丘陵山区履带式行走系统设计
购买设计请充值后下载,资源目录下的文件所见即所得,都可以点开预览,资料完整,充值下载可得到资源目录里的所有文件。【注】:dwg后缀为CAD图纸,doc,docx为WORD文档,原稿无水印,可编辑。具体请见文件预览,有不明白之处,可咨询QQ:12401814
关于装载适应性神经模糊系统的有两足行走的机器人的零刻点弹道造型D. Kim, S.-J. Seo and G.-T. Park摘要:对于制造机器人来说两足动物的体系结构高度适用于它们工作在人的环境里,因为这样将使机器人避免障碍变成一项相对的容易的任务。 然而,在走动的机制中介入复杂动力学,这使得制作这样的机器人的控制系统变成了一项富有挑战性的任务。 机器人脚部的零刻点(ZMP)弹道是机器人行走时的稳定性的重要保障。 如果ZMP可以在线测量那么就将使为机器人稳定行走创造条件成为可能,而且通过运用标准的ZMP还可以实现机器人的稳定控制。ZMP数据是通过两足行走机器人实时测量出来的,在这之后在通过一套适应性神经模糊系统(ANFS)将其造型。测量了在水平基准面的自然行走和在带有10度倾斜面的上下行走。通过改变模糊系统的成员作用和结果输出部分的规则,使得ANFS造型的表现最优化。由ANFS展示的优秀表现意味着它不仅可以运用于模型机器人的运动,还可以运用于控制真正的机器人。1 介绍两足动物结构是对走动的机器人的最多才多艺的设定之一。两足动物结构,使机器人即使在有台阶或障碍等的环境里也具备和人几乎同样的可支配的机械装置。然而,介入的动力学是高度非线性,复杂和不稳定的。因此,它是引入模仿人体行走的最大的困难。模仿人体行走是一个可观的研究领域(1)。与产业机器人的操作器相比,一个走动的机器人和地面之间的相互作用是复杂的。在这种相互作用的控制上零刻点(ZMP) 2概念被证明是有用的。在ZMP的弹道的帮助下机器人的脚在步行期间的行动是受其稳定性信息的诱导的。使用ZMP我们可以整合两足的机器人的走的模式并用实际机器人示范行走行为。 因此,ZMP标准决定了一个两足的机器人的动态稳定性。ZMP代表地面反作用力被采取发生的点。使用机器人的模型,ZMP的地点可以被计算。然而,ZMP价值指标与计算值价值指标之间有很大偏差也是有可能的,这是因为物理参量的偏差在数学模型和实际机器之间。 因此,实际ZMP是应该测量的,尤其是在它作为稳定行走的控制参数时。在这项工作中,实际ZMP整周期走动数据是通过一个实用两足走动机器人获得的。机器人将在水平基准面和10度倾斜面上被测试。一个适应性神经模糊系统(ANFS)将被用于控制一个复杂的真正的有两足的走动机器人,以便于ZMP的建模,使其能应用与控制中。2有两足的走动机器人2.1有两足的走动机器人的设计我们设计了并且制造了如图1所示的有两足的走动机器人。 机器人有19联接。 机器人的关键尺寸如图1所示.高度308mm,总重量约为1700 g,包括个别电池。 通过使用铝制结构使机器人的重量减到了最小。每一个联接都由一个遥控装置控制,这个遥控装置包括一个直流马达、齿轮和一个简单的控制器。每一台遥控装置都安装在联接结构上。 这个结构保证机器人是稳定的(即不会容易跌倒)并且给了机器人一个人类的外型。 我们的机器人系统结构如图2所示。机器人能在平面或小斜度面以1.4s一步,每步48mm的速度行走。机器人的配置如表一所示。机器人的行走动作如图36所示。图3、4分别为机器人在平面行走时正视图和侧视图。图5是机器人沿着倾斜面向下步行的快照,而图6是机器人沿着倾斜面向上步行的快照。行动时联接的位置如图7.所示。 被测量的ZMP弹道是从这十个自由(DOF)(如图7.所示)的数据得到的。 二个自由度被分配到臀部和脚腕,每个膝盖分配一个自由度。 使用这些连接角,一个循环走的样式就会体现出来。 我们的机器人能连续地走,无需跌倒。 在附录里总结了我们的机器人的四步行动的连接角。2.2 ZMP测量系统在一个机器人脚部的ZMP弹道是步行的稳定的一个重要标准。 在许多研究中, ZMP坐标是通过使用机器人模型和连接处的编码器传出的信息用计算机计算出来的。然而,我们使用更直接的方法,使用了机器人脚部上的传感器测量的数据。在机器人脚部的作用之下地面的反作用力的分布是复杂的。 然而,如图8.所示,在脚的脚底的任意点P点的反作用力都可以用力量N和M时刻之前在任意时候代的力表。 ZMP是在地面上的脚的压力的中心,并且关于这点的地面运用的片刻是零。 换句话说,在地面上的点P是惯性和重力在0刻没有沿轴的组分,平行与地面的点1, 7。图9说明了使用的传感器和他们的在机器人脚的脚底的安置情况。 用于我们的实验的力量传感器的种类是Flexi Force A201传感器8。 他们附在构成脚的脚底板材的四个角落。 传感器信号由一个ADC板数字化,与10ms的采样时光。 测量在实时被执行。脚压力通过求和力量信号得到。 使用传感器数据计算实际ZMP价值是容易的。 使用(1),计算位置脚坐标框架的ZMP。式中每fi在传感器ri的力量是传感媒介的传感器位置。 这些是在图10.的详细说明。 在图形中, O是位于低左手角落左脚坐标框架的起源。实验性结果如图1116所示。 图11,13和15显示的是走动机器人在平面和10度倾斜面的四步走动的x坐标和y坐标转化的实际ZMP位置。图12,14和16显示了机器人运用图11,13和15 的准确ZMP坐标的单步行走情况。如弹道所显示,ZMP存在于实线显示的一个长方形领域。因此,ZMP的位置是与机器人脚部相关的,因此机器人是稳定的。3 ZMP弹道建模在许多科学问题中,通往他们答案的实质性的一步就是在他们的实验下建立(数学)模型。 建模的重要性体现在是建立被观察物和可变物之间的经验性的关系。 机器人步行介入的复杂动力学使做机器人控制系统变为一项富挑战性的任务。 然而,如果高度非线性和复杂动力学可以被严密地建模,之后他的模型可以用于机器人的控制。 另外,建模,甚至能用于机器智能控制与干扰、噪声的最小化处理。3.1 ANFS模糊建模技术近些年已经成为一项活跃的研究领域,因为它在复杂的,不清楚的,不明确的系统中依然能有出色的表现,而这些时候常规的数学建模很难给出让人满意的答案9。就此而论我们打算使用此系统为ZMP弹道建模。模糊推理系统是以模糊集合理论的概念、模糊的if-then 语句和模糊推理为基础的一个普遍的计算的框架。 我们将使用Sugeno 模糊模型,因为在这个系统中,每一个规则都有明显的输出,总体的输出将通过加权平均值给出。这样就避免了计算的费时过程。当我们考虑在模糊建模时的模糊规则时发现,结果部分可以由一个恒定或一个线性的多项式表达。 可以用于模糊系统的多项式的不同的形式如表2.所示。建模的表现形式取决于用于建模的表示结果的多项式的种类。 而且,我们可以为模糊规则的前期部分的模糊嵌入拓展各种各样单元作用(MFs),例如三角和高斯。 这些是为算式贡献可行方法另一个因素。多项式的种类如下是建模系统的结构图如图17所示。 提出的方法首先用于建模,而后用于控制一个实际的两足结构行走机器人。为了得到模糊建模系统的模糊规则,我们必须记录一个非线性系统,这个系统是通过两足行走机器人的十个输入变量产生的模糊坐标建立的,每个输入变量会产生两个模糊坐标。模糊建模的if-then法规如下:在式中Ai,Bi,J1,在规则的假设部分中起到语言上判断的作用,分别结合输入变量x1, x2, , x10。 fj (x1、x2、, x10); 是常数,或者jth规则的已知结果多项式函数。如图18所示, 检定了MFs的二种类型。 一个是三角式,另一个是高斯式。图19是适应性神经模糊系统体系结构,考虑到让它等同于十输入模糊模型。在这个系统中假设每个输入有两个模糊值与它对应,如图18所示。标记P的值给出的是所有输入信号的乘积,而这些标记的N的值计算的是某一确定的反作用力与总反作用力之和的比。关于如何使ANFIS参量变化,我们使用梯度下降算法或一种递归最小平方的估计算法重复调整前提和结果参量。 然而,我们不使用复杂杂种学习算法,反而使用一般最小平方的估计算法并且只确定结果多项式函数的趋势。3.2模仿结果使用ANFS,模型大致建成了。 然后准确性在中间领域误差(MSE)中被量化了。ANFS系统被申请为两足走动机器人的ZMP弹道建模,通过运用机器人测量传出的数据。ANFS的表现取决于MF的机警性和模糊规则的结果输出。从我们的机器人输出的ZMP弹道数据(如附录的图3241所示)将用于过程参量。当三角和高斯MFs用于前提部分或用于结果部分的不变参数,那么相应的MSE值列在表3中。我们在图2025中绘出了我们的结果。由ANFS产生的ZMP弹道图如图20,22,24所示分别为水平基准面的行走图,10度倾斜面下行图和10度倾斜面上行图。在图21,23,25,我们可以看见由ANFS产生的相应的ZMP弹道。简而言之,两个膝盖的过程参数可以被忽略。 作为结果,我们可以减少模糊规则的维度和从而降低计算负担。 在这种情况下ANFS的仿真条件和它对应的MSE(均方的误差)价值在表4列出。从给出的模仿结果的图和表中,我们能看到从模糊系统得到的ZMP弹道非常类似于我们的行走机器人所测量出的实际ZMP弹道(如图1116所示)。ANFS被展示的高准确性能力,意味着ANFS可以有效地被用于建模和控制一个实际的两足结构走动机器人。3.3比较我们现在把ANFS的表现与三种统计回归模型的数学模型相比较。对于每个统计回归模型,四个不同案件类型被修建了。它们在两种输入下的一般表达式如下: 这里ci是回归常数。对应的MSE值在表57里被给出。它测量第二类型给x和Y坐标的最佳的结果所有被考虑的走的条件的。产生的ZMP弹道和相应的产生它们的第二类型回归模型如图2631所示。我们可以认为, ANFS比统计回归模型展示了一条相当地更好的ZMP弹道。4个结论一个实用的装载模糊神经系统的零弹道两足结构走动机器人被展示出来。ZMP弹道是确保机器人行走稳定性的重要保障。但是地面复杂的反作用力使控制变得困难。我们试图建立过程参数之间的经验的关系,并且通过将其运用于一个两足结构走动机器人来解释经验规律。整个走动过程的ZMP数据通过让一个实际两足结构机器人在水平基准面和斜面行走而获得。ANFS的适用性取决于使用的MF和模糊的规则的结果部分。 使用ANFS产生的ZMP弹道严密地匹配于被测量的ZMP弹道。 然后模仿结果也表示,使用ANFS引起的ZMP可以改善两足结构走动机器人的稳定性并且ANFS不仅可以有效地用于建模,而且可以用于控制实际两足结构走动机器人。如图3241所示。5鸣谢这项工作由韩国科学和工程学基金会的基础性研究计划的第R01-2005-000-11-44-0支持。6参考文献1 Erbatur、F.、Okazaki、A.、Obiya、K.、Takahashi、T.和Kawamura, A. :“一项关于两足结构走动机器人的零刻点测量的研究”。 Proc.7th Int。 关于先进的运动控制2002年,第 431436页。2 Vukobratovic、M.、Brovac、B.、Surla、D.和Stokic, D. : 运动机器人 (Springer-Veriag1990)3 Takanishi、A.、Ishida、M.、Yamazaki、Y.和Kato, I. : “动态走的机器人WL-10RD的认识”。 Proc。 Int. Conf。 先进机器人, 1985年, 第. 459466页。4 Hirai、K.、Hirose、M.、Haikawa、Y.和Takenaka, T. : “本田类人机器人的”。 Proc。国际电气电子工程师协会。 Conf。 在机器人技术和自动控制, 1998年,第 13211326页。5 Park,、J.H.和Rhee, Y.K. : 减少两足结构走动机器人的干线行动的ZMP弹道世代。 Proc。国际电气电子工程师协会。 Conf。 在智能机器人和系统, 1998年,第 9095页。6Park、J.H.和Cho, H.C. : “提高两足结构走动机器人的基本联接的在线ZMP弹道测量。 Proc。国际电气电子工程师协会。 Conf。 在机器人技术和自动控制, 2000年, 第. 33533358页。7 Tak、S.、Song、O.和Ko, H.S. : 行动平衡过滤。 Proc。 欧洲制图,第19卷,第3日2000年。8 FlexiForce A201传感器模型, http:/www.tekscan.com/ exiforce/exiforce.html, (访问2004 4月)。9 Takagi、T.和Sugeno, M. : 神经模糊系统和它的建模和控制, 国际电气电子工程师协会,传感器., 1985年, S-15,第116132页。10 Jang, J.S.: 适应性网络神经模糊系统: Adaptive-Networks-Based Fuzzy Inference Sys- tem, 国际电气电子工程师协会,传感器., 1993, 23, (3), 第 665685页。7附录这个附录总结了我们两足结构走动机器人的四步行动的连接角。 这些连接角如下。图1两足结构走动的机器人(所有尺寸单位为毫米)图2机器人系统的结构图 图3机器人在水平基准面行走的正视图 图4与图3对应的机器人的 图5机器人沿带有10度斜度 图6机器人沿带有10度斜侧视图 的斜坡向下步行的快照 度的斜坡向上步行图7由连接角的表示法构成的 图8 ZMP的概念 图9力量传感器和他们的安置十个自由程度 a力量传感器b安置在构成机器人脚部板材下面的四个角落图10传感器位置和左右脚的应用力图11在机器人的四步行动的实际ZMP位置在基准水平面的a x坐标的by坐标 图12一步行动的ZMP弹道与图11相对应图14 一步行动的ZMP弹道与图13相对应图13沿着一个10度倾斜的面向下步行的机器人的四步行动的实际ZMP位置的a x坐标 b y坐标图15沿着一个10度倾斜的面向上步行的机器人的四步行动的实际ZMP位置的a x坐标b y坐标图16一步行动的ZMP弹道与图15相应 图17塑造方法的ANFS的结构图图18在与二个模糊的标签的模糊的模型的三角和高斯MFs用于输入变数a三角MF b高斯MF图19与ANFIS是等效的能适应的神经模糊的结构图20引起了使用ANFS的四步行动的ZMP位置与被测量的数据(机器人在水平基准面行走)的比较a x坐标 b y坐标 图21一步行动的引起的ZMP弹道与图20相对应 图23一步行动的引起的ZMP弹道与图 22对应图22引起了使用ANFS的四步行动的ZMP位置与被测量的数据(机器人在一个10度斜面向下行走)的比较a x坐标 b y坐标24引起了使用ANFS的四步行动的ZMP位置与被测量的数据(机器人在一个10度斜面向上行走)的比较a x坐标b y坐标 图25一步行动的引起的ZMP弹道与图24相应 图27一步行动的引起的ZMP弹道与图26相对应图26引起了四步行动的ZMP位置使用一个统计回归模型与被测量的数据比较为案件机器人在水平基准面上走的a x坐标 b y坐标图28引起了四步行动的ZMP位置使用统计回归模型与被测量的数据比较为案件机器人步行沿着向下10倾斜的a x坐标 b y坐标 图29一步行动的引起的ZMP弹道与图28相应 图31一步行动的引起的ZMP弹道与图30相对应图30引起了四步行动的ZMP位置使用统计回归模型与被测量的数据比较为案件机器人向上走10倾斜的面a x坐标 b y坐标 图32我们的机器人的四步行动的连接角1 图33在我们的机器人的四步行动的连接角2 图34在我们的机器人的四步行动的连接角3 图35在我们的机器人的四步行动的连接角4 图36在我们的机器人的四步行动的连接角5 图37在我们的机器人的四步行动的连接角6图38在我们的机器人的四步行动的连接角7 图39在我们的机器人的四步行动的连接角8图40在我们的机器人的四步行动的连接角9图41在我们的机器人的四步行动的连接角10表1机器人规格尺寸高:300mm, 宽;225mm重1.7kgCPUS3C3410X驱动RC电机(11kg,4.8V)自由度19动力源AA号镍镉电池(2100MA)行走速度48mm/1.4s表2神经模糊系统运用的不同形式的多项式输入多项式1230命令不变不变不变1命令直线的双线性的三线性的表3我们两足结构走动机器人在仿真条件的下和相应的实际的四部走动的ZMP值行走条件度乐观因素前提的MF结果类型MSE mmX 坐标Y 坐标0三角常量4.3254.615103.5717.008108.1255.5790高斯常量4.2494.59103.5677.225107.9435.797表4我们两足结构走动机器人在仿真条件的下和相应的实际的四部走动的ZMP值行走条件度乐观因素前提的MF结果类型MSE mmX 坐标Y 坐标0三角常量6.71610.928106.09213.4461011.03112.25201命令4.5396.985104.1147.648108.8626.4430高斯常量6.40410.823105.67012.2071010.96611.17901命令4.1644.763103.8799.928108.5525.011表5我们两足结构走动机器人在仿真条件的下和相应的实际的四部走动的ZMP值行走条件度统计的回归模型MSE mmX 坐标Y 坐标0一型32.17548.793二型7.78013.558三型8.12615.353四型13.01821.420表6我们两足结构走动机器人在仿真条件的下和相应的实际的四部走动的ZMP值行走条件度统计的回归模型MSE mmX 坐标Y 坐标10一型34.56446.773二型7.73416.743三型8.19319.377四型11.60625.290表7我们两足结构走动机器人在仿真条件的下和相应的实际的四部走动的ZMP值行走条件度统计的回归模型MSE mmX 坐标Y 坐标10一型34.42150.216二型13.66115.560三型14.40917.436四型17.54324.889Zero-moment point trajectory modeling of a bipedwalking robot using an adaptive neuro-fuzzy systemD. Kim, S.-J. Seo and G.-T. ParkAbstract: A bipedal architecture is highly suitable for a robot built to work in human environmentssince such a robot will find avoiding obstacles a relatively easy task. However, the complex dynamics involved in the walking mechanism make the control of such a robot a challenging task.The zero-moment point (ZMP) trajectory in the robots foot is a signicant criterion for the robotsstability during walking. If the ZMP could be measured on-line then it becomes possible to createstable walking conditions for the robot and here also stably control the robot by using the measured ZMP, values. ZMP data is measured in real-time situations using a biped walking robot and this ZMP data is then modelled using an adaptive neuro-fuzzy system (ANFS). Natural walking motions on at level surfaces and up and down a 10 slope are measured. The modellingperformance of the ANFS is optimized by changing the membership functions and the consequentpart of the fuzzy rules. The excellent performance demonstrated by the ANFS means that it can not only be used to model robot movements but also to control actual robots.1 IntroductionThe bipedal structure is one of the most versatile setups for a walking robot. A biped, robot has almost the same movement mechanisms as a human and it able to operate in environments containing stairs, obstacles etc. However, the dynamics involved are highly nonlinear, complex and unstable. Thus, it is difcult to generate a human-like walking motion. The realisation of human-like walking robots is an area of considerable activity 14. In contrast to industrial robot manipulators, the interaction between a walking robot and the ground is complex. The concept of a zero-moment point (ZMP) 2 has been shown to be useful in the control of this interaction. The trajectory of the ZMP beneath the robot foot during a walk is after taken to be an indication of the stability of the walk 16. Using the ZMP we can synthesise the walking patterns of biped robots and demonstrate a walking motion with actual robots. Thus, the ZMP criterion dictates the dynamic stability of a biped robot. The ZMP represents the point at which the ground reaction force is taken to occur. The location of the ZMP can be calculated using a model of the robot. However, it is possible that there can be a large error between the actual ZMP value and the calculated value, due to deviations in the physical parameters between the mathematical model and the real machine. Thus, the actual ZMP should be measured especially if it is to be used in a to parameters a control method for stable walking.In this work actual ZMP data taken throughout the whole walking cycle are obtained from a practical biped waling robot. The robot will be tested both on a at oor and also on 10 slopes. An adaptive neuro-fuzzy system (ANFS) will be used to model the ZMP trajectory data thereby allowing its use to control a complex real biped walking robot.2 Biped walking robot2.1 Design of the biped walking robotWe have designed and implemented the biped walking robot shown in Fig. 1. The robot has 19 joints. The key dimensions of the robot are also shown in Fig. 1.The height and the total weight are about 380mm and 1700 g including batteries, respectively. The weight of the robot is minimised by using aluminium in its construction. Each joint is driven by a RC servomotor that consists of a DC motor, gears and a simple controller. Each of the RC servomotors is mounted in a linked structure. This structure ensures that the robot is stable (i.e. will not fall down easily) and gives the robot a human-like appearance. A block diagram of our robot system is shown in Fig. 2.Out robot is able to walk at a rate of one step (48mm) every 1.4 s on a at oor or an shallow slopes. The specications of the robot are listed in Table 1. The walkingmotions of the robot are shown in Figs. 36.- Figures 3 and 4 are show front and side views of the robot, respectively when the robot is on a at surface. Figure 5 is a snapshot of the robot walking down a slope whereas Fig. 6 is a snapshot of the robot walking up a slope.The locations of the joints during motion are shown in Fig. 7. The measured ZMP trajectory is obtained from ten-degree-of-freedom (DOF) data as shown in Fig. 7. Two degrees of freedom are assigned to the hips and ankles and one DOF to each knee. Using these joint angles, a cyclic walking pattern has been realised. Our robot is able to walk continuously without falling down. The joint angles in the four-step motion of our robot are summarised in the Appendix.2.2 ZMP measurement systemThe ZMP trajectory in a robot foot is a signicant criterion for the stability of the walk. In many studies, ZMP coordinates are computed using a model of the robot and information from the encoders on the joints. However, we employed a more direct approach which is to use data measured using sensors mounted on the robots feet.The distribution of the ground is reaction force beneath the robots foot is complicated. However, at any point P on the sole of the foot to the reaction can be represented by a force N and moment M, as shown in Fig. 8. The ZMP is simply the centre of the pressure of the foot on the ground, and the moment applied by the ground about this point is zero. In other words, the point P on the ground is the point at which the net moment of the inertial and gravity forces has no component along the axes parallel to the ground 1, 7.Figure 9 illustrates the used sensors and their placement on the sole of the robots foot. The type of force sensor used in our experiments is a FlexiForce A201 sensor 8. They are attached to the four corners of the plate that constitutes the sole of the foot. Sensor signals are digitised by an ADC board, with a sampling time of 10ms. Measurements are carried out in real time.The foot pressure is obtained by summing the force signals. Using the sensor data it is easy to calculate the actual ZMP values. The ZMPs in the local foot coordinate frame are computed using (1).Where each fi is the force at a sensor ri is the sensor position which is a vector. These are dened in Fig. 10. In the gure, O is the origin of the foot coordinate frame which is located at the lower-left-hand corner the left foot. Experimental results are shown in Figs. 1116. Figures 11, 13 and 15 show the x-coordinate and y-coordinate of the actual ZMP positions for the four-step motion of the robot walking on a at oor and also down and up a slope of 10 , respectively. Figures 12, 14 and 16 shown the ZMP trajectory of the one-step motion of the robot using the actual ZMP positions shown in Figs. 11, 13and 15. As shown in the trajectories, the ZMPs exist in a rectangular domain shown by a solid line. Thus, the positions of the ZMPs are with in the robots foot and hence the robot is stable.3 ZMP trajectory modellingIn many scientic problems an essential step towards their solution is to accomplish the modelling of the system under investigation. The important role of modelling is to establish empirical relationships between observed variables. The complex dynamics involved in making a robot walkmake the control of the robot control a challenging task. However, if the highly nonlinear and complex dynamics can be closely produced then this modelling can be used in the control of the robot. In addition, modelling, can even be used in robust intelligent control to minimise disturbances and noise.3.1 ANFSFuzzy modelling techniques have become an active research area in recent years because of their successful application to complex, ill-dened and uncertain systems in which conventional mathematical models fail to give satisfactory results 9. In this light we intend to use a system to model the ZMP trajectory.The fuzzy inference system is a popular computing framework that is based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. We will use the Sugeno fuzzy model in which since each rule has a crisp output, the overall output is obtained via a weighted average, thus avoiding the time-consuming process of defuzzication. When we consider fuzzy rules in the fuzzy model, the consequent part can be expressed by either a constant or a linear polynomial. The different forms of polynomials that can be used in the fuzzy system are summarised in Table 2. The modelling performance depends on the type of consequent polynomial used in the modelling. Moreover, we can exploit various forms of membership functions (MFs), such as triangular and Gaussian, for the fuzzy set in the premise part of the fuzzy rules. These are another factor that contributes to the exibility of the proposed approach.The types of the polynomial are as followsA block diagram of the modelling system is shown in Fig. 17. The proposed method is rst used to model and then control a practical biped walking robot.To obtain the fuzzy rules for the fuzzy modelling system we must notes that the nonlinear system to be identied is a biped walking robot with ten input variables and each input variables has two fuzzy sets, respectively. For the fuzzy model, the if-then rules are as follows:where Ai,Bi,, Ji in the premise part of the rules have linguistic values (such as small or big) associated with the input variable, x1,x2,x10; respectively. Fj (x1, x2, x10); is the constant, or rst-order consequent polynomial function for the jth rule. As depicted in Fig. 18, two types of MFs were examined. One is the triangular and the other is Gaussian.Figure 19 is an adaptive neuro-fuzzy inference system 10 architecture that is equivalent to the ten-input fuzzy model considered here, in which each input is assumed to have one of the twoMFs shown in Fig. 18. Nodes labelled P give the product of all the incoming signals and these labelled N calculate the ratio of a certain rules ring strength to the sum of all the rules ring strengths. Parameter variation in ANFIS is occured using either a gradient descent algorithm or a recursive least-squares estimation algorithm to adjust both the premise and consequent parameters iteratively. However, we do not use the complex hybrid learning algorithm but instead use the general least-squares estimation algorithm and only determine the coefcients in the consequent polynomial function.3.2 Simulation resultsApproximately models were constructed using the ANFS. Then accuracy was quantied in terms of there mean- squared error (MSE), values. The ANFS was applied to model the ZMP trajectory of a biped walking robot using data measured from out robot. The performance of the ANFS was optimised by warying the MF and consequent type in the fuzzy rule. The measured ZMP trajectory data from our robot (shown in Figs. 3241A in the Appendix) are used as the process parameters.When triangular and Gaussian MFs are used in the premise part and a constant in the consequent part then, the corresponding MSE values are listed in Table 3. We have platted our results in Figs. 2025. The generated ZMP positions from the ANFS are shown in Figs. 20, 22 and 24 for a at level oor, walking down a 10 slope and walking up a 10 slope, respectively. In Figs. 21, 23 and 25, we can see the corresponding ZMP trajectories which are generated from the ANFS.For simplicity, the process parameter of both knees can be ignored. As a result, we can reduce the dimension of the fuzzy rules and thereby lower the computational burden. In this case the simulation conditions of the ANFS and its corresponding MSE values are given in Table 4.From the Figures and Tables that present the simulation results, we can see that the generated ZMP trajectory from the fuzzy system is very similar to actual ZMP trajectory of measured for our walking robot shown in Figs. 1116. The demonstrated high performance ability of the ANFS, means that ANFS can be effectively used to model and control a practical biped walking robot.3.3 ComparisonsWe now compare the performance of ANFS with numerical methods including three types of statistical regression models. For each statistical regression model, four different case types were constructed. Their general forms in the case of two inputs are given as:where the ci are the regression coefcients.The corresponding MSE values are given in Tables 57 which reveals that type 2 gives the best results for the x and y coordinates for all the considered walking conditions. The generated ZMP positions and their corresponding trajectons generated using the type 2 regression model are shown in Figs. 2631. We can conclude that the ANFS demonstrated a considerably better ZMP trajectory than the statistical regression models.4 ConclusionsThe ANFS modelling at the ZMP trajectory of a practical biped walking robot has been presented. The trajectory of the ZMP is an important criterion for the balance of a IEE Proc.-Control Theory Appl., Vol. 152, No. 4, July 2005 walking robot but the complex dynamics involved make robot control difcult.We have attempted to establish empirical relationships between process parameters and to explain empirical laws by incorporating them into a biped walking robot. Actual ZMP data throughout the whole walking phase was obtained from a real biped walking robot both on a at level oor andon slopes. The applicability of the ANFS depends on the MF used and the consequent part of the fuzzy rule. The generated ZMP trajectory using ANFS closely matches the measured ZMP trajectory. Then simulation results also show that the ZMP generated using the ANFS can improvethe stability of the biped walking robot and therefore ANFS can be effectively used to not only to model but also control practical biped walking robots. Figs. 3241A5 AcknowledgmentsThis work was supported by grant no.R01-2005-000-11-44-0 from the Basic Research Program of the Korea Science & Engineering Foundation.6 References1 Erbatur, F., Okazaki, A., Obiya, K., Takahashi, T., and Kawamura, A.: A study on the zero moment point measurement for biped walking robots. Proc.7th Int. Workshop on Advanced Motion Control, 2002, pp. 4314362 Vukobratovic, M., Brovac, B., Surla, D., and Stokic, D.: Biped Locomotion (Springer-Verlag, 1990)3 Takanishi, A., Ishida, M., Yamazaki, Y., and Kato, I.: The realization of dynamic walking robot WL-10RD. Proc. Int. Conf. on Advanced Robotics, 1985, pp. 4594664 Hirai, K., Hirose, M., Haikawa, Y., and Takenaka, T.: The development of Honda humanoid robot. Proc. IEEE Int. Conf. on Robotics and Automation, 1998, pp. 132113265 Park, J.H., and Rhee, Y.K.: ZMP Trajectory Generation for Reduced Trunk Motions of Biped Robots. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, IROS 98, 1998, pp. 90956 Park, J.H., and Cho, H.C.: An On-line Trajectory Modier for the Base Link of Biped Robots to Enhance Locomotion stability. Proc. IEEE Int. Conf. on Robotics and Automation, 2000, pp. 335333587 Tak, S., Song, O., and Ko, H.S.: Motion Balance Filtering. Proc. EUROGRAPHICS, vol. 19, no. 3, 20008 FlexiForce A201 Sensor Model, http:/www.tekscan.com/exiforce/ exiforce.html, (accessed April 2004)9 Takagi, T., and Sugeno, M.: Fuzzy Identication of Systems and Its Applications to Modeling and Control, IEEE Trans. Syst. Man Cybern., 1985, S-15, pp. 11613210 Jang, J.S.: ANFIS: Adaptive-Networks-Based Fuzzy Inference Sys- tem, IEEE Trans. Sys. Man Cybern., 1993, 23, (3), pp. 6656857 AppendixThis Appendix summarise the joint angles in the four-step motion of our biped walking robot. These joint angles are as follows.
收藏