單軸接頭或行李箱的后部。
對(duì)于完好的功能性，步行機(jī)器人應(yīng)當(dāng)能夠以四腿構(gòu)型操作，其要求主干段KP / KM / KT之間的設(shè)計(jì)比接近20％/ 40％/ 40％或20％/ 30％/ 50 ％。
圖4.軀干部分相對(duì)于機(jī)器人的總重量的重量與三種不同姿勢(shì)的LSM值的重量。
所分析的六邊形雙壓電機(jī)器人的靜態(tài)穩(wěn)定姿勢(shì)在圖6的圖中示出。 圖5和圖6。 點(diǎn)表示與地面接觸的腿的尖端的位置，并且圓圈表示轉(zhuǎn)移階段中的腿。 點(diǎn)坐標(biāo)是根據(jù)手足動(dòng)物的正向運(yùn)動(dòng)學(xué)計(jì)算的。 質(zhì)心位置用十字標(biāo)記，并且其坐標(biāo)從仿真模型中計(jì)算出來(lái)。 這種表示方法使得能夠及時(shí)驗(yàn)證靜態(tài)穩(wěn)定性。
圖5.相對(duì)于以六足配置（姿勢(shì)No.1）在三腳架步態(tài)中行走的機(jī)器人的支撐多邊形示出的質(zhì)心位置，軀干部分的重量比為20％/ 40％/ 40％。
圖。6.相對(duì)于機(jī)器人的支撐多邊形顯示的質(zhì)心位置為四足構(gòu)型（姿勢(shì)3），軀干部分的20％/ 30％/ 50％重量比。
5. 結(jié)論
該論文已經(jīng)證明重量分布配置對(duì)靜態(tài)穩(wěn)定性以及因此速度，步幅長(zhǎng)度，機(jī)器人的控制方法和移動(dòng)性的顯著影響?？梢酝ㄟ^(guò)使用模擬模型對(duì)已經(jīng)在工程階段的步行機(jī)器人執(zhí)行這樣的分析。注意，盡管在常規(guī)六足機(jī)的情況下可以忽略重量的分布，但在六邊形雙壓電機(jī)器人的情況下它是最重要的。由于組件的重量設(shè)計(jì)不正確，機(jī)器人可能無(wú)法使用替代姿勢(shì)。在分析的六邊形雙晶機(jī)器人的原型的情況下，表示為相對(duì)于機(jī)器人的總重量的分量權(quán)重的權(quán)重分布接近于使用四極配置的關(guān)鍵值。通過(guò)驗(yàn)證所選擇的配置，這是本研究的主題，我們只能定義可以找到有效重量分布的范圍。為了找到這個(gè)參數(shù)，將需要在預(yù)定范圍內(nèi)執(zhí)行更復(fù)雜的分析。因此，這種分析可以包括在滿足初步計(jì)算的作用的工程過(guò)程中，在下一步設(shè)計(jì)的結(jié)構(gòu)特征被定義之后，需要進(jìn)行檢查檢查。
原文：
Abstract
The goal of this research is to find connections between construction parameters of walking machine and its stability. Further this paper shows how important mass distribution is for properly designed gait generation algorithms. This research was made based on the simulation model of a hexa-quad bimorphic robot developed in Matlab Simulink. The analyses were made for variable percent mass distribution between the legs and trunk of the robot.
Based on the results we can conclude that the ratio between the weight of legs and trunk of the walking robot has a great influence on most of the walking parameters like stride length and speed, stable postures of machine, method of control and mobility. It has also a huge influence on the centre-of-mass position, which is the key issue of static and dynamic stability of walking robots. Therefore, mass distribution of walking robots should be considered throughout the design and programming process.
Keywords: hexa-quad bimorphic robot; hexapod; mass distribution; centre of mass; gait stability;
1.Introduction
The centre-of-mass position defined by the percentage weight distribution of the body influences a number of parameters of the designed machine. First and foremost it is responsible for ensuring its stability both during work and when at rest. It has also a major effect on the kinematic and dynamic parameters, including, inter alia, inertial effects arising in motion. This makes the weight distribution analysis an important part of the design process,especially when designing robots, manipulators and handling equipment.
The studies on the robots' centre-of-mass position originate from biomechanical analyses of the movement of humans and animals. Such biological models can be successfully used in machine engineering. A major portion of contemporary robots are based on the above-mentioned biological models. The most important group among them are walking robots which move similarly to most animals using gait cycle consisting of steps [1].
In the current studies on the centre-of-mass (c.o.m.) position the focus is on ensuring static stability of the robot. A robot is considered statically stable when the c.o.m. projection falls within the support polygon. The support polygon is defined by all the contact points, which in the case of multi-legged robots are the tips of the robot legs in the support phase [1–3]. In the case of two-legged (biped) robots the dynamic stability is the analysed factor and the robot is considered dynamically stable when the moments acting on the centre of mass are balanced during motion.
In most studies the authors consider the c.o.m. position in relation to the robot's posture [4]. The effect of the structural characteristics defined by the robot design is ignored in most cases. It is considered primarily in the studies concerning biped robots for which the distribution of weight is the key issue for body balance [5]. The focus of this study is the influence of the weight distribution on the static stability of the walking machine on the basis of a hexa-quad bimorphic robot. Section 2 provides a brief description of the analysed design including the percentage weight distribution of the prototype. Section 3 describes the research methods used in this study and Section 4presents the results obtained with them.
2. Hexa-quad bimorphic robot
The hexa-quad bimorphic robot can transform from six- to four-legged configuration (or the other way round) without needing change over. Owing to this, the robot can move with a relatively high speed in rough terrain, while maintaining its manipulation functionality during standing and walking. The robot body (Fig. 1) is composed of three trunk segments: front segment KP, middle segment KM and rear segment KT. Each segment is equipped with a pair of three-link legs designated NL2, NP2, NL3, NP3 (locomotion only) and NP1 and NL1 (locomotion and manipulation capability). As a special feature the robot is equipped with an extendable weight enabling control of the c.o.m. position during locomotion [6].
Fig. 1. Schematic of hexa-quad bimorphic robot showing the prototype's percentage weight distribution KP – front trunk segment, KM – middle trunk segment, KT – rear trunk segment, 1P – single axis joint, 2P – biaxial joint, WM – extendable weight assembly, NP1(NL1) – right (left) front limb with manipulation and locomotion function, NP2(NL2) – right (left) limb with locomotion function,
NP3(NL3) – right (left) rear limb with locomotion function.
The weights of the prototype assemblies of the analysed walking robot are given in Table 1. The percentages of the total body weight can be calculated on this basis. The leg-to-trunk weight ratio ranges from 38.8% to 61.2%. The weights of the trunk segments together with the limbs attached to them expressed as a percentage of the total body weight are 24.4%/38.8%/36.8% (KP/KM/KT).
Table 1. Weights of the segments of hexa-quad bimorphic robot
3. Research methods
The research reported in this article was carried out using simulation model developed in the software program Matlab Simulink. The simulation model was developed on the basis of the mathematical model of hexa-quad bimorphic robot, derived analytically for previous studies. The parameter chosen to quantify the static stability of the robot was the longitudinal stability margin (LSM). It is defined as the smallest distance from the c.o.m. projection and the support polygon edge measured parallel to the c.o.m velocity vector of the machine [7].
Two analyses were carried out under the research. The first of them was to investigate the relationship between the weight of limbs relative to the total weight of the robot and the robot's static stability. Five limb-to-weight ratios were checked for three chosen postures of the analysed hexa-quad bimorphic robot. The ratios differed by 10% from 30% to 70%. For the purpose of carrying out the analyses it is necessary to assume a constant ratio between the body segments. The ratio closest to the actual construction was chosen with the front segment making up 20% of the total weight with the remaining weight split equally between the middle and rear segments (40% each). Note that in theseanalyses the weights of segments do not include the weights of limbs attached to them.
The objective of the second study was to examine the effect of a few weight distributions among the robot segments on its static stability. Five weight distribution patterns were chosen with the centre of mass positioned on the front segment of the trunk (40%/30%/30%), on biaxial joint (40%/40%/20%), on middle segment of the trunk (30%/40%/30%), on the single axis joint (20%/40%/40%) and on the rear segment of the trunk (20%/30%/50%). The analysis was carried out in the same way as in study No. 1, namely by reading the centre-of-mass position in the simulation model for the same three robot postures and each of the pre-defined weight distribution configurations followed by determination of the longitudinal stability margin during stance phase. In these analyses the limb weight was included assuming for all simulations 200 g weight of a single leg. The assumed body weight was 3000 g.
Three characteristic postures were considered, as presented in Fig. 2. Posture No. 1 (Fig. 2a) presents the robot walking in a tripod gait with three legs (NL1, NP2, NL3) in forward swing (transfer) phase and the remaining legs (NP1, NL2, NP3) in the stance phase. In Posture No. 2 (Fig. 2b) there is the greatest risk of losing static stability. In that posture the rear legs and the middle leg on the right-hand side are in the stance phase and the other legs are in the sway phase. In both postures the hexa-quad bimorphic robot is in hexapod (i.e. primary) configuration. Posture No. 3 represents the alternative configuration (quadruped) in which the robot is supported on legs NP2, NP3 and NL3. In the quadruped configuration the front segment of the trunk is tilted up by an angle of 90 degrees.
Fig. 2. Pictograms representing the analysed postures of hexa-quad bimorphic robot: a) tripod gait in hexapod configuration, b) the lowest stability situation in hexapod configuration, c) quadruped configuration.
4. Results of research
The relationship between the weight of limbs relative to the total weight of the robot and the robot's stability during the stance phase is presented in the graphs in Fig. 3. From the curves it can be seen that for the tripod gait a change in the weight of limbs relative to the total weight of the robot has little effect on the LSM value. Equal distribution of weight between the trunk and limbs offered the greatest stability. For Posture No. 2 and Posture No. 3 the LSM value decreases with the increasing weight of limbs in relation to the trunk weight. It is a more or less linear relationship. Low weight of limbs in Posture No. 2 changes the loss of postural stability to the limit stability condition. Hence, for small limb weights the generalized coordinates configuration has little effect on the change of c.o.m. position. Raising the trunk in Posture No. 3 produced higher LSM values. The value of 65% is considered the limit weight of limbs at which the robot can no longer operate in the alternative QUADRUPED configuration.
Fig. 3. Weight of limbs relative to the total weight of the robot vs. LSM value for three different postures.
The bar chart in Fig. 4 below represents the influence of the weight distribution between the segments of hexaquad bimorphic robot on its static stability. The dashed line represents the stability limit. As it can be figured out from the graph, also in this case the tripod gait features always a large stability margin. For the remaining postures stability can be achieved only when the c.o.m. is located on the single-axis joint or on the rear segment of the trunk.
For uncompromised functionality the walking robot should be able to operate in four-legged configuration which requires the design ratio between the trunk segments KP/KM/KT to be close to 20%/40%/40% or 20%/30%/50%.
Fig. 4. Weights of trunk segments relative to the total weight of the robot vs. LSM value for three different postures.
The statically-stable postures of the analysed hexa-quad bimorphic robot are illustrated in the graphs in Fig. 5 and Fig. 6. The dots represent the positions of the tips of legs in contact with the ground and the circles represent the legs in the transfer phase. The point co-ordinates were calculated on the basis of pedipulator forward kinematics. The centre-of-mass position is marked with a cross and its co-ordinates were figured out from the simulation model. This method of representation enables prompt verification of static stability.
Fig. 5. Centre-of-mass position shown against the support polygon of a robot walking in tripod gait in hexapod configuration (Posture No. 1),20%/40%/40% weight ratio of the trunk segments.
Fig. 6. Centre-of-mass position shown against the support polygon of a robot in quadruped configuration (Posture No. 3), 20%/30%/50% weightratio of the trunk segments.
5. Conclusions
The paper has demonstrated a significant influence of the weight distribution configuration on the static stability and, in consequence, also the speed, the stride length, the method of control and mobility of the robot. Such analyses can be carried out for walking robots already at the engineering stage by using simulation models. Note that while the distribution of weight can be ignored in the case of conventional hexapods it is of primary importance in the case of the hexa-quad bimorphic robots. With incorrectly designed weights of components it may be impossible for the robot to use the alternative posture. In the case of the analysed prototype of hexa-quad bimorphic robot the weight distribution expressed as the components weights relative to the total weight of the robot is close to the value critical for using the quadruped configuration. By verification of the chosen configurations, which was the subject of this research, we can only define the range in which effective weight distribution can be found. In order to find this parameter more complex analyses would need to be carried out in the pre-determined range. Therefore, such analyses can be included in process of engineering fulfilling the role of preliminary calculations, which need to be followed by check examinations after structural features have been defined in the next step of design.
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