Gait Analysis of a Radial Symmetrical Hexapod Robot Based on Parallel Mechanisms

Most gait studies of multi-legged robots in past neglected the dexterity of robot body and the relationship between stride length and body height.This paper investigates the performance of a radial symmetrical hexapod robot based on the dexterity of parallel mechanism.Assuming the constraints between the supporting feet and the ground with hinges,the supporting legs and the hexapod body are taken as a parallel mechanism,and each swing leg is regarded as a serial manipulator.The hexapod robot can be considered as a series of hybrid serial-parallel mechanisms while walking on the ground.Locomotion performance can be got by analyzing these equivalent mechanisms.The kinematics of the whole robotic system is established,and the influence of foothold position on the workspace of robot body is analyzed.A new method to calculate the stride length of multi-legged robots is proposed by analyzing the relationship between the workspaces of two adjacent equivalent parallel mechanisms in one gait cycle.Referring to service region and service sphere,weight service sphere and weight service region are put forward to evaluate the dexterity of robot body.The dexterity of single point in workspace and the dexterity distribution in vertical and horizontal projection plane are demonstrated.Simulation shows when the foothold offset goes up to 174 mm,the dexterity of robot body achieves its maximum value 0.164 4 in mixed gait.The proposed methods based on parallel mechanisms can be used to calculate the stride length and the dexterity of multi-legged robot,and provide new approach to determine the stride length,body height,footholds in gait planning of multi-legged robot.     

Gait Analysis of Quadruped Robot Using the Equivalent Mechanism Concept Based on Metamorphosis

The previous research regarding the gait planning of quadruped robot focuses on the sequence for lifting o and placing the feet, but neglects the influence of body height. However, body height a ects gait performance significantly, such as in terms of the stride length and stability margin. We herein study the performance of a quadruped robot using the equivalent mechanism concept based on metamorphosis. Assuming the constraints between standing feet and the ground with hinges, the ground, standing legs and robot body are considered as a parallel mechanism, and each swing leg is regarded as a typical serial manipulator. The equivalent mechanism varies while the robot moves on the ground. One gait cycle is divided into several periods, including step forward stages and switching stages. There exists a specific equivalent mechanism corresponding to each gait period. The robot's locomotion can be regarded as the motion of these series of equivalent mechanisms. The kinematics model and simplified model of the equivalent mechanism is established. A new definition of the multilegged robot stability margin, based on friction coe cient, is presented to evaluate the robot stability. The stable workspaces of the equivalent mechanism in the step forward stage of trotting gait under di erent friction coe cients are analyzed. The stride length of the robots is presented by analyzing the relationship between the stable workspaces of the equivalent mechanisms of two adjacent step forward stages in one gait cycle. The simulation results show that the stride length is larger with increasing friction coe cient. We herein propose a new method based on metamorphosis, and an equivalent mechanism to analyze the stability margin and stable workspace of the multilegged robot.     

Static Force Analysis of Foot of Electrically Driven Heavy-Duty Six-Legged Robot under Tripod Gait

The electrically driven six-legged robot with high carrying capacity is an indispensable equipment for planetary exploration, but it hinders its practicability because of its low efficiency of carrying energy. Meanwhile, its load capacity also affects its application range. To reduce the power consumption, increase the load to mass ratio, and improve the stability of robot, the relationship between the walking modes and the forces of feet under the tripod gait are researched for an electrically driven heavy-duty six-legged robot. Based on the configuration characteristics of electrically driven heavy-duty six-legged, the typical walking modes of robot are analyzed. The mathematical models of the normal forces of feet are respectively established under the tripod gait of typical walking modes. According to the MATLAB software, the variable tendency charts are respectively gained for the normal forces of feet. The walking experiments under the typical tripod gaits are implemented for the prototype of electrically driven heavy-duty six-legged robot. The variable tendencies of maximum normal forces of feet are acquired. The comparison results show that the theoretical and experimental data are in the same trend. The walking modes which are most available to realize the average force of distribution of each foot are confirmed. The proposed method of analyzing the relationship between the walking modes and the forces of feet can quickly determine the optimal walking mode and gait parameters under the average distribution of foot force, which is propitious to develop the excellent heavy-duty multi-legged robots with the lower power consumption, larger load to mass ratio, and higher stability.     

慧鱼六足仿生机器人步态研究与实现

在仿生学原理的基础上,对六足步行机器人三角步态的行走原理和稳定性进行了分析。采用慧鱼仿生机器人包搭接出六足步行机器人,进行了一系列步行的实验。并对机器人腿部机构中的足端轨迹进行了仿真与分析。结果表明该机器人能够严格按三角步态进行行走,实现诸如直线、转弯、躲避障碍物等行走功能,具有较好的机动性。     

Tripod gait-based turning gait of a six-legged walking robot

The turning gait planning and improvement methods of a six-legged walking robot on the basis of tripod gait are presented in this study. A projection method that considers an unstructured environment is proposed for the turning gait planning of the six-legged walking robot. The body and foot motion trajectories of the swing legs are planned with polynomial curves to keep the robot steady while walking. Two basic turning gaits, namely, circling and spinning gaits, are successfully designed with the planning method. An optimized method is proposed to improve the turning angle, which is subjected to stability, kinematics, and relief amplitude constraints in the unstructured environment. The turning ability of the turning gait is improved with the optimized turning angle. The circling and spinning gaits are implemented in simulations and experiments. Results demonstrate that the planning and improvement methods for the turning gait are valid and correct.

     

Method for six-legged robot stepping on obstacles by indirect force estimation

Adaptive gaits for legged robots often requires force sensors installed on foot-tips, however impact, temperature or humidity can affect or even damage those sensors. Efforts have been made to realize indirect force estimation on the legged robots using leg structures based on planar mechanisms. Robot Octopus III is a six-legged robot using spatial parallel mechanism(UP-2UPS) legs. This paper proposed a novel method to realize indirect force estimation on walking robot based on a spatial parallel mechanism. The direct kinematics model and the inverse kinematics model are established. The force Jacobian matrix is derived based on the kinematics model. Thus, the indirect force estimation model is established. Then, the relation between the output torques of the three motors installed on one leg to the external force exerted on the foot tip is described. Furthermore, an adaptive tripod static gait is designed. The robot alters its leg trajectory to step on obstacles by using the proposed adaptive gait. Both the indirect force estimation model and the adaptive gait are implemented and optimized in a real time control system. An experiment is carried out to validate the indirect force estimation model. The adaptive gait is tested in another experiment. Experiment results show that the robot can successfully step on a 0.2 m-high obstacle. This paper proposes a novel method to overcome obstacles for the six-legged robot using spatial parallel mechanism legs and to avoid installing the electric force sensors in harsh environment of the robot’s foot tips.     

Adjustable Mechanism for Walking Robots with Minimum Number of Actuators

Recent literature on walking robots deals predominantly with multi-degrees-of-freedom leg mechanisms and machines capable of adopting several gaits.This paper explores the other end of the spectrum suggesting mechanisms derived from a four bar coupler curve for a one degree of freedom walking robot.Simulation of the walk indicates that body of the robot is able to move with low variation in velocity.The best strategy for changing the gait to enable the robot to walk over obstacles and the effect of change i...     

Energetic walking gaits studied by a simple actuated inverted pendulum model

The mechanical structure and the joint torques configuration are the important parts in the biped robot design. Meanwhile, different walking speed and step length should be chosen to achieve efficient gait according to different need of walking environment. Therefore, this paper investigates the energetic walking gaits using a simple actuated inverted pendulum model. Joint torques and push-off impulse are both added in the model. The walking gaits with different joint torques configuration and with different combination of walking speeds and step lengths are analyzed. The results show that hip velocity direction is changed by the push-off impulse just before the heelstrike, which reduces the energy consumption of each step. The walking gait with minimal energy consumption is the walking pattern only with push-off, the energy cost of which is 1/4 of the walking pattern only with joint torque during the swing phase. The cost of transport (COT) and the push-off impulse of the walking gait is increasing with the increase of walking speed and step length. Using same value of push-off impulse, the walking with long step length and slow speed is more efficient. The paper can provide suggestions for designing advanced legged robot systems with high energy efficiency and various gaits. For example, the consideration of push-off mechanism can be used in the biped robots design.

     

一种新型四足变胞爬行机器人的步态规划研究

随着移动机器人在探测救援中的应用逐渐增多,活动灵巧、环境适应能力强的多足机器人越来越受到国内外学者的关注。介绍一种腰部可以活动的四足机器人的设计及其步态生成,并展示了活动腰部可提升机器人对极端环境的适应性。提出三个基本假设以简化机构模型,提出腰部构态变换规则,并用几何方法说明了腰部构型变化可扩大机器人腿部活动空间,从而提升对复杂环境的适应性。另外,腰部运动与步态融合,生成了两种新的基本步态——扭腰直行步态和原地旋转步态。基于提出的两种步态,对比了固定腰部与可动腰部条件下运动稳定裕度的变化,分别计算了狭窄弯道通过条件,并分析了所设计步态对头部视觉的影响,从而证明所设计机器人具有较高的极端环境适应能力。     

全方位六足步行机的运动设计

本文对六足步行机的全方位运动步态进行了探讨, 提出了基于静态稳定性考虑的最佳步态的选择方案.就横向运动六足步行机的广义三角步态, 分析了其静态稳定裕量、爬坡能力、越沟能力等运动性能, 并给出了采用广义三角步态的横向运动六足步行机总体几何参数CAD的实例.     

Motion error compensation of multi-legged walking robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot’s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot’s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.     

Method for analyzing articulated torques of heavy-duty six-legged robot

The accuracy of an articulated torque analysis influences the comprehensive performances of heavy-duty multi-legged robots. Currently, the extremal estimation method and some complex methods are employed to calculate the articulated torques, which results in a large safety margin or a large number of calculations. To quickly obtain accurate articulated torques, an analysis method for the articulated torque is presented for an electrically driven heavy-duty six-legged robot. First, the rearmost leg that experiences the maximum normal contact force is confirmed when the robot transits a slope. Based on the ant-type and crab-type tripod gaits, the formulas of classical mechanics and MATLAB software are employed to theoretically analyze the relevant static torques of the joints. With the changes in the joint angles for the abductor joint, hip joint, and knee joint, variable tendency charts and extreme curves are obtained for the static articulated torques. Meanwhile, the maximum static articulated torques and the corresponding poses of the robot are also obtained. According to the poses of the robot under the maximum static articulated torques, ADAMS software is used to carry out a static simulation analysis. Based on the relevant simulation curves of the articulated torques, the maximum static articulated torques are acquired. A comparative analysis of the maximum static articulated torques shows that the theoretical calculation values are higher than the static simulation values, and the maximum error value is approximately 10%. The proposed method lays a foundation for quickly determining accurate articulated torques to develop heavy-duty six-legged robots.     

五足步行机器人步态研究

将五足步行机规则步态分为奇异和非奇异两大类型,对步态各类数、负荷因子取值范围、稳定行走条件以及稳定裕度求算进行了分析,所得结论对于指导五足机的机构和实用步态设计有重要理论意义。     

四足、八足步行仿生机器人基本步态及时序研究

从步态和步态时序两方面对四足和八足仿生机器人能够采用的基本步态进行了研究，根据步行足的有荷系数分别对四足和八足步态进行了分类，并比较不同步态下的速度及稳定性，为步行机器人的合理驱动和控制提供了理论依据。     

六足步行机器人全方位步态的研究

研究六足步行机器人全方位行走步态,分析其静态稳定性;规划了典型直线行走步态和定点转弯步态,确定了直线行走步态最大跨步和定点转弯步态最大转角;进行了步态控制算法模拟仿真及实地步行实验,结果表明研究工作正确、有效。     

六足步行机器人仿生机制研究

从机械结构、运动模式和步态控制3个方面,对六足步行机器人的仿生机制进行了分析。提出一种灵活度评价函数,基于该函数对六足机器人的结构参数进行了优化;推导了步态模式与步行速度关系的数学表达;构建了分布式局部规则网络,可自适应地调整错乱的腿间相序,生成静态稳定的自由步态。仿真实验验证了上述仿生机制的有效性。     

Biped Robot with Triangle Configuration

A new biped robot with a triangle configuration is presented and it is a planar closed chain mechanism.The scalability of three sides of the triangle is realized by three actuated prismatic joints.The three vertexes of the triangle are centers of three passive revolute joints coincidently.The biped mechanism for straight walking is proposed and its walking principle and mobility are explained.The static stability and the height and span of one step are analyzed.Kinematic analysis is performed to plan the gaits of walking on an even floor and going upstairs.A prototype is developed and experiments are carried out to validate the straight walking gait.Two additional revolute joints are added to form a modified biped robot which can follow the instruction of turning around.The turning ability is verified by experiments.As a new member of biped robots,its triangle configuration is used to impart geometry knowledge.Because of its high stiffness,some potential applications are on the way.     

电驱动重载六足机器人关节转速分析方法

为合理匹配电驱动重载六足机器人关节的驱动装置和传动装置,提出一种快速、精确获得关节转速的方法。基于某一关节转动以实现机器人最大步行速度指标,建立该关节转角与机器人最大步行速度指标的数学关系式,研究螃蟹型三角步态下的髋关节和膝关节在最小摆角和最大摆角时的相应输出转速以及蚂蚁型三角步态下的跟关节输出转速,并获得跟关节转角和转速随髋、膝关节夹角的变化趋势。根据ADAMS软件和研制的机器人单腿与样机,进行关节转速的仿真验证和试验分析,分别获得机器人承载平台重心的速度曲线和关节伺服电动机脉冲数曲线。仿真和试验结果表明,机器人关节转速分析方法具有合理性和有效性,能够可靠地应用于重载多足机器人的研制。     

Gait Planning for a Quadruped Robot with One Faulty Actuator

Fault tolerance is essential for quadruped robots when they work in remote areas or hazardous environments. Many fault-tolerant gaits planning method proposed in the past decade constrained more degrees of freedom(DOFs) of a robot than necessary. Thus a novel method to realize the fault-tolerant walking is proposed. The mobility of the robot is analyzed first by using the screw theory. The result shows that the translation of the center of body(Co B) can be kept with one faulty actuator if the rotations of the body are controlled. Thus the DOFs of the robot body are divided into two parts: the translation of the Co B and the rotation of the body. The kinematic model of the whole robot is built, the algorithm is developed to actively control the body orientations at the velocity level so that the planned Co B trajectory can be realized in spite of the constraint of the faulty actuator. This gait has a similar generation sequence with the normal gait and can be applied to the robot at any position. Simulations and experiments of the fault-tolerant gait with one faulty actuator are carried out. The Co B errors and the body rotation angles are measured. Comparing to the traditional fault-tolerant gait they can be reduced by at least 50%. A fault-tolerant gait planning algorithm is presented, which not only realizes the walking of a quadruped robot with a faulty actuator, but also efficiently improves the walking performances by taking full advantage of the remaining operational actuators according to the results of the simulations and experiments.     

基于带反馈Hopf振荡器的六足机器人斜坡步态发生器设计

为了提高六足机器人斜坡运动的稳定性,基于三支撑足步态,分析六足机器人的斜坡运动,得到斜坡运动静态稳定裕度与躯体俯仰角的定性关系;研究带反馈Hopf振荡器的输出特性与收敛系数、反馈量之间的关系,并设计基于带反馈Hopf振荡器的单腿三关节信号和斜坡步态发生器模型;确定收敛系数的组合,并引入躯体俯仰角构造反馈信号,实现在只改变膝关节摆角而不影响步态其他特性的情况下提高六足机器人斜坡运动的稳定性;搭建Matlab-ADAMS联合仿真平台与实物样机进行验证。仿真表明：与Hopf模型相比,基于带反馈Hopf模型六足机器人上12°斜坡稳定裕度提高6.3%,下12°斜坡稳定裕度提高7.2%;试验表明：在12°斜坡上前进1 m时,基于Hopf模型的六足机器人向左偏移0.3 m,基于带反馈Hopf模型的六足机器人向左偏移0.05 m,稳定裕度显著提高。