外文翻译---四足机器人的步态适应

附录
Gait Adaptation in a Quadruped Robot
1. Introduction
A short time after birth a foal can walk and then run. It is remarkable that the animal learns tocoordinate the many muscles of the legs and trunk in such a short period of time. It is not likely that any learning algorithm could program a nervous system ab initio with so few training epochs. Nor is it likely that the foal’s locomotor controller is completely determined before birth. How can this a- bili ty be explained? How can this ability be incorporated into the control system of a walking machine?
Researchers in biology have presented clear evidence of a functional unit of the central nervous system, the Central Pattern Generator (CPG), which can cause rhythmic movement of the trunk and limb muscles(Grillner and Wall´en, 1985). In adult animals, the output of these cells can generate muscle activity that is very similar to activity during normal walking, even when sensory feedback has been eliminated (Grillner and Zangger, 1975). The CPG begins its ac- tivity before birth, although its activity does not appear to imitate the details of a particular walking animal, it is apparently correlated with the animal’s class, i.e., amphibian, reptile, mammal, etc. (Bekoff, 1985; Cohen, 1988).Apparently, the basic structure of the CPG network is laid down by evolution. How is this basic structure adapted to produce the detailed coordination needed to control a walk- ing animal?
The answer to this question is important to robotics for the following reason. CPGs have been well studied as a basic coordinating mechanism (Cohen et al., 1982; Bay and Hemami, 1987; Matsuoka, 1987; Rand et al., 1988; Taga et al., 1991; Collins and Stewart, 1993; Murray, 1993; Zielinska, 1996; Jalics et al., 1997; Ito et al., 1998; Kimura et al., 1999). However, the details of how this system can automatically adapt to control a real robot are not clear. A good goal would be to describe a general strategy for matching a generic CPG to a particular robot in real-time, with a minimal amount of interaction with the environment.
Reinforcement learning has been applied on long time scales to certain problems in walking (learning coordination and basic leg movement) (Ilg and Berns, 1995), but the time scales of such an approach is too long to explain the quick learning of animals just after birth.
The author suggests that part of the answer may be in the use of a number of simple innate internal models to evaluate the performance of the rapidly developing nervous system. These innate internal models could be used to adaptively tune CPGs during phases of rapid development. Figure 3 illustrates the training concept. A CPG generates a signal destined for a group of actuators (muscle) as well as a second signal, which is a copy of the signal sent to the actuators destined for an innate forward model. In biology, a copy of the motor signal is called an efference copy (Sperry, 1950). A forward model as described by Kawato (Kawato and Wolpert, 1998) is a functional model of the forward dynamics of the system.We use very simplified, innate forward models. These forward models predict the sensory expectation, or the desired consequence of CPG activity. This information is compared, and an adaptive rule then modifies the CPG.
The author suggests that a handful of adaptive mechanisms may be used for rapid tuning of a generic CPG. For example, the adaptive model can be used to ensure coordination of limbs with the environment.
The use of simplified, innate models is the most conservative stance possible. The intent is to make the fewest assumptions possible about the ‘knowledge’ that the nervous system has about the body that it is trying to control. By demonstrating how this process may be used in a physical device—a robot—we give compelling evidence that this approach is sufficient.
This article reports on an investigation into how a group of forward models could be used to adaptively tune a CPG in a real robot. As these models are innate, we assume they are simple; it would not be satisfying if these models were as complex as the behaviors that they help generate. Secondly, these models should not be detailed, accurate models of the forward dynamics of the robot. If innate models are used, their simplicity prohibits them from detailing accurate information about the structure of
the pattern generator. The study here supposes that once the CPGs have been tuned to produce basic locomotion, other, more general learning mechanisms would take over to create a more refined gait. These learning mechanisms might include reinforcement learning or supervised learning methods.
2. Experiments
The results of three experiments using GEO-II are described in this section. These experiments require progressively more adaptation to the environment and culminate in adaptive walking behavior. The robot learns to adjust key parameters of the CPG network to allow the robot to walk within minutes.
2.1 Experimental Setup
The robot platform is a four-legged robot, “GEO-II” (Fig. 1). Sensors include a force sensor on each foot, and a gyro scope which senses body roll. The unique features of this robot include a flexible, three-degrees of freedom spine. This allows spinal movement including twist. Model airplane servo actuators drive all axes.These servos are positional control devices. Geo II weighs 1.25 Kg.
Figure 1. The GEO-II robot. GEO-II features a flexible spine
Computation is divided between an onboard processor, a 68HC11 based ServoX24 board by Digital Designs and Systems, Inc., and a dual Intel Pentium workstation. The ServoX24 board is responsible for generating command signals for the servos as well as A/D sampling of sensor signals. The workstation is responsible for computing the ARRs, the AMs, and reflexes modules. The workstation also hosts a graphical user interface. All code runs under Windows 2000(C++ Microsoft) in a multi-threaded, windowed environment.
2.2 Adaptive Modules
2.2.1 Twist Adaptation Results.
The Twist ARR and Twist AM work together to generate a balanced, twisting of the body. When the Twist ARR is activated initially, the output gain of this module is near zero. Thus, no body twisting and no cyclic sensory feedback is sensed. The Twist AM gradually increases the gain as well as both the positive and negative twist uCPGs. (see Fig. 3B). Through time, as the robot shifts its weight, the paw forces vary periodically (see Fig.3A). As can be seen, the front legs of the robot move out of phase. The magnitude of the twist amplitude is decreased due to gyroscope feedback.
Figure3. Twist adaptation response. (A) Foot pressure of front legs.
(B) Change in amplitude Ai of the twist uCPGs.
In the end, the front legs periodically lifted symmetrically off the ground.
2.2.2 Burst Length Adaptation Results
In this setup, GEO-II is suspended in a test apparatus. This is done to facilitate data collection only. If a trunk twist is induced, the hip assembly will rock back and forth and will cause the legs to contact the ground periodically. The experimental procedure is as follows: The hip is placed in oscillation, the burst length is reset to zero and adaptation is then turned on. Note that adaptation is independently controlled for each leg.
The burst length is zero. As time progresses, the burst length lengthens and then stabilizes. As can be seen, the burst length adjusts until it stabilizes so that the burst
terminates just as the leg touches the ground. If the leg were to terminate its flexion too early, this leg would be locked forward. This may cause the robot to stumble as it swings its foot forward. If it did not extend soon enough, the limb would be flexed when the leg struck the ground, and the robot may lose its balance.
3. Discussion
Two key principles are combined in this work: (1) Innate forward models, (2) Distributed Control. Using these principles, the following three problems are addressed: (1) Static Postural Control, (2) Learning proper parameter settings for the output of a uCPG model (an ARR), and (3) Learning coordination with the environment.
Postural control is of primary importance. The postural control mechanism in this work relies on force sensors on the foot as the sole input to the control system. The idea behind the control scheme is to maintain three degrees of symmetry—front to back, side-to-side and diagonal symmetry. Thus, sensory signals become references for other signals related by a degree of symmetry; senses are compared to each other. Furthermore, each degree of symmetry is related to a particular ‘muscle group’ in the robot. Front to back symmetry generates commands for the hip rotation axes. Side-to-side symmetry drives hip adductors. Finally, diagonal symmetry drives twist about the body axis. It is fortunate that these degrees of symmetry map so easily onto the proximal actuators. In other mechanical walking machines, the twist axis is fixed. Thus asymmetries must be compensated for by leg flexion. By adding the twist, the torso and associated proximal actuators can compensate for imbalances (as defined here). It is also noted that compensation could be achieved on a slope. Also, postural adjustment can be made to compensate for weights placed on the robot. Such weight may mimic a payload dropped onto the ro bot’s back. It may also mimic constant perturbations such as dangling wires and cables. Thus, the system, by using the principle of symmetry, can simply drive muscles in a one-to-one fashion without the need for any detailed kinematic model of the robot. Yet this scheme achieves postural control in the face of significant outside disturbances.
The issue of control from higher level centers is not discussed here. The general strategy is to allow direct parameter modification from higher centers. The interested reader is directed to (Lewis and Sim´o, 1999, 2001) for an example of using high level vision to adaptively control ARR. In that work, an example is given of Burst Length Modulation by a higher center (communicating with visual centers).
Adaptive modules are used to tune the output of a CPG. Here the idea is to use a model of sensory expectation. The models are rudimentary and are sufficient to allow the system to bootstrap. It is not necessary to have any detailed model of the dynamics of the system.
Adaptive modules were also used to generate expectancies for when a foot strike should occur. This allows the adjustment of the flexor burst length. This adaptive mechanism was crucially important in assisting the robot in generating precisely the correct burst timing, preventing stumbling and foot dragging. Again the model used was rudimentary and did not depend on any detailed dynamics of the robot.
This idea of a rudimentary model is crucially important to understanding the value of this work. The idea of a detailed dynamic model is rejected. The power in this idea is that the adaptive system should, in principle, work over a very broad range of robotic devices with similar form. We made only the most general assumptions about the structure being controlled here. This also means that it is not necessary to identify a model (i.e., to instantiate by making detailed perturbations and observations) before learning can begin. That is why learning was achieved so rapidly in the cases presented.
The results of the present work illustrates the power of simple innate models in bootstrapping the system. In earlier work, it was assumed that adaptation should be made to occur in stages (Lewis et al., 1992). However, remarkably, all adaptive modules could be switched on simultaneously, and developmental stages seemed to emerge spontaneously. This was surprising.
The author suggests that once the system has overcome the basic problem of developing a rudimentary gait, using the techniques defined here, more generalpurpose learning would continue to refine the walking over time. In
vertebrates, this may be one of the roles of the cerebellum.
4. Summary and Conclusions
CPGs have been well studied by a number of researchers with possible applications to the control of walking machines. While a simple CPG circuit, consisting of a handful of oscillators, can be constructed, it is not clear how these CPGs can be made to adapt to a particular machine.
The approach presented here has the following elements: (i)ACPGmodel is chosen where the parameters controlling the behavior of the model are represented explicitly. This model is called an Adaptive Ring Rule (ARR). (ii) Included here is the idea of an innate internal model. That is, a model that predicts, even in a crude way, the sensory consequences of intended action. These models are used by Adaptive Modules (AMs) to alter the parameters of the ARR so that the sensory feedback more closely resembles the output of associated innate internal models.
By choosing the correct AMs, we demonstrate that critical elements of gait, such as flexor burst length adaptation, hip-knee phase, and the twisting of the body, can quickly be acquired. These AMs and ARRs, in conjunction with two basic reflexes (postural control and foot extension reflex) allowthe robot to quickly acquire a basic trot gait within minutes of inception. This quick learning is compatible with the learning exhibited by animals such as horses immediately after birth. Further, such adaptive mechanisms can be built into custom electronic circuits, which are under development (Lewis et al., 2000, 2001).
四足机器人的步态适应
1.导言
短的时间在出生后1 foal可以步行，然后运行。

值得注意的是，该动物学会Tocoordinate许多肌肉腿部和躯干在这么短的时间内。

这是不太可能的任何学习算法可程式中枢神经系统的从头算与这么少的培训时代。

也不是，它可能是foal 的运动控制器是完全取决于出生前。

怎么会是这样一个bili性加以解释？怎么会是这样的能力，被纳入控制系统的一步行机？
研究人员在生物，已明确的证据显示一个功能单位的中央神经系统，中枢模式发生器（CPG ）的，可以导致节奏的运动躯干和四肢肌肉（grillner和wall'en ，1985年）。

在成年动物，输出，这些细胞可以产生肌肉活动，这是非常类似的活动在正常散步，甚至当感官的反馈意见已被消灭，（grillner 和桑戈，1975年）。

中央人民政府开始交流tivity在出生之前，虽然其活动没有出现模仿的细节特别步行动物，这是很明显的相关性与动物的阶级，即两栖类，爬虫类，哺乳类等（贝克夫，1985年；科恩，1988年）。

很明显，基本结构，中央人民政府网络是所订下的演变。

这是怎样的基本结构，适应生产需要详细的协调控制散步-荷兰动物？
这个问题的答案是很重要的机器人由于下列原因。

cpgs已很好的研究作为一项基本协调机制（科恩等人,1982年;湾及hemami, 1987年;松冈， 1987年;兰德等人， 1988年;多贺等人， 1991年;柯林斯及史钊域， 1993年;默里， 1993年;泽林斯卡， 1996年;亚利奇等人， 1997年;伊藤等人， 1998年;木村等人，1999年）。

不过，详情如何，这系统可自动适应控制一个真正的机器人并不清楚。

一个很好的目标将是在描述一个总体战略匹配的一个通用的中央人民政府某一机器人在实时的时间，最小金额的互动与环境。

强化学习，已用于对长远的时间尺度的一些问题在散步（学习的协调和基本腿运动）（ilg和berns， 1995年），但时间尺度的这种做法是太长解释快速学习的动物，只是后出生。

作者认为，部分答案可能在使用一些简单的先天内部模型的业绩考核评价迅速发展的中枢神经系统。

这些先天的内部模型可以用来自适应调cpgs期间，分阶段的快速发展。

图3说明了训练的概念。

1 ，中央人民政府生成一个信号，目的地为一组驱动器（肌肉），以及作为第二信号，这是一个复制的信号发送到驱动器的目的地是一个天生的前进模式。

在生物学，副本汽车信号，是所谓的一efference复制（斯佩里， 1950年）。

前瞻性的模型所描述的kawato（kawato 和wolpert， 1998年）是一个功能模型的前沿动态的system.we使用非常简单，前进先天的模式。

这些前瞻性模型预测感官的期望，或所期望的后果，中央人民政府的活动。

这方面的资料比较，自适应规则，然后修改了中央人民政府。

作者表明，极少数的自适应机制，可用于快速调整的一个通用的中央人民政府。

举例来说，自适应模型可以用来确保协调四肢与环境。

使用简化，固有的模式是最保守的立场可能。

其意图是使最少的假设可能对'知识'神经系统大约有身体，这是试图控制。

通过展示如何这个过程中可用于在一个物理设备-机器人-我们给予令人信服的证据表明，这种做法是不够的。

此文章的报告进行调查，如何一组提出的模式可以用来自适应调重弹一，中央人民政府在一个真正的机器人。

由于这些模型是天生的，我们假定他们是简单
的;它不会满足，如果这些模型一样复杂的行为，帮助他们产生。

其次，这些模型不应该详细，准确的模式前进动力的机器人。

如果固有的模式，使用简单，禁止他们详细准确的资料，有关的结构模式发生器。

研究在这里支撑，一旦cpgs 已调整，以生产的基本运动，另一方面，更普遍的学习机制，将接管，以创造一个更精致的步态。

这些学习的机制可能包括强化学习或监督的学习方法。

2.实验
结果三个实验使用的地缘二是本节所描述的。

这些实验的需要，逐步更适应环境，并最终在自适应散步的行为。

机器人学会调整的关键参数，中央人民政府网络，让机器人步行数分钟之内完成。

2.1实验装置
该机器人平台是一种四足机器人,“地理Ⅱ”（图1 ）。

传感器包括一个力传感器在每个脚，和一个陀螺的范围，其中感官机构名册。

独特的特点，这个机器人包括一个灵活，三自由度的脊椎。

这使脊柱运动，包括扭曲。

模型飞机伺服致动器驱动器，所有的石斧。

这些都是位置伺服控制装置。

土力工程处二重1.25千克。

计算分之间的板载处理器,68hc11基于servox24局的数字设计和系统公司，和一个双Intel Pentium工作站。

该servox24局是负责生成指挥信号为伺服以及A / D采样的传感器信号。

工作站负责计算arrs，医疗辅助队，并反射模块。

工作站还举办了图形用户界面。

所有代码运行在Windows 2000下（C + +中的Microsoft）在一个多线程，窗口环境。

2.2 自适应模块
2.2.1 扭适应的结果
捻捻和终点时，携手合作，以产生一个均衡的，扭曲的尸体。

当扭终点是启动初期，输出增益模块，这是接近零。

因此，没有扭体和没有感觉的反馈循环是感受到了。

捻时逐渐增加的增益，以及正面和反面，都要扭ucpgs。

（见图3B 条）。

通过的时间，作为机器人轮班其重量，足势力有所不同，定期（见图3A）款。

可以看出，前面腿机器人迁出阶段。

规模捻度振幅降低是由于陀螺仪的反馈意见。

在最后，前面的腿定期解除对称离地面。

2.2.2突发长度适应的结果
在此安装，地缘二是悬浮在一种测试仪器。

这样做是为了方便数据收集只。

如果主干扭曲，是诱导，髋关节，大会将岩石回奔波，并会造成腿部接触地面定期。

实验程序如下：髋关节，是摆在振荡，突发长度是重置为零和适应，然后打开。

请注意，适应是独立控制每个站。

最初，突发长度是零。

随着时间的进展，突发长度延长，然后稳定下来。

可以看出，爆裂的长度调整，直至稳定，使该水管爆裂，终止正如腿触及地面。

如果腿部被终止其屈曲言之尚早，这腿将被锁定前进。

这可能会导致机器人蹒跚，因为它波动，其脚前进。

如果不延长，尽快还不够，肢体会弯曲时，腿击中地面，机器人可能会失去平衡。

3.讨论
两个关键的原则相结合，在这方面的工作：（1）先天提出的模式，（2）分布式控制。

使用这些原则，以下三个问题得到处理：（1）静态姿势控制，（2）学习正确的参数设置为输出一个ucpg模型（1终点），及（3）协调与学习环境。

姿势控制是首要的重要性。

该姿势控制机制，在这方面的工作依赖于力传感器对足部作为唯一的输入到控制系统。

背后的想法控制计划，是要维持3程度的对称前线回来，侧侧和对角线的对称性。

因此，感官信号成为参考其他信号有关的某种程度的对称性;感官比较，取长补短。

此外，每个程度的对称性是一个主题相关的，特别是'肌肉组'在机器人。

前线回到对称性生成命令髋关节旋转轴。

侧侧对称驱动器髋关节adductors。

最后，对角对称的驱动器捻有关机构轴。

这是幸运的是，这些程度的对称性地图这么容易走上近端动。

在其他机械步行机，扭轴是固定的。

因此，不对称性，必须予以赔偿腿部弯曲。

加入捻度，躯干及相关近端动可以弥补的不平衡（这里定义的）。

它也指出，补偿就可以实现一个斜坡。

此外，姿势的调整，可以作出赔偿的权重放置于机器人。

这样的重量可能会模仿有效载荷下降到机器人的回。

它也可能模仿不断的扰动，如悬挂电线电缆。

因此，该系统，使用的原则，对称性，可以简单的肌肉驱动器在一个以一对一的方式，而不需要任何详细的运动学模型机器人。

然而，这项计划取得姿势控制，在面对重大以外的骚乱事件。

控制问题，从更高层次中心是不是在这里讨论。

一般的策略是让直接参数修正，从更高的中心。

有兴趣的读者是针对（Lewis和sim'o，1999年， 2001年）的一个例子，使用高层次的眼光来自适应控制终点。

在这方面的工作，给出了一个应用实例的突发长度调制由上级中心（沟通与视觉中心）。

自适应模块可用来调整输出一个中央人民政府。

这里的构想是使用一个模型的感官的期望。

该模型是最起码的，并足以使该系统的Bootstrap。

这是没有必要有任何详细模型的动态系统。

自适应模块也被用来产生预期时，足部的罢工应该发生。

这使得调整的屈突发长度。

这种自适应的机制是非常重要，在协助机器人在发电，正是正确的水管爆裂的时机，防止绊脚拖。

再次使用的模型是最起码的，并没有依赖于任何详细的动态机器人。

这一想法的一个最起码的模型是非常重要的认识价值，这方面的工作。

构思一份详细的动态模型将被拒绝。

权力在这方面的想法是，自适应系统应在原则上，工作范围十分广泛的机器人设备与类似的形式。

我们所作的只是最普通的假设结构被控制在这里。

这也意味着，这是没有必要找出一个模式（即以实例作出详细的扰动和意见），然后就可以开始学习。

这就是为什么学习取得了如此迅速地在这些案件中。

结果，目前的工作说明的权力，简单的固有模式，在启动该系统。

在以前的工作，这是假设的适应，应作出发生在阶段（刘易斯等人，1992年）。

不过，值得注意的是，所有的自适应模块，可同时接通，和发育阶段，似乎出现自发性。

这是不足为奇的。

4.概述和结论
CPGS已很好的研究由一个研究人员的人数与可能的应用，以控制行走的机器。

而一个简单的中央人民政府电路，构成少数振荡器，可以兴建，目前尚不清
楚如何将这些CPGS可作，以适应特定的机器。

的做法，这里有以下内容：（一）acpgmodel是选择何处参数控制的行为模式的代表明确。

这个模型是所谓的一环自适应规则（终点）。

（二）包括在这里的想法是一个天生的内部模型。

这是，一个模型，预测，即使在原油的方式，感官的后果，打算采取行动。

这些模型所使用的自适应模块（医疗辅助队），以改变参数的终点，使感官反馈更加紧密地类似于输出相关的先天内部模式。

通过选择正确的医疗辅助队，我们证明的关键要素的步态，如屈突发长度适应，髋关节膝关节的阶段，扭曲身体，可以很快被收购。

这些AMS和arrs，联同两个基本反射（姿势控制和足部反射延长）allowthe机器人迅速获得一个基本的逐渐达到自己的战略步态几分钟内成立。

此快速的学习是与学习，展示由动物如马出生后立即。

此外，这种自适应机制可以建成自定义电子电路，这是根据发展（刘易斯等人，2000年，2001年）。

徐国华，谭民.移动机器人的发展现状及其趋势.机器人技术与应用. 2001.3
2 Ashraf Elnagar. Predicion of Moving Objects in Dynamic Environments
Using Kalman Filters.Proceedings of 2001 IEEE International Symposium on Computational Intelligence in Robotics and Automation.
July 29-August1,2001
3卢桂章.“863”计划智能机器人研究进展.机器人技术与应用.1995,2(1):7-8
4蔡自兴.智能机器人研究的进展.智能机器人.1993:1-6
5Song.S.M.Kinematic Optimal Design of a Six-Legged Walking Machine.ph.D dissertation,ohio state University,Columbus,OH,1984
6 R.Tomovic and R.B.Meghee,A finite state Approch to the Synthesis of
Bionengineering Control System IEEE Trans.On Human Factors in Electronics.Vol.HFE-7,No.2.1986
7R.b.Meghee and A.K.Jain.Someproperties of Regularly realizable Gait Matrices.Mathematical Biosciences.Vol.13,1972
8 史智敏、干东英、原培章.留足步行机器人再不平地面行走的运动学研究.机械工程学报.第三期，1986
9Tsu-Tian Lee and Ching-Long Shih.Astudy of Gait Control of AQuardru[ed Walking Vehicle.IEEE Journal of Robotics and Automation.Vol.ra-2,1996
0 P.Gonzalez De Santos and M.A.Jimwnez. Path Tarcking with Quadruped Walking
Machines Using Discontinuous Gaits. Computers Elect.Engng Vol.21,No.6,1998 11 孙汉旭.四足步行机构的研究.北京航天航空大学博士论文.1989
2 徐跌群，万隆军.四足步行机器人稳定性步态分析.机器人技术专栏，2001年
第23卷第8期5-7.
13 杨东超,汪劲松,刘莉,陈恳.基于ZMP 的拟人机器人步态规划.机器人,2003
23(6)
14 Hiroshi Kimura1, Yasuhiro Fukuoka1, Yoshiro Hada1, and Kunikatsu Takase1.
Adaptive Dynamic Walking of a Quadruped Robot on Irregular Terrain Using a Neural System Model. IEEE Int. Conf. Robotics and Automation, 1998.
5 陈佳品,程君实,冯萍,马培荪,潘俊民,席裕庚. 四足机器人对角小跑步态的研究.
上海交通大学学报.Vol.31 No.6 1997
6 M.伍科布拉托维奇.步行机器人和动力型假肢.马培荪,沈乃勋译.北京:科学出
版社,1988
7 Ryo Kurazume,Kan Yoneda and Shigeo Hirose. Feedforward and feedback
dynamic trot gait control for quadruped walking vehicle. IEEE International
Conference on Robotics and Automation , 2001:20-25
18 H.Kimura, Y.Fukuoka, K.Konaga, Y.Hada and K.Takase. Towards 3D Adaptive
Dynamic Walking of a Quadruped Robot on Irregular Terrain by Using Neural System Model. Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems Maui, Hawaii, USA, Oct. 29 - Nov. 03, 2001
9 张永学, 麻亮, 强文义,付佩琛.基于地面反力的双足机器人期望步态轨迹
规划.哈尔滨工业大学学报.2001 33(1)
20 蔡自兴.机器人学.清华大学出版社.2000:51-54
2 徐轶群, 万隆君. 四足步行机器人腿机构及其稳定性步态控制. 机械科学与
技术. Vol.22 ,No.1,2003
22 S.M. Song, K.J.Waltron. A study of the gait control of a quadruped walking
vehicle. The MIT Press, Cambridge, 2000
23 Ryo Kurazume,Kan Yoneda and Shigeo Hirose. Feedforward and feedback
dynamic trot gait control for quadruped walking vehicle. IEEE International Conference on Robotics and Automation , 2001:1-3
24 Hironori Adsachi,Noriho Koyachi and Eiji Nakano.Mechanism and Control of a
Quadruped Walking Bobot.IEEE Control Sysytems Magazine.2000
25 黄启育.模组化4+2足步行机械步态规划.国立中山大学硕士论文.2001。