双足行走机器人平衡控制译文

外文资料：
Robots
1. Introduction
Nowadays, the applications of machines and robots to assist human in performing their tasks has become increasingly extensive. In industrial applications, the use of robotics system has reached the level which surpasses human ability in terms of speed and accuracy. On the other hand, in the field of domestic robots or service robots, the developments are still far from perfection. The main factor that distinguishes industrial robots from service robots is their working environment. For a service robot to perfectly perform its tasks, it needs to be able to adapt and cope with the normal human living environment. From the practical point of view, bipedal robot is the most suitable robot structure due to its similarity of physical configuration with human especially in terms of locomotion method. However, the realization of bipedal robot is more challenging compared to other types of mobile robot due the unstable nature of bipedal walking. Therefore, many studies have been carried out especially concerning the stability sensing and control strategies of bipedal robot. The common approach in defining the stability of bipedal robot is by using the “Zero Moment Point” (ZMP) criterion[1]. The simplest implementation of ZMP is to generate the joint trajectories based on the pre-planned walking gait while maintaining the ZMP at the given references, but this approach has a limitation in maintaining the balance if there is any unknown external disturbance [2-5]. Many studies specifically focus on the techniques to monitor the real-time ZMP position from the physical system and used it as the feedback component [6-9]. Takanishi and Kato [7] proposed a method to monitor the ZMP position by measuring the force and moment acting on the robot’s shank by using universal forcemoment sensor. Another method utilizes an array of force sensitive resistor placed on the sole of the robot’s foot to obtain the ground reaction force at different locations of the foot. The reaction forces measured from the sensor array is then used to compute the position of the center of pressure which reflects the position of the ZMP [9]. The inverted pendulum technique is another alternative for analyzing the robot stability [10]. This method monitor the instability by constantly reading the body acceleration and tilt angle by means of accelerometer and gyroscope. However, the readings from both sensors are subject to noise and drift during the operation and the effort to apply filters in correcting the measurements often requires considerable amount of computing power [11]. This paper proposed a novel method for sensing and stability control of bipedal robot. The use of specially designed flexible ankle joint allows fast detection and prediction of robot sideway instability. Placing an additional one degree-offreedom rotary joint with built-in angle detection sensor at the robot ankle allows the robot’s body to tilt freely in any sideway direction and detect the tendency of imbalance that may potentially occur. Based on this essential sensor’s information, the controller will quickly adjust position of the counterbalance mass located at the robot waist in order to restore the sideway balance of the robot. The advantage of using counterbalance mass and rotary joint at the ankle is to allow the walking subsystem and sideway balancing subsystem of the robot to be decoupled from each other and work in
independently controlled modes. It is different from the traditional approach when the robot’s posture is corrected to satisfy both conditions at once, smooth forward walking and continuous sideway (sagittal) stability. Details of the proposed method are presented as follows. In section 2 the locomotion mechanism, ankle structure, sensing technique and balancing strategy are introduced. Section 3 discusses the mathematical model of the system. In section 4 experiment method is discussed and the viability of the proposed system is proven by the experimental result. Finally, the conclusions are described in section 5.
2. Mechanical Structure of Biped Robot
2.1. Robot locomotion mechanism
The biped robot is designed to realize two dimensional walking with minimum number of actuations. The locomotion system of the robot consists of four actuators, two for the hip joints and two for the knee joints. The ankle joint is not actuated by any actuators but instead it utilizes a series of parallelogram mechanism to passively control the ankle joint in order to maintain the position of the foot. The usage of parallelogram mechanism provides benefits by reducing the number of actuators needed which results in the simplification of the mechanism design and reduction of the overall robot’s weight. Fig 1(a) shows the stick diagram of the leg in different configuration. The orientation of link a is always parallel to the hip due to the constraint applied by link 1 and link 2. The orientation of link b which represents the foot is always parallel to link a due to the constraint applied by link 3 and link 4. Therefore, the foot is always kept parallel by the parallelogram mechanism regardless of any configuration of the leg. Fig 1(b), (c) show the physical implementation of the parallel leg in different postures. The prototype of the biped robot is mainly constructed using hollow sections of extruded aluminium due to its lightness and strength. The overall height of the biped robot is 0.9 m with the total weight of 7 kg. The length for both thigh and shank are 0.3 m and the spacing between two legs is 0.15 m. For the actuation, each joint is equipped with Robotis Dynamixel RX-64 Smart Actuator, which combines gear transmission, controller, driver and network function in a single package. The output of the hip motor is connected directly to the hip joint and the output of the knee motor is transmitted to the knee joint via a four bar linkage. The purpose of placing the actuators on the hip is to reduce the weight of the leg which will minimize the dynamics forces created by the leg movement. The other advantage of this structural arrangement is that the angular count at each joint is always referenced to the fixed vertical axis of the stationary world coordinate frame regardless of the leg postures.
(a) (b) (c)
Fig. 1. (a) Stick diagram of parallelogram leg; (b), (c) Robot standing with different leg configurations
2.2. Flexible ankle joint to utilize stability measurement
In order to achieve a stable walk on a biped robot, the ability to accurately detect any possible instability is quite crucial. This paper introduces a new approach of sensing the instability by introducing an additional degree of freedom in sideway direction next to the ankle joint. Fig 2(a) shows the structure of that degree of freedom where the free rotary joint on the frontal plane is placed at the ankle between the foot and ankle joint. It will let the unconstrained robot body standing on one leg to tilt (angle ) freely in sideway (sagittal) direction for any possible disturbance in that direction. By installing a rotary sensor on the free joint the controller will be able to detect instantly any instability and immediately react to restore the balance.
(a)(b)
Fig. 2 (a) Schematic picture of the flexible ankle structure; (b) Physical implementation of
flexible ankle
2.3. Split balancing mass for faster system response
The walking cycle of bipedal robot consists of single support phase and double support phase which are executed sequentially and repeatedly. In single support phase, the robot is standing on one leg while another leg is transferred forward. During this phase, the robot body will be tilted sideways due to the unbalanced torque created by the weight of the lifted leg and the dynamic forces generated due to the leg movement. In order to maintain stability of the robot, a set of counterbalance masses are located at a specific position to compensate the unbalanced mass of the lifted leg and other possible disturbance. Fig 3 shows the simplified 3-masses model of bipedal robot: mL represents the lumped mass of the hanging leg, mB1 represents the major balancing mass and mB2 represents the minor balancing mass.
Major balancing mass is mainly used to compensate the weight of the lifted leg. This mass is positioned at a precalculated location in order to balance the torque created by the mass of the lifted leg mL. The minor balancing mass mB2 is continuously repositioned based on the information gathered from the sensor located at the additional ankle joint. This mass works as a counterbalance to maintain the robot to be always vertical regardless of any external sideway disturbance.
The use of two separate counterbalance masses provides several advantages such as:
• Faster response time can be achieved by only moving small inerti a counterbalancing mass instead of moving a larger one,
• Energy efficiency can be improved by reducing load of the motor that drives a smaller inertia counterbalancing mass.
Fig. 3 Simplified model of the bipedal robot
3. System modeling and control
From the diagram on Fig 3, the dynamic equation using Newton’s second law about point O gives:
ΣT O=Iθ
T dis1+m L g(d cosθ+r sinθ)−m B2g(αcosθ+r sinθ)−m B1g(d s cosθ+sinθ)+
m B2α̈r−cθ−kθ=θ(m L(r2+d2)+m B2(r2+a2)+m B1(d s2+r2))（1）
Since the major balancing mass m B1is mainly use to compensate for the torque created by the weight of the hanging leg m L, the major balancing mass can be positioned at the pre-calculated location on the opposite side of the hanging leg. The required position of the major balancing mass d s can be calculated based on the equilibrium of torque at point O as follows:
ΣT O=0
m L d−m B1d s=0（2）
m L d=m B1d s
d s=m L m B1
d
Substituting d s from Eq.(2) into L.H.S of Eq.(1) gives:
T dis1+m L g(d cosθ+r sinθ)−m B2g(αcosθ+r sinθ)
−m B1g(m L
m B1
d cosθ+r sinθ)m B2α̈r−cθ−kθ
=θ(m L(r2+d2)+m B2(r2+a2)+m B1(d s2+r2)) T dis1+g cosθ(m L d−m L d−m B2a)+gr sinθ+m B2α̈r−m B2a2θ=
θ(m L(r2+d2)+m B2r2+m B1(d s2+r2))+cθ+kθ（3）
Rearranging the differential equation from Eq.(3) gives:
T dis1−m B2g∙a cosθ+(m L+m B2+m B1)g∙r sinθ+m B2α̈r−m B2a2θ=θ(m L(r2+ d2)+m B2r2+m B1(d s2+r2))+cθ+kθ (4) The differential equation in Eq.(4) has two distinct parts. The right hand side only presents parts of the ordinary differential equation with constant time invariant coefficients and the left hand side presents all remaining parts of the equation. Therefore, the left hand side includes:
● Non-linear functions of the main dependent argument θ, namely sinθ，cosθ
●Additional but independent from the main argument θparameter α̈
●The parameters that comprises both a and θarguments, namely m B2a2θ
Fig 4 shows the simplified control block diagram of the balancing system. The PID controller constantly monitors the tilt angle (θ) from the sensor of the additional ankle joint and compares the reading with that of the desired angle. If any tilt is detected, the controller will actuate the balancing mass to the opposite direction in order to regain the balance.
Fig. 4 Simplified block diagram of the stability control system
4. Experimental results
The experiment is carried out to verify the effectiveness of the proposed mechanical structure and control strategies in maintaining the robot’s balance in single support phase. During the experiment, the robot is standing on one leg with another leg lifted up and floating. The external disturbance is applied by making a push on the edge of the robot’s hip which will cause the robot to tilt sideways (Fig 5(a)). The intensity of the pushing force is measured by a force sensor mounted on the hip (Fig 5(b)).
Fig 6 shows the measurement of the tilt angle θfrom the additional ankle joint, balancing mass position a and the disturbance force when the external disturbance is applied. It is apparent from the figure that once the disturbance is applied the sensor detects change in tilt angle and the controller immediately reacts by moving the mass to the opposite direction of the tilt in order to regain the balance. Fig 7 shows the measurement when an excessive disturbance force is applied approximately at the 37th seconds, the tilt angle changes abruptly and the balancing mass is not able to recover the balance. The saturated angle measurement at the end of the plots indicates that the robot is falling. It is due to the fact that the value of minor mass mB2 and the allowable range of
its motion a are limited in this design. The overall resistance to the externally generated force can be increased by either increasing mB2 or a.
(a) (b)
Fig. 5 (a) Hip plane of the robot; (b) Force sensor attachment to measure applied
disturbance force
Fig. 6. System response to disturbance (balance maintained)
Fig. 7. System response to disturbance (excessive force applied)
5. Conclusion
This paper presents stability control method for bipedal walking robot which includes the leg design with additional (redundant) degree of freedom at the ankle joint and split balancing mass. The proposed method enables the sensing, control and balancing of bipedal robot to be implemented in a simple yet cost effective manner. The effectiveness of the design method is proven by the experimental results. The implementation of this method also allows the walk controlling algorithms to be decoupled from the stability control algorithms to increase the system response time.
References
[1] Vukobratovic M., Juricic D., 1969. Contribution to the synthesis of biped gait, IEEE Transaction on Biomedical Engineering 16, p.1-6.
[2] Erbatur K., Kurt O., 2006. “Humanoid Walking Robot Control with Natural ZMP References,” IEEE Industrial Electronics - Proceedings of the 32nd Annual Conference, p. 4100-4106.
[3] Lim H.-ok, Setiawan S. A., Takanishi A., 2001. “Balance and impedance control for biped humanoid robot locomotion,” Intelligent Robots and Systems - Proceedings of the 2001 IEEE/RSJ International Conference, p. 494-499.
[4] Liu L., Zhao M., Lin D., Wang J., Chen K., 2003. “Gait designing of biped robot according to human walking based on six-axis force sensors,”Computational Intelligence in Robotics and Automation - Proceedings of the 2003 IEEE International Symposium, p.
360–365.
[5] Sardain P., Bessonnet G., 2004. Zero moment point-measurements from a human walker wearing robot feet as shoes, IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 34, p. 638–648.
[6] Loffler K., Gienger M., Pfeiffer F., Ulbrich H., 2004. Sensors and control concept of a biped robot, IEEE Transactions on Industrial Electronics 51, p. 972-980.
[7] Takanishi A., Kato I., 1991. “A biped walking robot having a ZMP measurement system using universal force-moment sensors,” Intelligent Robots and Systems - Proceedings of the 1991 IEEE/RSJ International Workshop, p. 1568-1573.
[8] Kagami S., Takahashi Y., Nishiwaki K., Mochimaru M., Mizoguchi H., “High-speed matrix pressure sensor for humanoid robot by using thin force sensing resistance rubber sheet,” Sensors - Proceedings of the 2004 IEEE Conference, p. 1534–1537.
[9] Kalamdani A., Messom C., Siegel M., 2007. Robots with sensitive feet, IEEE Instrumentation and Measurement Magazine 10, p. 46–53.
[10] Caux S., Mateo E., Zapata R.,1998. “Balance of biped robots: special double inverted pendulum” Systems, Man and Cybernetics - IEEE International Conference, p. 3961-3969.
[11] Braunl T., 2006. Embedded Robotics, Springer, Germany.
译文资料：
机器人
1、介绍
现在，机械和机器人的应用帮助人类执行他们的任务已经变得越来越广泛。

在工业应用中，使用机器人系统已经达到了在速度和准确度上超过人类能力的水平。

另一方面，在家用或服务机器人的领域，发展的还很不完善。

区别工业机器人和服务机器人的主要因素在于它们的工作环境。

对于服务机器人，去完美的执行它的任务，需要适应和应对正常人的生活环境。

来自实践的观点，双足机器人是最合适的机器人结构，这归因于它的身体形态与人类相似，特别在运动方法方面（in terms of）。

然而，由于双足行走不稳定的天性，对比其它类型的移动机器人，双足机器人的实现（realization）更具挑战。

因此，很多研究一直在继续，尤其关心双足机器人的稳定感和控制策略。

通常定义双足机器人稳定性的途径是使用“零力矩点”（ZMP）标准。

ZMP最简单的实施办法是设法产生一个基于预先计划行走步法的节点轨迹，同时保持ZMP有一个给定参考，但是这个途径在存在不明外部干扰的情况下有一个限制。

许多技术研究尤其关注从物理系统中监视ZMP的实时位置，并且把它当作反馈元件。

T akanishi和Kato提出了一个监视ZMP 位置的方法，就是通过使用普通的力学传感器测量作用于机器人小腿的力和力矩。

另一种方法是利用大量的布置在机器人脚底的力敏传感器，去获得脚底上不同位置的地面反作用力。

随后用这些传感器阵列测得的数据计算出能反映ZMP中心位置的受力中心。

倒立摆技术是另一个可供选择的分析机器人稳定性的方法。

这个方法通过加速度计和陀螺仪不断读取身体加速度和倾角信息，来监测不稳定性。

然而，从这两个传感器读到的数据受制于（be subject to）操作过程中的噪声和漂移，并且修正测量数据的努力需要强大的计算能力。

本文提供了双足机器人的感知和稳定控制的新方法。

使用特制的灵活踝关节，快速探测和预报机器人的侧面失稳。

在机器人的踝关节上放置一个额外的单自由度角位移传感器，允许机器人向任何方向自由倾斜，探测潜在发生的不稳趋势。

基于这个必要的传感器的信息，控制器将会快速调整平衡块的位置，为了恢复机器人的侧面平衡，抵消聚集在机器人腰部的不平衡力。

使用平衡块和回转头的优势在于让行走子系统和平衡子系统彼此不挂钩，并运行在独立的两个控制模块里。

这与传统方法不同，当机器人的姿态同时满足两个条件，顺利的向前行走和不断地稳定调整。

该方法提出了如下（as follows）的细节。

第二节介绍了运动装置、关节结构、测知技术和平衡策略。

第三节讨论了系统的数学模型。

第四节，用实验结果证实了所讨论的实验方法和所提出系统的可行性。

最终，第五章描述了结论。

2、双足机器人的机械结构
2.1 机器人行走机构
设计双足机器人的目的是驱动最小量实现二维面的行走。

机器人的运动系统包含了四个驱动器，两个用在髋关节，两个用于膝关节。

踝关节不由驱动器驱动，但是代替它的是一系列的平行四边形机构，来被动控制踝关节，为维持脚的位置。

使用平行四边形机构能提供利益通过减少所需驱动器的数量，还能简化机械设计，减轻机器人质量。

图1（a）展示了机械腿在不同位置下的符号图。

由于1杆和2杆的约束作用，A杆的连接方向总是跟臀部平行。

由于3杆和4杆的约束作用，B杆（脚）的连接方向始终跟A 杆平行。

这样，脚总是通过平行四边形机构保持平行，不管腿怎样配置。

图1（b）（c）展
示了平行的腿在不同姿态下的物理实现。

出于轻盈和强度的需要，双足机器人的模型主要使用挤制铝材的空心管构造。

机器人全高0.9m，总质量7kg。

每条大腿和小腿的长度为0.3m，两腿间距0.15m。

为了驱动，每个关节配备有Robotis Dynamixel RX-64 Smart Actuator，它结合了齿轮传动装置、控制器、驱动程序和网络功能在单一封装里。

臀部的输出马达直接连接臀部关节，膝盖的输出马达通过四杆机构给膝盖传递动力。

把驱动器放在臀部的目的是减轻腿部的重量，这样可以让使腿部运动的驱动力最小化。

这种结构布局的其它优势在于不管腿的姿势，每个关节的角度计算都能参照固定坐标系的纵轴。

(a)(b)(c)
图1(a)平行四边形腿的符号图；(b)，(c)机器人腿在不同配置下的站立图
2.2 灵活的踝关节利用稳定的测量
为了在双足机器人上实现稳定行走，精确探测任何可能不稳的能力十分重要。

本文介绍了一种新的测知不稳的途径，通过在侧面引进一个额外的自由度放在踝关节之后。

图（2）展示了前面板上自由旋转节的结构，它被放在脚和踝关节的连接之间。

这将会让无约束的机器人在身体站立的同时，一只脚能在侧面（矢状面）方向自由倾斜（角度θ）任意可能的距离。

通过在自由关节处安装角位移传感器，控制器将能够立刻(instantly)探测到任何不稳并立即(immediately)反应恢复平衡。

(a)(b)
图2(a) 灵活踝关节的结构图片；(b)灵活踝关节的物理实现
2.3 分割平衡块为更快的系统响应
双足机器人的行走周期包含被顺序（sequentially）和循环（repeatedly）执行的单足支
撑阶段和双足支撑阶段。

在单足支撑阶段，当机器人另一条腿移动时，一条腿站立。

在这个阶段，由于抬腿重量产生(created)的不平衡扭矩以及腿部运动产生(generated)的动态力，机器人的身体会向侧面倾斜。

为了保持机器人的稳定，一套抵消平衡质量块被放置在特别的位置去补偿抬腿的不平衡质量。

图（3）展示了已简化的双足机器人3质量块模型：m L代表腿在挂立时的集中质量，m B1代表主要质量平衡块，m B2代表次要质量平衡块。

主要质量平衡块主要用于抬腿时的重量补偿。

为了平衡抬腿质量m L产生的扭矩，这个质量块被安放在预先计算好的位置。

次要质量平衡块m B2基于放置在踝关节的额外传感器收集到的信息，不断改变位置。

这个质量块作为一个平衡力维持机器人垂直，无论侧面怎么受干扰。

使用两个分离的平衡质量块能提供不少优势，例如：
●获得更快的响应时间，能使平衡质量块移动很小的距离，而不是很大距离，
●能源效率能提高，通过驱动小的平衡质量块，减少电机的负载。

图3 双足机器人的简化模型
3.系统模型和控制
图3中，动力方程使用牛顿第二定律关于坐标系原点O给出：
ΣT O=Iθ
T dis1+m L g(d cosθ+r sinθ)−m B2g(αcosθ+r sinθ)−m B1g(d s cosθ+sinθ)+
m B2α̈r−cθ−kθ=θ(m L(r2+d2)+m B2(r2+a2)+m B1(d s2+r2))（1）
由于主要的平衡质量块m B1主要用于补偿悬挂着的腿的重量m L所产生的扭矩，主要平衡质量块能放置在预先计算好的位置，在悬挂腿的相反方向。

主要平衡质量块所需的位置d s 能基于在坐标系原点计算出的平衡扭矩，建立方程如下：
ΣT O=0
m L d−m B1d s=0（2）
m L d=m B1d s
d s=m L m B1
d
把方程（2）中的代入方程（1）得：
T dis1+m L g(d cosθ+r sinθ)−m B2g(αcosθ+r sinθ)
−m B1g(m L
m B1
d cosθ+r sinθ)m B2α̈r−cθ−kθ
=θ(m L(r2+d2)+m B2(r2+a2)+m B1(d s2+r2))
T dis1+g cosθ(m L d−m L d−m B2a)+gr sinθ+m B2α̈r−m B2a2θ=
θ(m L(r2+d2)+m B2r2+m B1(d s2+r2))+cθ+kθ（3）
整理方程（3）得：
T dis1−m B2g∙a cosθ+(m L+m B2+m B1)g∙r sinθ+m B2α̈r−m B2a2θ=θ(m L(r2+ d2)+m B2r2+m B1(d s2+r2))+cθ+kθ (4)
方程（4）中的微分方程有两个明显的部分。

等式的右边只列出了常微分方程系数不随时间变化的部分，左边列出了方程全部的剩余部分。

因此，等式左边包含：
●主要取决于角度θ的非线性方程，即sinθ，cosθ
●额外的独立于主要角度θ的参数ä
●包含角度α和θ的参数，即m B2a2θ
图（4）展示了已简化的平衡系统的控制框图。

这个PID控制器从附加的踝关节传感器中不断监视倾斜角（θ），比较读取值与所需值。

若有一点倾斜被检测到，控制器就会驱动平衡块去反向运动，恢复平衡。

图4 已简化的稳定控制系统的方框图
4.实验结果
这个实验证实了所提机械结构和控制策略在维持单腿支撑机器人身体平衡的有效性。

在实验期间，机器人一条腿站立，另一条腿抬起或浮空运动。

图6显示了来自额外踝关节连接的倾角θ的测量，平衡质量块的位置a和实施外部干扰时产生的扰动。

一旦在身体上实施明显干扰，传感器就会探测到倾角变化然后控制器立即通过移动质量块向反方向倾斜来使机器人恢复平衡。

图7展示了当外部干扰施加过多时大约37秒，倾角突然改变，平衡质量块不能再恢复平衡。

最后环节的饱和角度测试表明机器人正在摔倒。

由于次要平衡质量块m B2的价值和运动a的允许范围在设计中被限制。

全部对外力的抵抗能通过增加参数m B2和a的大小得到提高。

(a) (b)
图5(a)机器人的臀部平台；(b)测量干扰外力的力传感器连接
图（6）系统对干扰的响应（维持平衡）
图（7）系统对干扰测响应（施力过度）
5.结论
本文介绍了双足步行机器人稳定控制方法,包括腿部额外在踝关节的自由度和分裂平衡质量设计。

该方法使感知、控制和平衡双足机器人以简单而有效的方式实现的。

设计方法的有效性通过实验结果证明。

这个方法还允许行走控制的实现算法与稳定控制算法无关，提高系统的响应速率。

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