【外文翻译】双足机器人上楼梯的步态规划

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步行机器人中英文对照外文翻译文献

步行机器人中英文对照外文翻译文献(文档含英文原文和中文翻译)图1 远程脑系统的硬件配置图2 两组机器人的身体结构图3 传感器的两个水银定位开关图4 层次分类图5 步行步态该输入处理器是作为参考程序块和一个图像搜索窗口形象该大小的搜索窗口取决于参考块的大小通常高达16 * 16且匹配。

该处理器计算价值块在搜索窗口，还找到最佳匹配块，这就是其中的最低当目标平移时块匹配是非常有力的。

然而，普通的块匹配方法当它旋转时无法跟踪目标。

为了克服这一困难，我们开发了一种新方法，跟随真正旋转目标的图6 双足步行图6 双足步行图7 双足步行实验图8 一系列滚动和站立运动通过集成传感器网络转型的综合为了使上述描述的基本动作成为一体，我们通过一种方法来描述一种被认为是根据传感器状况的网络转型。

图9显示了综合了基本动作机器人的状态转移图：两足行走，滚动，坐着和站立。

这种一体化提供了机器人保持行走甚至跌倒时的problems and advance the study of vision-based behaviors, we have adopted a new approach through building remote-brained robots. The body and the brain are connected by wireless links by using wireless cameras and remote-controlled actuators.As a robot body does not need computers on-board,it becomes easier to build a lightweight body with many DOFS in actuation.In this research, we developed a two-armed bipedal robot using the remote-brained robot environment and made it to perform balancing based on vision and getting up through cooperating arms and legs. The system and experimental results are described below.2 The Remote-Brained SystemThe remote-brained robot does not bring its own brain within the body. It leaves the brain in the mother environment and communicates with it by radio links. This allows us to build a robot with a free body and a heavy brain. The connection link between the body and the brain defines the interface between software and hardware. Bodies are designed to suit each research project and task. This enables us advance in performing research with a variety of real robot systems[10].A major advantage of remote-brained robots is that the robot can have a large and heavy brain based on super parallel computers. Although hardware technology for vision has advanced and produced powerful compact vision systems, the size of the hardware is still large. Wireless connection between the camera and the vision processor has been a research tool. The remote-brained approach allows us to progress in the study of a variety of experimental issues in vision-based robotics.Another advantage of remote-brained approach is that the robot bodies can be lightweight. This opens up the possibility of working with legged mobile robots. AsFigure 4 shows some of the classes in the programming environent for remote-brained robot written in Euslisp. The hierachy in the classes provides us with rich facilities for extending development of various robots.4 Vision-Based BalancingThe robot can stand up on two legs. As it can change the gravity center of its body by controling the ankle angles, it can perform static bipedal walks. During static walking the robot has to control its body balance if the ground is not flat and stable.In order to perform vision-based balancing it is re-quired to have high speed vision system to keep ob-serving moving schene. We have developed a tracking vision board using a correlation chip[l3]. The vision board consists of a transputer augmented with a special LSI chip(MEP[14] : Motion Estimation Processor) which performs local image block matching.The inputs to the processor MEP are an image as a reference block and an image for a search window.The size of the reference blsearch window depends on the size of the reference block is usually up to 32 by 32 pixels so that it can include 16 * 16 possible matches. The processor calculates 256 values of SAD (sum of absolute difference) between the reference block and 256 blocks in the search window and also finds the best matching block, that is, the one which has the minimum SAD value.Clock is up to 16 by 16 pixels.The size of the search window depends on the size of the reference block is usually up to 32 by 32 pixels so that it can include 16 * 16 possible matches. The processor calculates 256 values of SAD (sum of absolute difference) between the reference block and 256 blocks in the search window and also finds the best matching block, that is, the one which has the minimum SAD value.Block matching is very powerful when the target moves only in translation. However, the ordinary block matching method cannot track the target when it rotates. In order to overcome this difficulty, we developed a new method which follows up the candidate templates to real rotation of the target. The rotated template method first generates all the rotated target images in advance, and several adequate candidates of the reference template are selected and matched is tracking the scene in the front view. It remembers the vertical orientation of an object as the reference for visual tracking and generates several rotated images of the reference image. If the vision tracks the reference object using the rotated images, it can measures the body rotation. In order to keep the body balance, the robot feedback controls its body rotation to control the center of the body gravity. The rotational visual tracker[l5] can track the image at video rate.5 Biped WalkingIf a bipedal robot can control the center of gravity freely, it can perform biped walk. As the robot shown in Figure 2 has the degrees to left and right directions at the ankle position, it can perform bipedal walking in static way.The motion sequence of one cycle in biped walking consists of eight phases as shown in Figure 6. One step consists of four phases; move-gravity-center-on-foot,lift-leg, move-forward-leg, place-leg. As the body is described in solid model, the robot can generate a body configuration for move-gravity-center-on-foot according to the parameter of the hight of the gravity center. After this movement, the robot can lift the other leg and move it forward. In lifting leg, the robot has to control the configuration in order to keep the center of gravity above the supporting foot. As the stability in balance depends on the hight of the gravity center, the robot selects suitable angles of the knees.Figure 7 shows a sequence of experiments of the robot in biped walking6 Rolling Over and Standing UpFigure 8 shows the sequence of rolling over, sitting and standing up. This motion requires coordination between arms and legs.As the robot foot consists of a battery, the robot can make use of the weight of the battery for the roll-over motion. When the robot throws up the left leg and moves the left arm back and the right arm forward, it can get rotary moment around the body. If the body starts turning, the right leg moves back and the left foot returns its position to lie on the face. This rollover motion changes the body orientation from face up to face down. It canbe verified by the orientation sensor.After getting face down orientation, the robot moves the arms down to sit on two feet. This motion causes slip movement between hands and the ground. If the length of the arm is not enough to carry the center of gravity of the body onto feet, this sitting motion requires dynamic pushing motion by arms. The standing motion is controlled in order to keep the balance.7 Integration through Building Sensor-Based Transition NetIn order to integrate the basic actions described above, we adopted a method to describe a sensor-based transition network in which transition is considered according to sensor status. Figure 9 shows a state transition diagram of the robot which integrates basic actions: biped walking, rolling over, sitting, and standing up. This integration provides the robot with capability of keeping walking even when it falls down.The ordinary biped walk is composed by taking two states, Left-leg Fore and Right-leg Fore, successively.The poses in ‘Lie on the Back’ and ‘Lie on the Face’are as same as one in ‘Stand’. That is, the shape ofthe robot body is same but the orientation is different.The robot can detect whether the robot lies on the back or the face using the orientation sensor. When the robot detects falls down, it changes the state to ‘Lie on the Back’ or ‘Lie on the Front’ by moving to the neutral pose. If the robot gets up from ‘Lie on the Back’, the motion sequence is planned to exe cute Roll-over, Sit and Stand-up motions. If the state is ‘Lie on the Face’, it does not execute Roll-over but moves arms up to perform the sitting motion.8 Concluding RemarksThis paper has presented a two-armed bipedal robot which can perform statically biped walk, rolling over and standing up motions. The key to build such behaviors is the remote-brained approach. As the experiments have shown, wireless technologies permit robot bodies free movement. It also seems to change the way we conceptualize robotics. In our laboratory it has enabled the development of a new research environment, better suited to robotics and real-world AI.The robot presented here is a legged robot. As legged locomotion requires dynamic visual feedback control, its vision-based behaviors can prove the effectiveness of the vision system and the remote-brained system. Our vision system is based on high speed block matching function implemented with motion estimation LSI. The vision system provides the mechanical bodies with dynamic and adaptive capabilities in interaction with human. The mechanical dog has shown adaptive behaviors based on distance。

采用DDPG的双足机器人自学习步态规划方法

步态规划是机器人控制领域的研究热点和重要的研究内容。

双足机器人结构复杂，其行走过程是由连续的摆腿和离散的碰撞组成，具有众多自由度，难以通过传统控制理论方法建立动力学模型[1]。

即便勉强采用此类方法，也会导致双足机器人运动过程消耗大，行走速度低，环境适应性差。

实际上相比精准的步态，功能性和抗干扰性更为重要，也能使双足机器人能面对不同环境的需求。

随着信息技术的发展，以强化学习为代表的智能算法以其自适应特性越来越多运用于机器人控制领域[2-3]，但过去强化学习在机器人控制领域的实践都局限于低维的状态空间和动作空间，且一般是离散的情境下。

然而现实世界的复杂任务通常有着高维的状态空间和连续的动作空间。

2013年，DeepMind团队提出了结合深度神经网络和强化学习的DQN算法[4]，解决了高维输入问题。

但DQN仍是一个面向离散控制的算法，对连续动作处理能力不足。

在机器人的实际控制中，每个关节的角度输出是连续值，若把每个关节角取值范围离散化，则行为的数量随自由度的数量呈指数增长。

若进一步提升这个精度，取值的数量将成倍增长。

采用DDPG的双足机器人自学习步态规划方法周友行，赵晗妘，刘汉江，李昱泽，肖雨琴湘潭大学机械工程学院，湖南湘潭411105摘要：为解决多自由度双足机器人步行控制中高维非线性规划难题，挖掘不确定环境下双足机器人自主运动潜力，提出了一种改进的基于深度确定性策略梯度算法（DDPG）的双足机器人步态规划方案。

把双足机器人多关节自由度控制问题转化为非线性函数的多目标优化求解问题，采用DDPG算法来求解。

为解决全局逼近网络求解过程收敛慢的问题，采用径向基（RBF）神经网络进行非线性函数值的计算，并采用梯度下降算法更新神经网络权值，采用SumTree来筛选优质样本。

通过ROS、Gazebo、Tensorflow的联合仿真平台对双足机器人进行了模拟学习训练。

经数据仿真验证，改进后的DDPG算法平均达到最大累积奖励的时间提前了45.7%，成功率也提升了8.9%，且经训练后的关节姿态角度具有更好的平滑度。

双足机器人平衡控制及步态规划研究

摘要摘要驱动技术，人工智能，高性能计算机等最新技术已经使双足机器人有了粗略模拟人体运动的灵巧性，能够进行舞蹈展示，乐器演奏，与人交谈等。

然而这与投入实际应用所需求的能力还有不小差距。

主要体现在缺乏与人类相近的平衡能力和步伐协调能力，对工作环境要求高，在非结构化环境中适应能力差。

因此，本文以自主研制的双足机器人为研究对象，重点研究了双足机器人的平衡控制，阻抗控制以及步态规划等内容。

本文首先简要介绍了自主研制的双足机器人的软硬件构架，建立了ADAMS 和Gazebo仿真来协助对控制算法性能预测和优化并减少对物理机器人的危险操作。

接着分析了双足机器人的正逆运动学并引入运动学库KDL来简化运动学运算。

稳定的平衡控制对于双足机器人而言在目前还是个不小的挑战。

本文就此研究了两种处理平衡的阻抗调节方案。

一种是基于LQR的固定阻抗模型，这种方案简单有效，但存在易产生振动的问题，本文结合滤波改善了平衡控制效果。

另一种是基于增强学习的自适应阻抗模型。

该方法可以在不知道系统内部动态信息的情况下利用迭代策略在线得到最优解，是对前述LQR方法的进一步优化。

随后本文通过仿真和实验进行了验证并分析了优缺点。

步态规划是机器人运动控制中最基础的一环。

本文从五连杆平面机器人入手对其运动控制进行了研究。

首先采用基于ZMP的多项式拟合法实现了机器人平地行走的步态规划。

然后分析其动力学模型并利用PD控制器进行运动仿真，就仿真中出现双腿支撑阶段跟踪误差较大的问题提出了PD与径向基神经网络混合控制的新策略。

再次通过仿真证实该方案能够减小跟踪误差。

最后，本文利用前述多项式拟合法对实验平台的物理机器人进行静态行走和上楼梯的步态规划。

针对上楼梯的步态规划的特殊性，本文提出了分段拟合来实现各关节的协同规划，并引入了躯干前倾角来辅助身体平衡。

由于时间所限，本文实现了双足机器人的稳定步行实验，上楼梯实验还尚缺稳健性，这将作为下一步的工作。

关键词：双足机器人，平衡控制，步态规划，ADAMS仿真，增强学习IABSTRACTDriving technology, artificial intelligence, high-performance computers and other latest technology has enable bipedal robots to roughly emulate the motor dexterity of humans, able to dance show, musical instruments, and talking. However, this ability still have big gap between putting into practical application. Mainly reflected in the lack of the ability of balance, and the coordination of walking. High demands on the working environment, poor adaptability in unstructured environments. In this paper, the self-developed bipedal humanoid robot is researched, and the balance control, impedance control and gait planning are mainly studied.This paper first introduces the hardware and software architecture of the biped robot, and establishes the ADAMS and Gazebo simulation to assist in the prediction and optimization of the performance of the control algorithm, so as to reduce the risk operation of the physical robot and avoiding the potential risks. Then the forward kinematics and inverse kinematics of the biped robot are analyzed and the kinematic library KDL is introduced to simplify the kinematic operation.Stable balance control is still a challenge for biped robots. In this paper, we present two schemes for impedance adjustment when dealing with the balance. One is the fixed impedance model, which is simple and effective, but there is a problem of vibration, a filter is combined in this paper to improve the balance control effect. The other is an adaptive impedance model based on integral reinforcement learning. This method can obtain the optimal solution online by using the policy iteration without knowing the dynamic information of the system. It is a further optimization of the LQR method. Then the scheme is simulated and experimented, and the advantages and disadvantages are analyzed.Gait planning is the most basic part of robot motion control. First, a simplified five-link planar robot model is established to facilitate the study. Then, the ZMP-based polynomial fitting method is used to realize the gait planning of the robot's horizontal walking. Then the dynamic model is analyzed and the PD controller is used to simulate the motion. A new strategy of PD and RBF neural network hybrid control is proposed to reduce the tracking error during DSP. Again, the simulation results show that the scheme can reduce the tracking error.IIFinally, this paper applies the polynomial fitting method to carry on the static walking and the stairway gait planning of the physical robot of the experimental platform. In view of the particularity of the gait planning of the stairs, this paper proposes a partition fitting to realize the cooperative planning of each joint and introduces the trunk leaning forward to assist the body balance. Due to time constraints, this paper has achieved a stable walking experiment of bipedal robots, and the stair experiment is still lacking in robustness, which will be the next step of the work.Keywords: biped robot, balance control, gait planning, ADAMS simulation, reinforcement learningIII目录第一章绪论 (1)1.1 研究工作的背景与意义 (1)1.2 国内外研究历史和发展态势 (2)1.2.1双足机器人的发展现状 (2)1.2.2双足机器人平衡控制概况 (6)1.2.3机器人阻抗控制概况 (7)1.2.4双足机器人步态规划及运动控制概况 (8)1.3 本文的主要工作 (9)1.4 本论文的结构安排 (10)第二章双足机器人控制系统架构与仿真平台设计 (11)2.1 双足机器人机体结构 (11)2.2 双足机器人控制系统框架设计 (13)2.2.1硬件系统设计 (13)2.2.2控制软件设计 (15)2.3 双足机器人仿真平台的设计 (16)2.3.1机器人系统常用仿真软件 (16)2.3.2ADAMS虚拟样机建模 (17)2.3.3G AZEBO模型建立 (18)2.4 本章小结 (19)第三章双足机器人运动学建模分析 (20)3.1 双足机器人位姿的描述 (20)3.2 正向运动学求解 (21)3.3 逆运动学求解 (22)3.4 五连杆平面机器人的运动仿真 (26)3.4.1开源运动学和动力学库KDL (26)3.4.2基于KDL的双足机器人运动学仿真 (26)3.5 本章小结 (27)第四章双足机器人站姿下的平衡控制 (28)4.1 双足机器人的平衡控制策略 (28)4.2 双足机器人的踝关节平衡策略 (30)IV4.2.1基于倒立摆的固定阻抗模型 (31)4.2.2基于增强学习的自适应阻抗模型 (33)4.3 仿真结果 (38)4.3.1固定阻抗与自适应阻抗仿真结果及对比 (38)4.3.2仿真算法的进一步优化 (41)4.4 实验结果 (43)4.4.1实验设计 (43)4.4.2实验结果与分析 (44)4.5 本章小结 (47)第五章五连杆双足机器人行走步态规划及控制 (48)5.1 步态规划依据和方法 (48)5.1.1步态规划的依据 (48)5.1.2离线步态规划的方法 (49)5.2 五连杆平面机器人模型的建立 (49)5.2.1五连杆模型简介 (50)5.2.2五连杆的运动学与动力学模型 (51)5.3 五连杆机器人的步态规划 (53)5.3.1摆动腿的轨迹规划 (53)5.3.2髋关节的轨迹规划 (55)5.3.3轨迹规划展示 (56)5.4 基于PD控制器的五连杆运动控制 (57)5.4.1PD控制器设计 (58)5.4.2仿真实验结果及分析 (59)5.5 基于RBFNN的五连杆运动控制 (61)5.5.1基于动力学模型的控制分析 (61)5.5.2RBF神经网络控制器设计 (62)5.5.3仿真实验结果及分析 (64)5.6 本章小结 (65)第六章双足机器人步态规划与实验 (66)6.1 双足机器人步态规划的约束 (66)6.2 双足机器人静态行走的步态规划 (66)6.2.1步行准备阶段运动规划 (67)6.2.2周期步行阶段运动规划 (69)V6.2.3步态仿真验证 (71)6.2.4双足机器人步行实验 (73)6.3 双足机器人上楼梯的步态规划 (73)6.3.1起步阶段运动规划 (73)6.3.2上楼梯双腿支撑阶段运动规划 (74)6.3.3跨两层台阶运动规划 (75)6.3.4双足机器人上楼梯仿真及实验 (76)6.4 本章小结 (78)第七章全文总结与展望 (79)7.1 全文总结 (79)7.2 后续工作展望 (80)致谢 (81)参考文献 (82)攻读硕士学位期间取得的成果 (87)VI第一章绪论第一章绪论1.1 研究工作的背景与意义上世纪60年代初，工业机器人和自主移动机器人成为现实，为实现大规模自动化生产，降低制造成本提升产品质量做出了巨大贡献。

双足行走机器人平衡控制译文

外文资料：Robots1. IntroductionNowadays, 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 inindependently 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 Robot2.1. Robot locomotion mechanismThe 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 configurations2.2. Flexible ankle joint to utilize stability measurementIn 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 offlexible ankle2.3. Split balancing mass for faster system responseThe 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 robot3. System modeling and controlFrom the diagram on Fig 3, the dynamic equation using Newton’s second law about point O gives:ΣT O=IθT 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=0m L d−m B1d s=0（2）m L d=m B1d sd s=m L m B1dSubstituting 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 Lm B1d 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 B2a2θFig 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 system4. Experimental resultsThe 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 ofits 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 applieddisturbance forceFig. 6. System response to disturbance (balance maintained)Fig. 7. System response to disturbance (excessive force applied)5. ConclusionThis 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。

教学用双足步行机器人步态规划及软硬件设计

第45卷第3期2017年3月林业机械与木工设备FORESTRY MACHINERY & WOODWORKING EQUIPMENTVol45 No.3Mar.2017研究与设计教学用双足步行机器人步态规划及软硬件设计张蔓，高宇博，邓佳玉，魏庆媛，赵英妤(哈尔滨石油学院，黑龙江哈尔滨150〇28)摘要：阐述了教学用步行机器人的自由度选择及步态规划，分析了六自由度双足机器人行走规律，用CAXA软件画出自由度分部图，运用三点规划法确定了摆动腿踝关节、髋关节的3个步态姿态点，配合多项式插值法确定踝关节运动。

选择32路妮机控制器为主控板，并给出直线行走程序。

关键词:教学；双足机器人;步态;规划中图分类号:TP242 文献标识码:A 文章编号:2095 -2953(2017)03 -0038 -02Teaching - type Bipedal Walking Robot Gait Planningand Software and Hardware DesignZHANG Man,GAO Yu-bo，DENG Jia-yu,WEI Qing-yuan,ZHAO Ying-yu(Harbin Institute of Petroleum,Harbin Heilongjiang 150028,China)Abstract： The freedom degree choice and gait planning of teaching - type bipedal walking robots are stated, the walking pattern of six DOF biped robots is analyzed, CAXA software is used to draw the segment graph of the degree of freedom, a three - point planning method is used to determine the three gait posture points of the swinging leg ankle joints and hip joints,and a polynomial interpolation method is adopted to determine the movement of ankle joints. A 32 - way steering servo controller is used as the main control board and straight line walking procedures are given. Key words： teaching ； biped robot ； gait ； planning机器人是一种智能化机械装置，广泛应用在危险、繁重的工业现场。

双足机器人结构设计与步态规划

双足机器人结构设计与步态规划贠今天;杜萌萌;桑宏强;武爱华【摘要】为了增强机器人的行走效率，使机器人的步态更自然，且具有良好适应复杂路况的特点，设计了一款双足机器人研究平台，并建立双足机器人行走机构的运动学模型，同时对机器人的前向运动进行了步态规划，从而提高了机器人运动过程中的稳定性。

采用三次样条插值方法得到机器人各关节的平滑运动轨迹。

%In order to enhance the efficiency of the biped robot, make the robot has a more natural gaitand has good features to adapt to complex road, a biped robot research platform is designed, and a bipedal robot kinematics model is set up, the forward movement of bipedal robot gait is planned, so as to improve the stability of the robot motion process. The cubic spine interpolation is used to get smooth motion trajectory of the robot joints.【期刊名称】《天津工业大学学报》【年(卷),期】2014(000)005【总页数】4页(P80-83)【关键词】双足机器人;运动学建模;结构设计;步态规划【作者】贠今天;杜萌萌;桑宏强;武爱华【作者单位】天津工业大学机械工程学院，天津 300387; 天津工业大学天津市现代机电装备技术重点实验室，天津 300387;天津工业大学机械工程学院，天津300387;天津工业大学机械工程学院，天津 300387;天津工业大学机械工程学院，天津 300387【正文语种】中文【中图分类】TP242.6目前，机器人的移动方式[1]主要包括3种形式：轮式、履带式和足式.在行走方式中，双足机器人自动化程度最高，最为复杂，是目前最具有代表性的先进智能化机器人，其应用技术是目前机器人研究领域的一个重要组成部分[2-3].步态规划对双足机器人的稳定行走起着至关重要的作用.在步态规划中，产生实现某种步态的各关节期望运动轨迹[4]，为机器人稳定行走提供了理论依据.因此对双足机器人的步态研究具有深远的现实意义[5].本文提出一种新型双足机器人结构，对其建立数学模型，并采用三次样条插值方法规划机器人的前向运动，得到各关节的平滑运动轨迹[6-7].双足机器人结构由髋关节、膝关节、踝关节、大腿连杆和小腿连杆（履带式结构）组成，如图1所示.其特点是膝关节为四连杆闭链结构.其中，由膝关节的驱动电机带动膝关节四连杆前后摆动，如图2所示.此结构的优点是有利于提高脚离地面的高度，使得小腿摆动过程中不会碰到地面，增强了机器人在行走过程中的避障能力. 当膝关节的四连杆摆动到一定角度时，机器人构换到另一种工作形态—履带式行走，如图3所示.2种构态的转换，使得此结构能在复杂多变的环境下行走，极大地增强了双足机器人的灵活性.单腿模型如图4所示.图中：Li（i=1、2……）为单腿中相应的连杆长度；Lic为单腿中相应连杆质心位置；θi为连杆广义角度的坐标变量；P0为机器人胯中心点.本文建立了单腿关键点笛卡尔坐标和角度之间的关系.以胯部中心点坐标为计算起点，其运动学模型为：利用上面的运动学模型可以在已知P6笛卡尔坐标情况下，求得腿部各个关节角度，也可以在已知各个关节角度和任意一点坐标情况下，求得另外一些关键点的笛卡尔坐标值.3.1 脚掌倾角规划行走设计以左脚支撑，右脚前迈开始分析，选取脚掌与地面的夹角为样条插值函数，设脚掌与地面的夹角为Q（t），示意图如图5所示.t0时刻脚掌开始转动，脚掌与地面夹角为qs；t1时刻脚尖离开地面形成摆动角，脚掌与地面夹角为qb；t2时刻踝关节达到最大高度，脚掌与地面的夹角为qm；t3时刻脚跟着地，脚掌与地面的夹角为qf；t4时刻脚掌完全着地，脚掌与地面的夹角为qe.假设机器人前进一步的时间为T.脚掌倾角在步态周期内满足以下约束条件：式中：qs、qe均为位于支撑腿下面的地面倾斜角度，当地面水平时，两者都为零.利用三次样条插值得到脚掌倾角的角度规划，如图6所示.3.2 踝关节规划当双足机器人通过障碍物或在粗糙的地面上行走时，摆动腿必须抬得足够高才得以越过障碍.令（Ln，Hn）为摆动脚到达最高点时的坐标，根据运动学约束条件：式中：DS为步长；La为脚掌的高度；Lb为脚掌中心到脚尖的距离；LC为脚掌中心到脚跟的距离；Hs和He均为支撑脚脚底下面地面的高度，当地面水平时，两者都为零.利用三次样条插值得到踝关节在X、Z方向运动轨迹，如图7所示.3.3 髋关节规划从稳定性的角度来分析，当腰部自由度为零时，最好是躯干和倾斜角度始终为常量.假设在单腿支撑期的中间时刻，髋关节达到最高点Hmax；在双腿支撑期的中间时刻，髋关节达到最低点Hmin；Ta是双腿支撑期的时间.于是髋关节Z（t）应该满足以下约束条件：同样通过三次样条插值得到髋关节的运动轨迹，如图8所示.3.4 膝关节规划膝关节模型如图9所示.图中，θ表示大腿连杆与小腿连杆的夹角，四边形BCDE为膝关节四连杆模型.在双足机器人前向行走过程中，小腿的弯曲程度随∠CBE角度变化，改变∠CBE的角度，即实现膝关节的步态.在四边形BCDE中：在四边形BCDE中有微分方程由微分方程组可得∠CBE.膝关节运动轨迹如图10所示.本文采用三次样条插值方法进行步态规划，得到了双足机器人前向行走过程中重要关节的运动轨迹，确保了机器人在行走期间速度的连续性，步态的稳定性.同时，Matlab仿真结果也表明所设计的步态规划是合理可行的，双足机器人能够实现预期的运动.【相关文献】[1]代良全，张昊，戴振东.仿壁虎机器人足端工作空间分析及其实现协调运动的步态规划[J].机器人，2008，30（2）：182-186.[2]绳涛，王剑，马宏，等.驱动双足步行机器人运动控制与动力学仿真[J].系统仿真学报，2008，20（24）：6745-6753.[3]MOUSAVI P N，BAGHERI A.Mathematicalsimulationof a seven link biped robot on various surfacesand ZMP considerations [J].Applied MathematicalModelling，2007，31（1）：18-37.[4]梁少芳.仿人机器人步态规划及其控制系统的研究[D].广州:广东工业大学，2010.[5]韩亚丽，王兴松.行走助力机器人研究综述[J].机床与液压，2008，36（2）：165-169.[6]许小勇，钟太勇.三次样条插值函数的构造与Matlab实现[J].兵工自动化，2006，25（11）：76-78.[7]张伟，杜继宏.双足步行机器人的步态规划[J].计算机工程与应用，2002（13）：214-216.。

双足步行机器人相关翻译

本科毕业论文外文文献及译文文献、资料题目：Ｗalking Coｎtrol alｇorithm oｆBipｅd Huｍaｎoｉd Roｂｏｔ文献、资料来源：期刊文献、资料发表（出版）日期：１999.６。

3院（部）：理学院专业：光信息科学与技术班级：光信112姓名：王若宇学号: 201１1211３5指导教师:赵俊卿翻译日期：20１５。

5．１4外文文献:Waｌkｉng Contｒｏｌalgｏrithm of Ｂｉped ＨumaｎoｉdRobotManｙstudieｓon bipｅd ｗalｋing robots ｈave beｅn perfoｒmed ｓince1970 ［1-４]。

Duｒiｎg thaｔperiｏd，biped wａlking robots have t ｒansfoｒmed inｔo biｐed humanoiｄrobots thｒoｕgｈthe techｎoｌｏgｉcaｌdｅvelｏｐmeｎt。

Furtheｒmore, the biｐeｄhumａnoid robot haｓｂeco ｍe a one ｏf repreｓentａtｉve reｓeａrch topics in tｈe intelliｇenｔｒoｂｏt researcｈsocｉｅty. Ｍａny reseａrchｅrs anticipate that the ｈumanoiｄrobｏt iｎｄuｓtrｙｗｉlｌｂe the inｄusｔry leader oｆthｅ21st ceｎtury anｄwe eveｎtualｌy enter an era of onｅrobot ｉn everyｈｏmｅ．The stｒong fｏcuｓoｎｂｉｐｅd ｈｕmaｎoid rｏbots stems from a lｏn ｇ-standinｇｄesｉre ｆor hｕman—lｉke robots．Ｆurtheｒｍorｅ，ａhuman—like apｐearaｎce isｄesirａｂlｅｆoｒcoｅxiｓtence in a huｍａn－robot societｙ. Howｅver, wｈiｌe ｉｔis not haｒd ｔｏdｅveｌoｐa ｈuman－lｉｋe bｉpeｄrobot pｌａtｆorm，tｈe reａｌizaｔion of staｂle bip ｅd roboｔｗalkiｎg poseｓ a considerable cｈalleｎｇe.Thｉsｉs bｅcａuse of a lack oｆunderｓtandｉnｇｏn hｏw humans walk stably．Ｆｕrthermore, ｂiped wａlｋiｎg iｓan unstabｌe ｓuccessivｅmｏｔion of a ｓingle suｐport pｈａｓe.Early ｂｉｐed ｗalking of robots inｖoｌved static wａlkｉng wiｔh a veｒｙlow walｋinｇspeｅｄ[5,6］。

双足竞步机器人的步态规划

双足竞步机器人的步态规划翟胜杭;姜豪;祝铠甲;张鹏;刘利;史颖刚;胡国田【摘要】以双足竞步机器人为研究对象,提出了一种可以对机器人进行快速调试的方法.该方法先建立机器人的数学模型和运动学方程,求出机器人正运动学的解,并进行步态规划,计算出机器人行走或其他动作过程中各关节摆动的角度,再进行上机调试.测试结果表明,在该方法所得结果的基础上,进行一定的调节,就能够让机器人完成预期动作.这种离线规划、在线微调的快速调试方法,能够有效提高同类型机器人的调试效率.【期刊名称】《机械研究与应用》【年(卷),期】2017(030)001【总页数】5页(P10-14)【关键词】双足竞步机器人;舵机;自由度;步态规划;快速调试【作者】翟胜杭;姜豪;祝铠甲;张鹏;刘利;史颖刚;胡国田【作者单位】西北农林科技大学机械与电子工程学院,陕西杨凌 712100;西北农林科技大学机械与电子工程学院,陕西杨凌 712100;西北农林科技大学机械与电子工程学院,陕西杨凌 712100;西北农林科技大学机械与电子工程学院,陕西杨凌712100;西北农林科技大学机械与电子工程学院,陕西杨凌 712100;西北农林科技大学机械与电子工程学院,陕西杨凌 712100;西北农林科技大学机械与电子工程学院,陕西杨凌 712100【正文语种】中文【中图分类】TP242.6人形机器人的双足运动，具有行走灵活性，在上下楼梯、跨越障碍、奔跑运动等方面，优于轮式移动和履带式移动等运动方式。

但是，机器人在双足行走过程中，容易摔倒。

同时，摆动脚与地面的撞击，会加剧机器人的不稳定，所以，动态运动是双足机器人研究领域的难点之一，在机器人步态规划中，要确保机器人姿态，不发生突变，脚的落地速度为零[1-4]。

人的腿部一共有髋、膝、踝三个关节。

其中髋关节的自由度为3，膝关节的自由度为1，踝关节的自由度为2[5-7]。

此研究的双足竞步机器人，如图1所示，其自由度由舵机运动实现，只拥有躯干、大腿、小腿、脚，是一个很容易搭建的实验平台，是双足机器人中，结构最简洁的机器人。

双足步行机器人直线行走步态规划及关节轨迹研究

双足步行机器人直线行走步态规划及关节轨迹研究张蔓;高宇博;邓佳玉;张晶;任欢【摘要】对教学用双足机器人物理样机进行步态规划,运用仿生学方法,参考人类稳态步行特点,规划出一个步行周期内机器人直线行走过程中各个阶段重心移动的规律,建立双足机器人局部坐标系,确定一个步态周期中摆动腿关节运动初始条件,采用多项式插值算法规划出机器人摆动腿部踝关节和髋关节轨迹.%Gait planning for the physical prototype of teaching-type biped robots is developed,and with a bionics method,with reference to the characteristics of human steady-state walking,the law of gravity movement at each stage in the robot straight-line walking process within a walking cycle is planned,the local coordinate system of biped robots is established,the initial conditions for swinging movement of leg joints within a gait cycle are determined and a polynomial interpolation algorithm is used to plan the trajectory of robot swinging leg ankle joints and hip joints.【期刊名称】《林业机械与木工设备》【年(卷),期】2017(045)006【总页数】4页(P35-37,52)【关键词】双足机器人;直线行走;步态;关节轨迹【作者】张蔓;高宇博;邓佳玉;张晶;任欢【作者单位】哈尔滨石油学院,黑龙江哈尔滨 150028;哈尔滨石油学院,黑龙江哈尔滨 150028;哈尔滨石油学院,黑龙江哈尔滨 150028;哈尔滨石油学院,黑龙江哈尔滨 150028;哈尔滨石油学院,黑龙江哈尔滨 150028【正文语种】中文【中图分类】TP242机器人的研究水平在一定程度上代表了一个国家的综合科技水平，机器人能替代人类完成各种危险、精确的工作。

双足步行机器人快速步行与仿真_英文_

YU Wei, WU Wei-guo
(Department of Mechanism Design, Harbin Institute of Technology, Harbin 150001, China)
Abstract: Integrating advantages of the preview control of ZMP method with rotation about the front edge of the stance foot, a fast walking pattern generation was proposed to generate COM and ankles trajectories. Furthermore, by introducing a method to gradually decrease the COM lateral swing range, smaller joint drive torque was gotten under conditions of fast walking. The walking pattern generated with speed 2 [km/h], and by using mechanism design and dynamic analysis software biped dynamic walking was realized to validate the effectiveness of this method under physical environment. Key words: walking pattern generation; fast walking; biped robot; preview control

教学型双足步行机器人转向步态规划方法的研究

教学型双足步行机器人转向步态规划方法的研究赵瑞林;孟彦京;张顺星【摘要】双足机器人的步态规划包括直线行走和转向两个部分。

在直线行走中，髋关节偏转的自由度被限制，而在转向过程中，最终的转向则必须通过髋关节的偏转才能实现。

针对双足机器人转向时的步态规划问题，利用关节转向角进行多项式插值的方法，对机器人转向时的步态进行了规划。

通过MATLAB和ADAMS建立虚拟样机，对步态规划结果进行仿真，仿真结果验证了步态规划的正确性。

%Gait planning of biped robot including a straight walking and turning two parts. In a straight line walking, hip joint deflection degree of freedom is limited, but in the process of turning, eventually steering must be realized by deflection to hip joint. The gait of a biped robot steering, by using the method of polynomial interpolation of joint steercng angle, the robot steering gait is planned. The virtual prototype is established by MATLAB and ADAMS simulation of the gait planning results, the simulation results verify the correctness of the gait planning.【期刊名称】《工业仪表与自动化装置》【年(卷),期】2016(000)005【总页数】4页(P117-120)【关键词】双足机器人;转向步态规划;MATLAB仿真;ADAMS仿真【作者】赵瑞林;孟彦京;张顺星【作者单位】陕西工业职业技术学院电气工程学院，陕西咸阳712000;陕西科技大学电气与信息工程学院，西安710021;陕西工业职业技术学院电气工程学院，陕西咸阳712000【正文语种】中文【中图分类】TP24步态规划是根据双足机器人运动学的特性规划出每个关节的运动轨迹。

六自由度平面双足机器人的步态规划

六自由度平面双足机器人的步态规划李彬;李界家【摘要】稳定高效的行走是双足机器人在独立工作或者协助人类工作所必备的条件,也是最终目标实现的基础.稳定高效的行走可以通过合理的步态规划来实现.论文根据六自由度双足平面机器人的特点,并考虑到单、双足支撑的光滑过度的重要性,对机器人进行了正逆运动学分析,最后基于三次样奈插值法规划出机器人步态,并用仿真试验进行了验证.【期刊名称】《机电产品开发与创新》【年(卷),期】2015(028)006【总页数】4页(P17-20)【关键词】步态;三次样条;稳定;双足机器人【作者】李彬;李界家【作者单位】沈阳建筑大学机械工程学院,辽宁沈阳110168;沈阳建筑大学机械工程学院,辽宁沈阳110168【正文语种】中文【中图分类】TP242双足机器人具有多关节连接的腿部结构，相比轮式、履带式机器人就能很容易的越过较高的障碍物，双足机器人对行走的地形环境要求更低，效率很高。

这些显著的优势使双足机器人在军事领域、地形探测和、抗震救灾这些复杂多变的环境下，能够在短时间内完成各种复杂的动作，从而达到所规定的任务指标。

所以对双足机器人的步态规划研究具有很大的潜在价值。

双足步态的实现需要解决非常复杂的控制难题。

双足系统不仅是非线性的，而且对于开环和闭环模型都是不连续的而且还受地面约束。

本文对六自由度双足机器人进行正逆运动学分析，基于三次样条差值对双足机器人的步态进行合理规划。

由于双足机器人具有复杂的运动学、动力学和控制特性，我们需要提取机器人的具体特征进行建模，这样一来可以有效的降低步态规划和步行控制的难度，从而实现稳定的步行和控制。

建立运动学方程我们需要建立坐标变换方程，把一系列的坐标系建立在连接连杆的关节上，这些坐标之间的相对位置和方向用齐次坐标变换来描述，就可以建立起机器人的运动学方程。

但我们需要解决的问题是如何在每个关节上确定坐标系的方向、如何确定相邻两个坐标系之间的相对平移和旋转量，因此需要采用一种合适的方法来描述相邻连杆之间的坐标方向和参数。

双足机器人设计及步态规划研究

双足机器人设计及步态规划研究
王新亭;张峻霞;尹立苹
【期刊名称】《制造业自动化》
【年(卷),期】2013(035)003
【摘要】@@%针对双足机器人数学描述复杂、分析较为困难等问题,本文提出一种4自由度双足机器人结构,具有驱动关节少且足底始终与地面保持平行等特点.对此双足机器人的前向运动进行了步态规划,其特点是在单腿支撑阶段,机器人躯干的重心始终保持在支撑腿足部中心范围内,仅在双腿支撑阶段,机器人躯干重心向前移动,提高了机器人运动过程中的稳定性.根据机器人运动轨迹的边界点,采用三次多项式拟合得到机器人关节的平滑运动轨迹,有效减小运动过程中动态特性的影响,为机器人各关节在运动周期内的角度规划和样机的研制提供理论依据.
【总页数】4页(P50-53)
【作者】王新亭;张峻霞;尹立苹
【作者单位】天津科技大学机械工程学院,天津300222;天津科技大学机械工程学院,天津300222;天津科技大学实验室管理处,天津300222
【正文语种】中文
【中图分类】TP242.6
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