A Disturbance Rejection Measure for Limit Cycle Walkers: The Gait Sensitivity Norm

The construction of more capable bipedal robots highly depends on the ability to measure their performance. This performance is often measured in terms of speed or energy efficiency, but these properties are secondary to the robot's ability to prevent falling given the inevitable presence of disturbances, i.e., its disturbance rejection. Existing disturbance rejection measures (zero moment point, basin of attraction, Floquet multipliers) are unsatisfactory due to conservative assumptions, long computation times, or bad correlation to actual disturbance rejection. This paper introduces a new measure called the Gait Sensitivity Norm that combines a short calculation time with good correlation to actual disturbance rejection. It is especially suitable for implementation on limit cycle walkers, a class of bipeds that currently excels in terms of energy efficiency, but still has limited disturbance rejection capabilities. The paper contains an explanation of the Gait Sensitivity Norm and a validation of its value on a simple walking model as well as on a real bipedal robot. The disturbance rejection of the simple model is studied for variations of floor slope, foot radius, and hip spring stiffness. We show that the calculation speed is as fast as the standard Floquet multiplier analysis, while the actual disturbance rejection is correctly predicted with 93% correlation on average.     

基于主支撑腿运动优化的仿人机器人快速步态规划算法

提出一种基于主支撑腿运动优化的快速步态规划算法,利用快速动态步行的特点,规划ZMP(Zero Moment Point)适时地离开质心投影并始终停留在稳定的支撑区域内．规划过程中考虑了仿人机器人摆动足触地时的碰撞,整个步态产生于深度的优化过程．     

Adding an Upper Body to Passive Dynamic Walking Robots by Means of a Bisecting Hip Mechanism

Passive dynamic walking is a promising idea for the development of simple and efficient two-legged walking robots. One of the difficulties with this concept is the addition of a stable upper body; on the one hand, a passive swing leg motion must be possible, whereas on the other hand, the upper body (an inverted pendulum) must be stabilized via the stance leg. This paper presents a solution to the problem in the form of a bisecting hip mechanism. The mechanism is studied with a simulation model and a prototype based on the concept of passive dynamic walking. The successful walking results of the prototype show that the bisecting hip mechanism forms a powerful ingredient for stable, simple, and efficient bipeds     

Passivity-Based Control of Bipedal Locomotion

In this article, we have shown how to design energy-based and passivity-based control laws that exploit the existence of passive walking gaits to achieve walking on different ground slopes, to increase the size of the basin of attraction and robustness properties of stable limit cycles, and to regulate walking speed. Many of the results presented in this are the compass gait are equally applicable to bipeds with knees and a torso. Practical considerations such as actuator saturation, ground reaction forces, and ground friction need to be addressed. The problem of foot rotation introduces an underactuated phase into the walking gait, which greatly challenges the application of energy shaping ideas. For walking in 3D, finding purely passive limit cycles, which is the first step in applying our energy control results, may be difficult. It was shown how ideas of geometric reduction can be used to generate 3D stable gaits given only 2D passive limit cycles.     

Mechanical design of powered prosthetic leg and walking pattern generation based on motion capture data

In this paper, we describe the design procedure of an above-knee powered prosthetic leg and an algorithm to generate appropriate gait patterns that are synchronized with the movement of the user. The developed prosthetic leg has powered knee and ankle joints for transfemoral amputees, and its weight and dimensions were determined on the basis of human body data. In particular, two degrees of freedom (roll and pitch axes) were adopted in the ankle joint to achieve dynamic balance control on uneven ground, and passive toe joints using a crank-rocker mechanism and torsional springs were attached at the foot to increase the walking stability. In addition, we developed a walking pattern simulator that is able to test the walking patterns of the powered prosthetic leg in the air. By attaching two inertial sensors on both thighs of the user and measuring both thigh motions, the per cent of gait cycle is suitably calculated from the proposed algorithm, and smooth gait motions are generated according to the gait cycle percent. Finally, walking patterns of the powered prosthetic leg were successfully generated by synchronizing to the human gait, and the generated gaits were analyzed by comparing them to the human gait.     

How to keep from falling forward: elementary swing leg action for passive dynamic walkers

Stability control for walking bipeds has been considered a complex task. Even two-dimensional fore-aft stability in dynamic walking appears to be difficult to achieve. In this paper we prove the contrary, starting from the basic belief that in nature stability control must be the sum of a number of very simple rules. We study the global stability of the simplest walking model by determining the basin of attraction of the Poincare/spl acute/ map of this model. This shows that the walker, although stable, can only handle very small disturbances. It mostly falls, either forward or backward. We show that it is impossible for any form of swing leg control to solve backward falling. For the problem of forward falling, we devise a simple but very effective rule for swing leg action: "You will never fall forward if you put your swing leg fast enough in front of your stance leg. In order to prevent falling backward the next step, the swing leg shouldn't be too far in front." The effectiveness of this rule is demonstrated with our prototype "Mike.".     

变长度弹性伸缩腿双足机器人半被动起步行走仿人控制

传统双足机器人行走使用轨迹跟踪控制,而人类行走大部分时间处于被动状态.针对半被动变长度弹性伸缩腿双足机器人从静止状态开始起步行走的问题,提出了一种起步行走仿人控制方法.首先,使用串联弹性驱动双足弹簧负载倒立摆(B-SLIP)模型;然后,利用拉格朗日方法建立行走动力学方程,并利用模型的自稳定性在双支撑阶段采用能量误差比例...     

Robust pseudo virtual passive dynamic walking with control of swing-leg retraction

This paper proposes a simplified method of underactuated virtual passive dynamic walking without having any singularities in the control input, which is termed as the pseudo virtual passive dynamic walking (PVPDW), and analyzes the gait properties considering quasiconstraint on the impact posture. First, we introduce a planar underactuated biped model that added an upper body by means of a bisecting hip mechanism and formulate the method of PVPDW based on the concept of pseudo center of mass. Second, we introduce a control law for inhibiting swing-leg retraction and analyze the effect on the gait stability. The simulation results show that falling down as a 1-DOF rigid body dramatically increases the stable domain even though the hip angle at impact is not precisely kept constant. Finally, we discuss the mechanism from the energy-loss coefficient point of view.     

一种新的双足机器人模型设计与相关研究

针对双足机器人最简模型在行走过程中出现摆动腿足部擦地的问题,提出了一种通过摆动腿膝关节弯曲达到摆动腿缩短的新模型。当摆动腿开始摆动时,摆动腿膝关节弯曲锁定,摆动腿缩短;当摆动腿摆动到最大位置时,膝关节解锁,摆动腿伸直再锁定,此后摆动腿回摆,系统变为直腿模型。采用脚后跟冲击控制,在摆动腿落地前,拖后的支撑腿与地面接触处施加一指向髋关节的瞬时冲击力,冲击力可以减小摆动腿着地时能量的损耗,同时驱动被动机器人向前行走。设计了迭代学习控制算法,找到极限环与不动点,实现不同给定期望步长跟踪的冲击力的计算。仿真结果表明,迭代学习控制可以有效的实现不同期望步长的跟踪,可以很快的找到机器人系统的不动点,通过收敛的相平面,得到稳定的极限环,保证了机器人行走过程稳定。     

变长度柔性双足机器人行走控制及稳定性分析

针对传统双足机器人模型缺少脚质量和躯干的问题,提出考虑摆动腿动态及躯干影响的柔性双足机器人模型,并对其行走控制及稳定性进行研究。首先,建立系统的动力学模型并采用欧拉-拉格朗日法推导了系统的动力学方程;同时,在弹簧负载倒立摆（SLIP）模型的基础上添加刚性躯干、脚质量及采用变长度伸缩腿,充分考虑躯干及摆动腿动力学对机器人行走步态的影响;其次,设计基于变长度腿的反馈线性化控制器来跟踪目标轨迹,以及调节摆动腿和躯干的姿态;最后,利用Newton-Raphson迭代法和庞加莱映射分析机器人的不动点及轨道稳定性条件,并在理论分析的基础上进行仿真。仿真结果表明,所提控制器可以实现机器人的周期行走,对外界干扰具有良好的鲁棒性,且雅可比矩阵所有特征值的模均小于1,能形成稳定的极限环,证明系统是轨道稳定的。     

Demonstration and Analysis of Quadrupedal Passive Dynamic Walking

Animals, including human beings, can travel in a variety of environments adaptively. Legged locomotion makes this possible. However, legged locomotion is temporarily unstable and finding out the principle of walking is an important matter for optimum locomotion strategy or engineering applications. As one of the challenges, passive dynamic walking has been studied on this. Passive dynamic walking is a walking phenomenon in which a biped walking robot with no actuator walks down a gentle slope. The gait is very smooth (like a human) and much research has been conducted on this. Passive dynamic walking is mainly about bipedalism. Considering that there are more quadruped animals than bipeds and a four-legged robot is easier to control than a two-legged robot, quadrupedal passive dynamic walking must exist. Based on the above, we studied saggital plane quadrupedal passive dynamic walking simulation. However, it was not enough to attribute the result to the existence of quadrupedal passive dynamic walking. In this research, quadrupedal passive dynamic walking is experimentally demonstrated by the four-legged walking robot 'Quartet 4'. Furthermore, changing the type of body joint, slope angle, leg length and variety of gaits (characteristics in four-legged animals) was observed passively. Experimental data could not have enough walking time and could not change parameters continuously. Then, each gait was analyzed quantitatively by the experiment and three-dimensional simulation.     

Gait and foot trajectory planning for versatile motions of a six-legged robot

This article deals with the problem of planning and controlling a radially symmetric six-legged walker on an uneven terrain when a smooth time-varying body motion is required. The main difficulties lie on the planning of gaits and foot trajectories. As for the gaits, this article discusses the forward wave gait of a variable duty factor and a variable wave direction. With the commanded body motion, the maximum possible duty factor is computed using the speed limit of the leg swing motion. Guaranteeing this maximum duty factor contributes to obtain higher stability. We prove the “continuity” of this forward wave gait planning algorithm adds the versatility to gaits planned. The foot trajectory planning algorithm dynamically generates a smooth foot trajectory as a function of the instantaneous body motions by modifying standard leg motion templates. The robot can negotiate an uneven terrain by modifying a vertical leg motion by a signal of tactile sensors on the foot. The experiments prove that the robot can successfully track smooth curves with body rotations on an uneven terrain, and thus prove the robustness of the algorithms. © 1997 John Wiley & Sons, Inc.     

Kinematic Constraints on Fault-Tolerant Gaits for a Locked Joint Failure

Fault-tolerant gaits in legged locomotion are defined as gaits with which legged robots can continue their walking after a failure event has occurred to a leg of the robot. For planning an efficient fault-tolerant gait, kinematic constraints and remaining mobility of the failed leg should be closely examined with each other. This paper addresses the problem of kinematic constraints on fault-tolerant gaits. The considered failure is a locked joint failure which prevents a joint of a leg from moving and makes it locked in a known place. It is shown that for the existence of the conventional fault-tolerant gait for forward walking on even terrain, the configuration of the failed leg must be within a range of kinematic constraints. Then, for coping with failure situations where the existence condition is not satisfied, the conventional fault-tolerant gait is adopted by including the adjustment of the foot trajectory of the failed leg. The foot trajectory adjustment procedure is analytically derived to show that it can help the fault-tolerant gait avoid dead-lock resulting from the kinematic constraint. To demonstrate its effectiveness, the proposed method is applied to the fault-tolerant gait generation for a quadruped robot walking with the wave-crab gait before a locked joint failure.     

A brief review of dynamics and control of underactuated biped robots

Humans as bipeds enjoy certain advantages over other terrestrial systems, which motivate us to study and develop biped robots. Underactuated biped robots adopt the energy efficient gait of the biological counterparts and passive walkers. However, the control design for such robots is challenging due to lesser controllable joints, non-linear hybrid system dynamics and the goal of utilizing the natural dynamics. This paper summarizes various designs, models and control strategies used to enable stable walking and running for the underactuated biped robots. It gives a brief about how the mechanism of such bipeds evolved to incorporate the design variations which significantly improved the system performance. The few basic mathematical models which are used to simulate, analyze and predict the system dynamics and test control designs, are described, highlighting the difference in walking and running models. An introduction to the various stability criteria and control methods, successful in enabling stable walking for the robots on flat or uneven terrains, is provided. This paper gives a brief of the significant achievements in this field and ends with the highlights of the abilities inherent to humans but lacking in underactuated bipeds, and adopting or improving which should be the focus of the future research.     

一种基于多传感器的步态相位实时检测系统

对人体步态相位进行准确实时的判断是智能假肢等康复机器人控制的基础,提出并建立了一种实时状态相位检测系统.该系统包含了4只压力传感器和2只姿态传感器,能够准确地区分出平地行走时足跟着地、足放平、足跟离地、足尖离地、摆动弯曲以及摆动伸展等五种状态相位,实验表明:该系统能够适应不同测试者的不同步幅和步速,并能够应用在假肢的实时控制中.     

Individual muscle contributions to the swing phase of gait: An EMG-based forward dynamics modelling approach

Muscle activation patterns and kinematic conditions at the beginning of the swing phase of gait were used as input to a forward dynamics simulation of the swing leg. A neuromusculoskeletal model was used to account for the non-linearity between muscle excitation and muscle force outputs. Following model tuning a close agreement between simulated and measured swing phase kinematics was obtained. Simulation results suggest that swing leg muscles play an important role in controlling the motion of the swing leg during walking, and that the effect of individual muscles is not necessarily restricted to the joints they span or their basic anatomical classifications.     

The Relationships Between Length of Stride,Step Frequency,Time of Swing and Speed of Walking for Children and Adults

Fifty males and females between 1 and 35 years of age were studied during locomotion. During the first few months of walking the step frequency bears no apparent relationship to the speed of walking. A log-log regression equation describes the adult relationship better than a linear equation. A few adolescents were better described by a linear equation and either log-log or linear equations can be used for children.

The product of maximum step frequency and the square root of the stature is approximately constant after 5 years of age.

The time of swing initially shows a positive regression with the time for a complete cycle of one leg. The child abandons this pattern in favour of an approximately constant time of swing and by 4-5 years of age the negative linear regression of the adult appears. The time of swing is usually much less than half the natural period of either the whole leg about the hip or of the lower leg and foot about the knee. The effects of wearing shoes upon step frequency and time of swing were investigated.     

表面垂足刺激器的研究现状与趋势

足下垂是由腓总神经功能障碍引起踝关节无法背屈、行走时足趾拖地的症状。它不仅影响患者日常行走,还会使 其产生自卑心理。表面垂足刺激器将刺激电极贴附在腓总神经或者胫骨前肌上,使用传感器来侦测脚步动作,通过电刺 激使脚踝产生背曲屈及翻转动作,改善步行摆动期所发生的足下垂现象。本文阐述了表面垂足刺激器的工作原理及研究 进展,并对基于生物信号反馈的闭环足下垂刺激器的研究趋势进行了介绍。     

Position-based impedance control of a biped humanoid robot

This paper describes position-based impedance control for biped humanoid robot locomotion. The impedance parameters of the biped leg are adjusted in real-time according to the gait phase. In order to reduce the impact/contact forces generated between the contacting foot and the ground, the damping coefficient of the impedance of the landing foot is increased largely during the first half double support phase. In the last half double support phase, the walking pattern of the leg changed by the impedance control is returned to the desired walking pattern by using a polynomial. Also, the large stiffness of the landing leg is given to increase the momentum reduced by the viscosity of the landing leg in the first half single support phase. For the stability of the biped humanoid robot, a balance control that compensates for moments generated by the biped locomotion is employed during a whole walking cycle. For the confirmation of the impedance and balance control, we have developed a life-sized humanoid robot, WABIAN-RIII, which has 43 mechanical d.o.f. Through dynamic walking experiments, the validity of the proposed controls is verified.     

Hardware design and gait generation of humanoid soccer robot Stepper-3D

This paper presents the hardware design and gait generation of humanoid soccer robot Stepper-3D. Virtual Slope Walking, inspired by Passive Dynamic Walking, is introduced for gait generation. In Virtual Slope Walking, by actively extending the stance leg and shortening the swing leg, the robot walks on level ground as it walks down a virtual slope. In practical, Virtual Slope Walking is generated by connecting three key frames in the sagittal plane with sinusoids. Aiming for improving the walking stability, the parallel double crank mechanism are adopted in the leg structure. Experimental results show that Stepper-3D achieves a fast forward walking speed of 0.5 m/s and accomplishes omnidirectional walking. Stepper-3D performed fast and stable walking in the RoboCup 2008 Humanoid competitions.