Stability and control of dynamic walking for a five-link planar biped robot with feet

During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.     

Principle and method of speed control for dynamic walking biped robots

In this paper, the method of speed control for 3D biped robots is addressed. First, the primary principle of speed control by regulation of input energy is studied, the feature of which is to regulate the speed and the step length synchronically. The method of Poincaré mapping is used to prove the stability of speed control in the common range. Second, a method of speed control for an 18 DOFs bipedal 3D robot, which is characterized by the two-point-foot, is proposed. The method is developed on the basis of the 3D walking pattern proposed previously, with the new function of speed regulation being added in. The simulations show that the performances of regular walking, acceleration, and deceleration are effective and stable, and therefore verify the feasibility of the proposed method. Furthermore, some walking features, such as the walking efficiency and lateral control, are demonstrated.     

Neuro-fuzzy gait synthesis with reinforcement learning for a biped walking robot

 A reinforcement learning-based neuro-fuzzy gait synthesizer, which is based on the GARIC (Generalized Approximate Reasoning for Intelligent Control) architecture, is proposed for the problem of biped dynamic balance. We modify the GARIC architecture to enable it to generate the trunk trajectory in both sagittal and frontal plane. The proposed gait synthesizer is trained by reinforcement learning that uses a multi-valued scalar signal to evaluate the degrees of failure or success for the biped locomotion by means of the ZMP (Zero Moment Point). It can form the initial dynamic balancing gait from linguistic rules, which are obtained from human intuitive balancing knowledge and biomechanics studies, and accumulate dynamic balancing knowledge through reinforcement learning, and thus constantly improve its gait during walking. The feasibility of the proposed method is verified through a 5-link biped robot simulation.     

Passive dynamic turning in 3D biped locomotion: an extension to passive dynamic walking

Passive dynamic walking usually refers to a kind of walking where a biped walker is able to walk downhill, without any actuation or control, just due to the gravity. Although most of works done in this regard have concentrated on passive walking along a straight line, in this paper we extend this concept to a more general case of locomotion, i.e. turning or walking along curved path. We call the novel extension passive turning, and categorize it to two types of finite and infinite. We showed that the finite type is still applicable on a typical downhill or ramp, while the infinite type is only practical on a specific surface profile that we call it helical ramp. Furthermore, several stability and parameter analysis are also conducted to evaluate more aspects of this notion. We highlighted that surprisingly, the passive straight walking is actually a special case of passive turning, just with infinite radius of turn and less asymptotical stability. It should be noted that the present study is performed using a model of an arc-foot three-dimensional (3D) compass gait walker.     

仿人机器人动态步行控制综述

综述了仿人机器人动态步行的研究历史和研究现状。归纳了动态步行的特点,分析了动态步行稳定性判定方法,介绍了基于ZMP的姿态稳定判据和基于庞加莱映射（Poincaré Map）的步态稳定判据。总结了仿人机器人学习适应复杂地面环境步行的方法,概述了动态步行控制实现的典型解决方案,指出了动态步行控制中待解决的问题,并探讨了未来的发展方向。     

双足步行机器人能量成型控制

为了使双足被动行走机器人的行走步态符合仿生规律,且当路面坡度变化后,迅速进入新的稳定步态行走,提出了角度不变能量成型控制策略.研究了欠驱动双足机器人能量匹配条件和能量成型控制器的求解;由于动能相对于旋转变换不具有对称性,通过在能量成型控制中附加一个辅助控制量,实现角度不变控制.仿真结果表明,该算方法可实现仿生控制,既能扩大吸引域,又改善系统的鲁棒性.     

双足机器人动态步行实时步态生成

针对双足机器人动态步行生成关节运动轨迹复杂问题,提出了一种简单直观的实时步态生成方案。建立了平面五杆双足机器人动力学模型,通过模仿人类步行主要运动特征并根据双足机器人动态步行双腿姿态变化的要求,将动态步行复杂任务分解为顺序执行的四个过程,在关节空间相对坐标系下设计了躯干运动模式、摆动腿和支撑腿动作及步行速度调整模式,结合当前步行控制结果反馈实时产生稳定的关节运动轨迹。仿真实验验证了该方法的有效性,简单易实现。     

Sensory-based walking motion instruction for biped humanoid robot

This paper describes a sensory-based biped walking motion instruction strategy. Visual and auditory sensors are employed to generate walking patterns according to human orders and to memorize various complete walking patterns effectively and systematically. The motion of lower-limbs for locomotion is created by an online pattern generator based on the sensory information. At the same time, the motion of the trunk and the waist for stability is generated online by a balance control method. Combining these locomotive and balance motions, a complete walking pattern is hierarchically constructed and memorized on a database. The walking instruction is conducted through computer simulation, and its effectiveness is verified.     

Stability analysis and time-varying walking control for an under-actuated planar biped robot

This paper presents two walking controllers for a planar biped robot with unactuated point feet. The control is based on the tracking of reference motions expressed as a function of time. First, the reference motions are adapted at each step in order to create a hybrid zero dynamic (HZD) system. Next, the stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the HZD. When the controlled outputs are selected to be the actuated coordinates, most periodic walking gaits for this robot are unstable, that is, the eigenvalues of the linearized Poincaré map (ELPM) is larger than one. Therefore, two control strategies are explored to produce stable walking. The first strategy uses an event-based feedback controller to modify the ELPM and the second one is based on the choice of controlled outputs. The stability analysis show that, for the same robot and for the same reference trajectory, the stability of the walking (or ELPM) can be modified by some pertinent choices of controlled outputs. Moreover, by studying some walking characteristics of many stable cases, a necessary condition for stable walking is proposed. It is that the height of swing foot is nearly zero at the desired moment of impact. Based on this condition, the duration of the step is almost constant in presence of initial error, so a method for choosing controlled outputs for the second controller is given. By using this method, two stable domains for the controlled outputs selection are obtained.     

基于Fuzzy–CPG的双足机器人适应性行走控制

为提高双足机器人的环境适应性,本文提出了一种基于模糊控制与中枢模式发生器(CPG)的混合控制策略,称之为Fuzzy–CPG算法.高层控制中枢串联模糊控制系统,将环境反馈信息映射为行走步态信息和CPG幅值参数.低层控制中枢CPG根据高层输出命令产生节律性信号,作为机器人的关节控制信号.通过机器人运动,获取环境信息并反馈给高层控制中枢,产生下一步的运动命令.在坡度和凹凸程度可变的仿真环境中进行混合控制策略的实验验证,结果表明,本文提出的Fuzzy–CPG控制方法可以使机器人根据环境的变化产生适应的行走步态,提高了双足机器人的环境适应性行走能力.     

Experiments with nontraditional hybrid control technique of biped locomotion robots

By using the previously established zero-moment point theory and the semi-inverse approach [1–4] for solving the artificial gait synthesis based on the prescribed dynamics to part of the active mechanism, in this new approach to dynamic control of legged locomotion robots, the conventional control synthesis, based on complete dynamic robot model, is abandoned. The paper describes the simulation experiments of biped control with a hybrid approach that combines the traditional model-based and fuzzy logic-based control techniques. The combined method is developed by extending a model-based decentralized control scheme by fuzzy logic-based tuners for modifying parameters of joint servo controllers. The simulation experiments performed on a simplified two-legged mechanism demonstrate the suitability of fuzzy logic-based methods for improving the performance of the robot control system.     

伸缩腿双足机器人半被动行走控制研究

研究半被动伸缩腿双足机器人行走控制和周期解的全局稳定性问题.使用杆长可变的倒立摆机器人模型,以支撑腿的伸缩作为行走动力源,采用庞加莱映射方法分析了双足机器人行走的不动点及其稳定性.当脚与地面冲击时,假设两腿间的夹角保持为常数,设计了腿伸缩长度的支撑腿角度反馈控制率.证明了伸缩腿双足机器人行走过程不动点的全局稳定性.仿真结果表明,本文提出的腿伸缩长度反馈控制可以实现伸缩腿双足机器人在水平面上的稳定行走,并且周期步态对执行器干扰和支撑腿初始角速度干扰具有鲁棒性.     

Efference copies in neural control of dynamic biped walking

In the early 1950s, von Holst and Mittelstaedt proposed that motor commands copied within the central nervous system (efference copy) help to distinguish ‘reafference’ activity (afference activity due to self-generated motion) from ‘exafference’ activity (afference activity due to external stimulus). In addition, an efference copy can be also used to compare it with the actual sensory feedback in order to suppress self-generated sensations. Based on these biological findings, we conduct here two experimental studies on our biped “RunBot” where such principles together with neural forward models are applied to RunBot’s dynamic locomotion control. The main purpose of this article is to present the modular design of RunBot’s control architecture and discuss how the inherent dynamic properties of the different modules lead to the required signal processing. We believe that the experimental studies pursued here will sharpen our understanding of how the efference copies influence dynamic locomotion control to the benefit of modern neural control strategies in robots.     

双足机器人稳定行走的仿人预测控制研究

针对双足机器人的稳定行走,提出了一种新的仿人预测控制在线步行模式生成方法。把期望零力矩点（ZMP）分解成离线规划好的参考ZMP和实时变化的可变ZMP之和,通过预测控制和其逆系统共同作用对质心运动进行控制,从而生成具有自适应性的步行模式。但单一的预测控制系统对诸如矩形齿状扰动的可变ZMP的跟踪存在较大的误差,结合仿人智能控制对误差的强抑制能力,设计了与预测控制相结合的仿人预测控制系统。仿真实验验证对矩形齿状扰动的可变ZMP,仿人预测系统也能实现较好的跟踪。     

Central pattern generator parameter search for a biped walking robot using nonparametric estimation based Particle Swarm Optimization

A parameter search for a Central Pattern Generator (CPG) for biped walking is difficult because there is no methodology to set the parameters and the search space is broad. These characteristics of the parameter search result in numerous fitness evaluations. In this paper, nonparametric estimation based Particle Swarm Optimization (NEPSO) is suggested to effectively search the parameters of CPG. The NEPSO uses a concept experience repository to store a previous position and the fitness of particles in a PSO and estimated best position to accelerate a convergence speed. The proposed method is compared with PSO variants in numerical experiments and is tested in a three dimensional dynamic simulator for bipedal walking. The NEPSO effectively finds CPG parameters that produce a gait of a biped robot. Moreover, NEPSO has a fast convergence property which reduces the evaluation of fitness in a real environment. Recommended by Editorial Board member Euntai Kim under the direction of Editor Jae-Bok Song. Jeong-Jung Kim received the B.S. degree in Electronics and Information Engineering from Chonbuk National University in 2006 and the M.S. degree in Robotics from Korea Advanced Institute of Science and Technology in 2008. He is currently working toward a Ph.D. at the Korea Advanced Institute of Science and Technology. His research interests include biologically inspired robotics and machine learning. Jun-Woo Lee received the B.S. degree in Electronics, Electrical and Communication Engineering from Pusan National University in 2007. He is currently working toward an M.S. in the Korea Advanced Institute of Science and Technology. His research interests include swarm intelligence and machine learning. Ju-Jang Lee was born in Seoul, Korea, in 1948. He received the B.S. and M.S. degrees from Seoul National University, Seoul, Korea, in 1973 and 1977, respectively, and the Ph.D. degree in Electrical Engineering from the University of Wisconsin, in 1984. From 1977 to 1978, he was a Research Engineer at the Korean Electric Research and Testing Institute, Seoul. From 1978 to 1979, he was a Design and Processing Engineer at G. T. E. Automatic Electric Company, Waukesha, WI. For a brief period in 1983, he was the Project Engineer for the Research and Development Department of the Wisconsin Electric Power Company, Milwaukee. He joined the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, in 1984, where he is currently a Professor. In 1987, he was a Visiting Professor at the Robotics Laboratory of the Imperial College Science and Technology, London, U.K. From 1991 to 1992, he was a Visiting Scientist at the Robotics Department of Carnegie Mellon University, Pittsburgh, PA. His research interests are in the areas of intelligent control of mobile robots, service robotics for the disabled, space robotics, evolutionary computation, variable structure control, chaotic control systems, electronic control units for automobiles, and power system stabilizers. Dr. Lee is a member of the IEEE Robotics and Automation Society, the IEEE Evolutionary Computation Society, the IEEE Industrial Electronics Society, IEEK, KITE, and KISS. He is also a former President of ICROS in Korea and a Counselor of SICE in Japan. He is a Fellow of SICE and ICROS. He is an Associate Editor of IEEE Transactions on Industrial Electronics and IEEE Transactions on Industrial Informatics.     

Balance recovery control for biped robot based on reaction null space method

A biped walking robot should be able to keep balance even in the presence of disturbing forces. This paper presents a step strategy concept of biped walking robot that is stabilized by using reaction null space method. The called ＂step strategy＂ can be modeled by means of the reaction null space method that introduced earlier to tackle dynamic interaction problems of free-floating robots, or moving base robots in general. 6-DOF biped robot model simulations are used to confirm the validity.     

Balance recovery control for biped robot based on reaction null space method

A biped walking robot should be able to keep balance even in the presence of disturbing forces.This paper presents a step strategy concept of biped walking robot that is stabilized by using reaction null space method.The called "step strategy" can be modeled by means of the reaction null space method that introduced earlier to tackle dynamic interaction problems of free-floating robots,or moving base robots in general.6-DOF biped robot model simulations are used to confirm the validity.     

Adaptive behavior in turning of an oscillator-driven biped robot

This paper concentrates on a biped robot’s turning behavior that consists of straight and curved walking and the transition between these two patterns. We investigate how a robot achieves adaptive walking during such turning by focusing on rhythm control and propose a locomotion control system that generates robot motions by rhythmic signals from internal oscillators and modulates signal generation based on touch sensor signals. First, we verify that the robot attains limit cycles of straight and curved walking by numerical simulations and hardware experiments. Second, we examine the transition between these walking patterns based on the basin of attraction of the limit cycles in numerical simulations. Finally, we verify whether the robot actually accomplishes transition and turning by hardware experiments. This paper clarifies that the robot establishes such turning motions by adequate modulation of walking rhythm and phase through interactions between the dynamics of its mechanical system, oscillators, and environment.

Development of minimalist bipedal walking robot with flexible ankle and split-mass balancing systems

This paper presents a novel design of minimalist bipedal walking robot with flexible ankle and split-mass balancing systems.The proposed approach implements a novel strategy to achieve stable bipedal walk by decoupling the walking motion control from the sideway balancing control.This strategy allows the walking controller to execute the walking task independently while the sideway balancing controller continuously maintains the balance of the robot.The hip-mass carry approach and selected stages of walk implemented in the control strategy can minimize the efect of major hip mass of the robot on the stability of its walk.In addition,the developed smooth joint trajectory planning eliminates the impacts of feet during the landing.In this paper,the new design of mechanism for locomotion systems and balancing systems are introduced.An additional degree of freedom introduced at the ankle joint increases the sensitivity of the system and response time to the sideway disturbances.The efectiveness of the proposed strategy is experimentally tested on a bipedal robot prototype.The experimental results provide evidence that the proposed strategy is feasible and advantageous.     

Gait generation and control for biped robots with underactuation degree one

The paper develops a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. First, inspired by the controlled symmetries approach, a general result on gait generation on different slopes based on a periodic orbit on a specific slope is obtained. Second, the time-scaling control approach is integrated to reproduce geometrically same periodic orbits for biped robots with one degree of underactuation. The degree of underactuation is compensated by one degree-of-freedom in the temporal evolution that scales the original periodic orbit. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. Finally, the proposed approach is illustrated by two kinds of underactuated biped robots: one has a passive gait on a specific ground slope and the other does not have a natural passive gait.