Trajectory optimization with GA and control for quadruped robots

This paper proposes an optimal galloping trajectory, which costs low energy and guarantees the stability of the quadruped robot. In the realization of fast galloping, the trajectory design is important. For a galloping trajectory, we propose an elliptic leg trajectory, which provides simplified locomotion to complex galloping motions of animals. However, the elliptic trajectory, as an imitation of animal galloping motion, does not guarantee stability and minimal energy consumption. We propose optimization based on energy and stability using a genetic algorithm, which provides a robust and globally optimized solution to this multi-body, highly nonlinear dynamic system. To evaluate and verify the effectiveness of the proposed trajectory, a series of computer simulations were carried out. This paper was recommended for publication in revised form by Associate Editor Doo Yong Lee Jong Hyeon Park received the B.S. degree in mechanical engineering from Seoul National University, Seoul, Korea, in 1981 and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, in 1983 and 1991, respectively. Since 1992, he has been with the School of Mechanical Engineering at Hanyang University, Seoul, Korea, where he is currently a professor. He was a KOSEF (Korea Science and Engineering Foundation)-JSPS (Japan Society for the Promotion of Science) Visiting Researcher with Waseda University, Tokyo, Japan, in 1999, and a KOSEF-CNR (Consiglio Nazionale delle Ricerche) Visiting Researcher with Scuola Superiore Sant’Anna, Pisa, Italy, in 2000, a Visiting Scholar with MIT, Cambridge, USA, in 2002–2003. He was also associated with Brooks Automation Inc., Chelmsford, MA, in 1991–1992 and 2001–2002. His research interests include biped robots, robot dynamics and control, haptics, and bio-robots. He is a member of the IEEE (Institute of Electrical and Electronics Engineers), KSME (Korea Society of Mechanical Engineers), ICROS (Institute of Control, Robotics and Systems), KROS (Korea Robotics Society), KSAE (Korean Society of Automotive Engineers), KSPE (Korean Society of Precision Engineering) and KSEE (Korean Society for Engineering Education).     

四足机器人腿部运动空间和足端运动轨迹研究

机器人的单腿的运动空间及足端点运动轨迹决定了所设计的机器人的应用范围。为了研究四足步行机器人摆动腿在一定参数条件下的运动空间大小及足端的运动轨迹,通过对机器人摆动腿正运动学方程,足端点轨迹在y、z轴上对时间的函数进行计算,并将计算结果运用MATLAB软件进行仿真,不仅直观地观测到机器人的运动情况,还得到所需的数据,且以图形的形式显示出来,达到了预期目的。     

Design and simulation for a hydraulic actuated quadruped robot

This paper describes the mechanical configuration of a quadruped robot firstly. Each of the four legs consists of three rotary joints. All joints of the robot are actuated by linear hydraulic servo cylinders. Then it deduces the forward and inverse kinematic equations for four legs with D-H transformation matrices. Furthermore, it gives a composite foot trajectory composed of cubic curve and straight line, which greatly reduces the velocity and acceleration fluctuations of the torso along forward and vertical directions. Finally, dynamics cosimulation is given with MSC.ADAMS and MATLAB. The results of co-simulation provide important guidance to mechanism design and parameters preference for the linear hydraulic servo cylinders.     

中枢模式发生器与足端轨迹的非线性映射

控制的仿生性和行走的稳定性是四足机器人步态研究中重要的两个方面。 为了提高四足机器人运动的稳定性,本文通 过 Hopf 振荡器搭建了 CPG 模型,分别实现了多种步态及步态之间的转换。 比较了基于 CPG 的步态控制方法和轨迹规划的步 态规划方法在行走上的优劣性。 为了同时利用 CPG 控制和轨迹规划的优点,提出采用神经网络将 CPG 控制曲线与足端轨迹 逆运动学获得的驱动曲线进行非线性映射,使得四足机器人在控制上具备仿生特性,在足端接触上具备零冲击特性。 仿真和实 验结果表明,采用 CPG 的步态生成方法和轨迹规划方法四足机器人的行走速度理论行走速度 80 mm/ s 相近,但采用 CPG 的步 态生成方法四足机器人侧向位移在±10 mm 以内且俯仰角在±1. 5°之间,而采用轨迹规划的控制方法四足机器人侧向位移在 ±35 mm 以内且俯仰角在±4°之间,可见两种控制方式对侧向偏移和俯仰运动的表现不一致。 通过实验测量可知,机器人采用 walk 步态行走速度为 18. 57 mm/ s,与理论行走速度 20 mm/ s 接近,步态转换后以 trot 步态行走,行走速度为 76. 15 mm/ s,与理 论行走速度 80 mm/ s 接近,少许误差可能是装配和行走过程打滑导致的。 测量其侧向偏移程度可知,其侧向的偏移量左侧在 15 mm 内,右侧在 25 mm 内,其侧向偏移量均在合适的范围内,证明所提算法的有效性。     

平面四足步行机器人结构设计

设计了一种平面四足步行机器人原理样机,用以验证一种用于平面复杂地貌的行走方式。该机器人由四个伸缩式步行足组成,末端带有弹性足端,可以在支撑杆的协助下沿着圆形模拟复杂地貌行走。该样机采用四个可以实现两维平面运动的步行足构成,用于验证平面步行的期望落地步行方法。利用DSPACE半平台对机器人足部运动轨迹进行实验,结果表明,该样机的设计完全合理。     

Energy efficiency analysis of quadruped robot with trot gait and combined cycloid foot trajectory

Quadruped robots consume a lot of energy, which is one of the factors restricting their application. Energy efficiency is one of the key evaluating indicators for walking robots. The relationship between energy and elastic elements of walking robots have been studied, but different walking gait patterns and contact status have important influences on locomotion energy efficiency, and the energy efficiency considering the foot-end trajectory has not been reported. Therefore, the energy consumption and energy efficiency of quadruped robot with trot gait and combined cycloid foot trajectory are studied. The forward and inverse kinematics of quadruped robot is derived. The combined cycloid function is proposed to generate horizontal and vertical foot trajectory respectively, which can ensure the acceleration curve of the foot-end smoother and more successive, and reduce the contact force between feet and environment. Because of the variable topology mechanism characteristic of quadruped robot, the leg state is divided into three different phases which are swing phase, transition phase and stance phase during one trot gait cycle. The non-continuous variable constraint between feet and environment of quadruped robot is studied. The dynamic model of quadruped robot is derived considering the variable topology mechanism characteristic, the periodic contact and elastic elements of the robot. The total energy consumption of walking robot during one gait cycle is analyzed based on the dynamic model. The specific resistance is used to evaluate energy efficiency of quadruped robot. The calculation results show the relationships between specific resistance and gait parameters, which can be used to determine the reasonable gait parameters.     

用于抗洪打桩的四足机器人结构设计

为解决抗洪抢险打桩中机构进入现场的问题,建立了一种四足机器人的结构设计方案。对四足机器人的结构进行了分析,建立了机架、腿、关节以及足的4部分组成结构,该机器人单腿采用三关节三自由度结构,机架与胯部、胯部与上臂、上臂与下臂分别采用3个转动副连接,并在结构设计的基础上对JQR100四足机器人进行了驱动方式设计以及逆运动学分析,为步态规划和运动学分析打下了基础。研究结果表明,JQR100四足机器人足底能够达到一定范围空间内的任意位置,机器人能够满足抗洪抢险进入现场和进行自由运动的要求。     

适应不同重力环境的仿壁虎机器人运动仿真

针对不同重力环境下仿壁虎机器人的运动稳定性、运动高效协调性等问题,基于四足机器人的步态规划现状和仿壁虎机器人自身特定的机械结构,设计了仿壁虎机器人在g、0、-g 3种环境下的足端轨迹和运动步态。在ADAMS仿真软件中研究了机器人的运动学和动力学特性,得到了仿壁虎机器人稳定爬行与脚掌黏附力、足端轨迹和运动步态的关系。探讨了仿真结果的合理性和局限性,为仿壁虎机器人在实际环境中的稳定运动奠定了理论基础。     

液压四足机器人机身扰动抑制及实验研究

针对液压四足机器人在运动过程中的机身扰动较大的问题,提出基于运动学和虚拟模型的液压四足机器人机身扰动抑制策略。分析机器人机身扰动产生的机理及其影响,建立四足机器人整机运动学方程,根据机器人实时姿态反馈抑制机身扰动。同时在机器人机身横滚和俯仰自由度上引入弹簧阻尼虚拟元件,通过调整虚拟力的大小控制机身姿态。面向机器人对角小跑步态,对机器人摆动相和支撑相进行足端轨迹规划。通过液压四足机器人平台进行实验验证,实验结果表明,该扰动抑制策略能够根据机器人的机身姿态调整关节角度,机器人机身起伏小,机器人实际运动轨迹与理论运动轨迹接近,验证了所提方法的有效性。     

基于螺旋理论的冗余液压驱动四足机器人运动学分析

四足机器人的各种研究大多基于四条腿弯曲方向一致展开的。对于液压驱动且具有冗余度的四足机器人,静止姿态下,其前面两条腿与后面两条腿成对称弯曲状。为了研究这种机器人单腿运动和躯体运动状态,文中建立了基于螺旋理论的液压驱动四足机器人运动学模型,包括给出了单腿串联运动学逆解和躯体并联运动学正解。然后根据机器人行走过程设计出后面两条腿的髋关节与膝关节摆幅角度,通过建立的运动学模型,得到前面两条腿的关节变量及躯体姿态。最后通过MATLAB数值仿真和ADAMS虚拟样机实验,对机器人在一种行走方案下的躯体运动姿态进行仿真对比,验证了所建运动学模型的可靠性。     

NOVEL FORMULATION OF STATIC STABILITY FOR A WALKING QUADRUPED ROBOT

By defining the static stable area for foot placement, a new approach to analysis of quadruped robot stability is presented. Unlike conventionally, the method avoids solving complicated direct kinematics of quadruped robot and shows the information on the robot stability and the selection of swing leg. Especially, the proposed algorithm can be used as real-time operation for on-line gait generation and control for quadruped robots. The effectiveness of the proposed approach is shown through a practical crawling experiment of the quadruped robot TITAN-VIII.     

A new approach for development of quadruped robot based on biological concepts

This paper proposes the design and development results of a new quadruped robot. The proposed new quadruped robot has a couple of advantages of flexible locomotion. The quadruped robot is designed and modeled based on a new concept that is the structure model with three segments of quadruped legs. New leg configuration with the simplified operation of four hip actuators is introduced. The posture of the new quadruped robot is more similar to the posture of dog than that of the previous quadruped robots. The objective of this paper is to develop a quadruped robot, which can walk and run in a trot gait with a simple PID controller. Numerical simulation and experimental results are shown to prove the locomotion performance of the proposed controller for the proposed quadruped robot.     

四足轮腿式移动机器人的步态分析及轨迹规划

针对外星复杂的地表环境,基于2-UPS/(S+SPR)R闭环并联机构,设计了一种四足轮腿式移动机器人。通过对比机器人在运动过程中的稳定裕度与重心调整量得到最优步态,利用ZMP法衡量了机器人在静步态下的稳定性,并用改进的复合摆线法规划了足端的运动轨迹。在整个运动过程中,机械腿运动平稳,速度、加速度变化较为平滑,不会出现对机械腿造成损坏的较强冲击;且在抬腿和着地瞬间,速度、加速度均为0,不会对机身产生冲击。分析结果表明,该四足轮腿式移动机器人运动灵活且平稳,适用于外太空的探测。     

Energy dissipation rate control and parallel equations solving method for planar spined quadruped bouncing robot

This paper continues our investigation into Energy dissipation rate control (EDRC) and Parallel equations solving method (PESM). Our previous works showed how EDRC enables us to provide stable walking or running gaits for legged robots via controlling robot’s loss of energy rate during Impact phases (IP). This is while PESM facilitates the trajectory designing process of the robot’s active joints during each Single support phase (SSP) by solving the robot’s inverse kinematic and inverse dynamic equations in parallel. Even though PESM is very powerful and suitable for both quadruped robot, and despite the under actuation problem at the ankle joint, and biped robots, despite the presence of Zero momentum point criteria (ZMP) at the ankle joint, still, this method is limited to robots just with three and five DoFs. Therefore, the main purpose hereis to show how it is possible to extend the application of PESL to a spined quadruped robot with four DoFs by employment of the Central pattern generator (CPG) controller units and finding a connection among CPG’s output, PESM and the robot’s foot placement. Besides, as EDRC is employed to realize a stable bouncing gait for the robot, a whole numerical study is performed on the robot’s impact dynamic equations to evaluate the effect of spine joint on the robot’s impact dynamics.

     

四足机器人改进型对角小跑步态研究

传统的四足机器人对角小跑步态一般在机体坐标系中进行规划,在实际应用中存在着摆动腿无法同时着地、机体翻转无法有效抑制等问题,这些都降低了机器人运动的稳定性和精确性。针对以上问题,提出了一种在世界坐标系下规划的改进型对角小跑步态方法,该方法通过浮动机体运动学对摆动相进行规划,在足端的雅可比矩阵中引入机体姿态相关项,从而保证了摆动腿能同时着地,同时在支撑相和摆动相之间增加了四腿同时着地的调整相,对机器人机体位姿进行调整。对比仿真和样机试验结果表明：与传统方法相比,所提方法能够使摆动腿同时着地并能连续调整机体位姿,使机器人获得更好的运动稳定性和更高的位移控制精度。     

单自由度腿部机构的四足机器人稳定性研究

以基于切比雪夫连杆腿部机构的四足机器人为原型,建立了其足端的运动轨迹方程,并推导出速度方程; 分别从静态及动态两种步态对单自由度四足机器人的稳定性进行研究,给出了各种步态下保持平衡行进的稳定判据; 并通过Adams仿真进行了验证。     

基于机体翻转的四足机器人翻越台阶过程的运动学分析

为了提高四足机器人的越障能力,提出一种基于机体翻转的台阶翻越方法。在台阶翻越过程中,可以将四足机器人等效为平面连杆机构。对一个完整的翻越过程进行了运动规划,将其划分为5个阶段;然后分别对每个阶段进行了运动学建模与仿真分析,得到机器人各关节角位移的变化曲线以及机体重心的位移曲线。最后讨论了机器人台阶翻越能力与几何参数之间的关系,分析结果表明,采用该方法研制的四足机器人具有较强的台阶翻越能力。从运动学角度验证了四足机器人翻转式翻越台阶的可行性,对足式机器人的越障方式进行了有益的探索,为进一步的研究提供了理论基础。     

四足爬行机器人步态分析与运动控制

为了实现液压作动的四足步行机器人的稳定行走,根据运动稳定裕量原则规划四足机器人的直行步态,保证三足支撑机体时稳定裕量为100 mm;针对液压缸运动加速度突变导致机体冲击振动的问题,提出了利用S型曲线作为各自由度的运动位移控制规律的方法。按照JQRI00型四足步行机器人原理样机的结构建立了虚拟样机模型,应用仿真软件对所设计步态进行了仿真,分析了步态的运动学、动力学特征和位移控制方法的运动特征;在四足步行机器人原理样机上进行了试验,并将试验与仿真结果进行了比较。研究结果表明,所设计的机器人步态可行,保证了机器人具有较好的行走稳定性;将S型曲线用于位移控制,消除了液压缸运动加速度的突变,进一步提高了机体运行的平稳性。     

四足步行机器人关节位姿和稳定性研究

四足机器人爬行控制的关键是关节位姿的确定、机器人稳定性的判断和摆动腿顺序的选择.提出了一种求解关节位姿驱动变量的有效方法,此方法能获得满意的四足机器人步行步态.通过定义立足点的静态稳定区域提出了一种机器人稳定性分析的新方法,该方法不仅避免了复杂的机器人正动力学求解问题,同时还可给出机器人稳定性和立足点稳定范围的信息.实际爬行实验验证了所提方法的有效性.     

基于ADAMS的新型四足爬行机器人设计及其步态研究

足式机器人具有极强的环境适应能力。传统的四足爬行机器人通常将机身设计为整体,机身连接4条具有3个自由度的腿部机构,这种结构控制较为复杂,基于创新性,将传统空间机构转化为平面机构,添加腰部自由度,这种结构自由度数更少,更易于控制,同时还具有传统四足爬行机器人的优点。