Experimental studies on passive dynamic bipedal walking

Passive dynamic walking is a gait developed, partially or in whole, by the energy provided by gravity. The research on passive dynamic bipedal walking helps create an understanding of walking mechanics. Moreover, the experimental passive dynamic research provides a base to compare and validate computer simulation results. An improved kneed bipedal walking mechanism was designed and built to study the passive gait patterns. The first aim of this study is to determine the equivalency of testing a passive dynamic biped walker on a treadmill to testing on a ramp. Based on the small difference between the gait patterns measured on the two test platforms, testing on a treadmill was found equivalent to testing on a ramp. Gait measurements were then conducted on the treadmill to evaluate the effects of the treadmill inclination angle, mass distribution of the biped, and the length of flat feet on the gait pattern. Results show that most of these parameters had significant effects on the step length, step period and hip velocity of the passive walker. Our experimental results are also compared with previous experimental results.     

动态双足机器人的控制与优化研究进展

对动态双足机器人的可控周期步态的稳定性、鲁棒性和优化控制策略的国内外研究现状与发展趋势进行了探讨.首先,介绍动态双足机器人的动力学数学模型,进一步,提出动态双足机器人运动步态和控制系统原理;其次,讨论动态双足机器人可控周期步态稳定性现有的研究方法,分析这些方法中存在的缺点与不足;再次,研究动态双足机器人的可控周期步态优化控制策略,阐明各种策略的优缺点;最后,给出动态双足机器人研究领域的难点问题和未来工作,展望动态双足机器人可控周期步态与鲁棒稳定性及其应用的研究思路.     

Energy-Efficient and High-Speed Dynamic Biped Locomotion Based on Principle of Parametric Excitation

We clarified that the common necessary condition for generating a dynamic gait results from the requirement to restore mechanical energy through studies on passive dynamic walking mechanisms. This paper proposes a novel method of generating a dynamic gait that can be found in the mechanism of a swing inspired by the principle of parametric excitation using telescopic leg actuation. We first introduce a simple underactuated biped model with telescopic legs and semicircular feet and propose a law to control the telescopic leg motion. We found that a high-speed dynamic bipedal gait can easily be generated by only pumping the swing leg mass. We then conducted parametric studies by adjusting the control and physical parameters and determined how well the basic gait performed by introducing some performance indexes. Improvements in energy efficiency by using an elastic-element effect were also numerically investigated. Further, we theoretically proved that semicircular feet have a mechanism that decreases the energy dissipated by heel-strike collisions. We provide insights throughout this paper into how zero-moment-point-free robots can generate a novel biped gait.      

Hybrid-state driven autonomous control for planar bipedal locomotion

The focus of this paper is on the development of a human inspired autonomous control scheme for a planar bipedal robot in a hybrid dynamical framework to realize human-like walking projected onto sagittal plane. In addition, a unified modelling scheme is presented for the biped dynamics incorporating the effects of various locomotion constraints due to varying feet-ground contact states, unilateral ground contact force, contact friction cone, passive dynamics associated with floating base etc. along with a practical impact velocity map on heel strike event. The autonomous control synthesis is formulated as a two-level hierarchical control algorithm with a hybrid-state based supervisory control in outer level and an integrated set of constrained motion control primitives, called task level control, in inner level. The supervisory level control is designed based on a human inspired heuristic approach whereas the task level control is formulated as a quadratic optimization problem with linear constraints. The explicit analytic solution obtained in terms of joint acceleration and ground contact force is used in turn to generate the joint torque command based on inverse dynamics model of the biped. The proposed controller framework is named as Hybrid-state Driven Autonomous Control (HyDAC). Unlike many other bipedal control schemes, HyDAC does not require a preplanned trajectory or orbit in terms of joint variables for locomotion control. Moreover, it is built upon a set of basic motion control primitives similar to those in human walk which provides a transparent and easily adaptable structure for the controller. These features make HyDAC framework suitable for bipedal walk on terrain with step and slope discontinuities without a priori gait optimization. The stability and agility of the proposed control scheme are demonstrated through dynamic model simulation of a 12-link planar biped having similar size and mass properties of an adult sized human being restricted to sagittal plane. Simulation results show that the planar biped is able to walk for a speed range of 0.1–2 m/s on level terrain and for a ground slope range of $+/-$20 deg for 1 m/s speed.     

A Novel Method of Gait Synthesis for Bipedal Fast Locomotion

Common methods of gait generation of bipedal locomotion based on experimental results, can successfully synthesize biped joints’ profiles for a simple walking. However, most of these methods lack sufficient physical backgrounds which can cause major problems for bipeds when performing fast locomotion such as running and jumping. In order to develop a more accurate gait generation method, a thorough study of human running and jumping seems to be necessary. Most biomechanics researchers observed that human dynamics, during fast locomotion, can be modeled by a simple spring loaded inverted pendulum system. Considering this observation, a simple approach for bipedal gait generation in fast locomotion is introduced in this paper. This approach applies a nonlinear control method to synchronize the biped link-segmental dynamics with the spring-mass dynamics. This is done such that while the biped center of mass follows the trajectory of the mass-spring model, the whole biped performs the desired running/jumping process. A computer simulation is done on a three-link under-actuated biped model in order to obtain the robot joints’ profiles which ensure repeatable hopping. The initial results are found to be satisfactory, and improvements are currently underway to explore and enhance the capabilities of the proposed method.     

基于deep Q-network双足机器人非平整地面行走稳定性控制方法

针对双足机器人在非平整地面行走时容易失去运动稳定性的问题,提出一种基于一种基于价值的深度强化学习算法DQN（Deep Q-Network）的步态控制方法。首先通过机器人步态规划得到针对平整地面环境的离线步态,然后将双足机器人视为一个智能体,建立机器人环境空间、状态空间、动作空间及奖惩机制,该过程与传统控制方法相比无需复杂的动力学建模过程,最后经过多回合训练使双足机器人学会在不平整地面进行姿态调整,保证行走稳定性。在V-Rep仿真环境中进行了算法验证,双足机器人在非平整地面行走过程中,通过DQN步态调整学习算法,姿态角度波动范围在3°以内,结果表明双足机器人行走稳定性得到明显改善,实现了机器人的姿态调整行为学习,证明了该方法的有效性。     

Efficiency and Optimality of Two-Period Limit Cycle Walking

This paper investigates the efficiency of a two-period gait from the kinetic energy viewpoint. First, we formulate a steady two-period gait for a compass-like bipedal robot by using a simple recurrence formula for the kinetic energy of an asymmetric rimless wheel. Then, we theoretically show that, in the case where the mean value of the hip angle is constant, the generated two-period steady gait is less efficient than a one-period symmetric gait in terms of kinetic energy. We also show that the symmetric gait is not always optimal from another viewpoint. We then extend the analysis to biped walking and investigate the validity of the derived method through numerical simulations of virtual passive dynamic walking.     

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain.     

双足机器人自然ZMP轨迹生成方法研究

为了实现双足机器人类人行走,提出了一种基于自然ZMP轨迹的双足机器人步行模式生成方法。在单腿支撑相,根据基于三维线性倒立摆模型,在设定从脚跟到脚趾移动的自然ZMP轨迹后,得到质心轨迹方程;在双腿支撑相采用线性摆模型生成质心轨迹方程。同时给出了在统一坐标系中的多步规划质心轨迹方程。在RoboCup 3D仿真平台实现了采用自然ZMP轨迹的双足机器人类人稳定步行,实验和竞赛结果都验证了该方法的有效性。     

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...     

可侧向摆动的欠驱动双足机器人

为解决机器人的侧向平衡问题,同时为使机器人的行走空间由二维扩展到三维,确立了可以侧向周期稳定偏转的有弹性脚的欠驱动步行机器人模型。根据混合动力系统的特点,建立了侧向摆动方程及脚碰撞地面的方程,并利用数值仿真得到了不同初始状态下的稳定极限环。根据运动状态分析,找到了弹性脚的欠驱动步行机器人所允许的侧向偏转范围。施加基于能量的控制可以消除摆动过程中出现的干扰,使欠驱动步行机器人回归到稳定状态,稳定的侧向摆动保证了欠驱动步行机器人的稳定行走。     

Knee and torso kinematics in generation of optimum gait pattern based on human-like motion for a seven-link biped robot

Multibody System Dynamics - Gait pattern affects the quality of a walking robot. In this paper, an optimum human-like gait generation method is proposed for a seven-link biped robot. This method...     

Generating human-like soccer primitives from human data

Recently, interest in analysis and generation of human and human-like motion has increased in various areas. In robotics, in order to operate a humanoid robot, it is necessary to generate motions that have strictly dynamic consistency. Furthermore, human-like motion for robots will bring advantages such as energy optimization.This paper presents a mechanism to generate two human-like motions, walking and kicking, for a biped robot using a simple model based on observation and analysis of human motion. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like motions. The approach presented here rests on the principle that in most biological motor learning scenarios some form of optimization with respect to a physical criterion is taking place. In a similar way, the equations of motion for the humanoid robot systems are formulated in such a way that the resulting optimization problems can be solved reliably and efficiently.The simulation results show that faster and more accurate searching can be achieved to generate an efficient human-like gait. Comparison is made with methods that do not include observation of human gait. The gait has been successfully used to control Robo-Erectus, a soccer-playing humanoid robot, which is one of the foremost leading soccer-playing humanoid robots in the RoboCup Humanoid League.     

半被动双足机器人的准开环控制

目前的被动行走机器人还只能完成单一的步态,且非常容易摔倒,为此对半被动双足机器人的稳定行走控制问题进行了研究．通过结合被动行走和主动控制两种原理的优点,提出了一种准开环的行走控制方法．通过检测安装在机器人足底和髌骨处的接触开关信号,在髋关节处施加一个间断的、微小的开环振荡力矩,进而实现高效的稳定步行．仿真结果表明,当控制参数在较大范围内变化时,双足机器人仍可实现稳定行走,且步行能耗特性与人类相似;通过调节振荡力矩的参数,机器人可实现稳定的行走模式转换．     

Level-ground walking for a bipedal robot with a torso via hip series elastic actuators and its gait bifurcation control

Recent studies have shown that a bipedal robot with a torso supported by springs on the hip can have a stable passive gait on a slope, while such a robot walking on level ground is a new challenge and has rarely been studied. This research adds actuators in series with the springs to form series elastic actuators on the hip and applies a state machine as controller to achieve stable walking on level ground. During walking, hip series elastic actuators support the torso from the legs as well as complement the energy to the system via elastic potential energy. The state machine uses the landing impact of the swing leg and the actuation durations as events to make the robot switch between successive active and passive walking processes. Because this simple scheme makes full use of the dynamics of the robot, it can lead to an efficient and natural gait. By means of numerical simulation, in addition to the stable period-1 gait, we found a variety of gait bifurcation phenomena, including the period-doubling bifurcation, the Neimark–Sacker bifurcation, the Neimark–Sacker-2 bifurcation, the period-X bifurcation, and the Neimark–Sacker-X bifurcation, among which many types have never been reported in previous studies. We also show that the unstable period-1 gait embedded in the bifurcation gait can be stabilized by applying the Ott–Grebogi–Yorke method. Not only can the gait bifurcation be suppressed, but also higher gait performance can be achieved.     

Two-level control strategy of an eight link biped walking model

This paper presents an adaptive two-level control strategy for a biped walking model and demonstrates its performance in a wide range of walking modes with considerably diverse model and control parameter settings. Proposed control strategy inherits a push off that resembles considerably to forceful extension of the trailing leg during push off in human locomotion and represents a very important source of forward propulsion. Extensive simulations have shown that adjustments in the push off related parameter on higher between-step control level after each step enable evolution of various walking modes of the biped walker at selected walking speeds and distinctive gait patterns. It also allows us to investigate the changes in gait kinematics and kinetics of the biped walking model due to changes in gait velocity, torso inclination and propulsion distribution profiles.     

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.     

Modeling, stability and control of biped robots—a general framework

The focus of this survey is the modeling and control of bipedal locomotion systems. More specifically, we seek to review the developments in the field within the framework of stability and control of systems subject to unilateral constraints. We place particular emphasis on three main issues that, in our view, form the underlying theory in the study of bipedal locomotion systems. Impact of the lower limbs with the walking surface and its effect on the walking dynamics was considered first. The key issue of multiple impacts is reviewed in detail. Next, we consider the dynamic stability of bipedal gait. We review the use of discrete maps in studying the stability of the closed orbits that represent the dynamics of a biped, which can be characterized as a hybrid system. Last, we consider the control schemes that have been used in regulating the motion of bipedal systems. We present an overview of the existing work and seek to identify the needed future developments. Due to the very large number of publications in the field, we made the choice to mainly focus on journal papers.     

欠驱动两足步行机器人研究现状

针对欠驱动两足步行机器人的研究现状与发展趋势进行了探讨。首先,总结了被动行走和踝关节欠驱动两足机器人的研究现状,介绍了欠驱动两足步行机器人的基本研究方法,包括问题描述、步态规划、运动控制和稳定性判定等,并对欠驱动两足机器人需要进一步研究的问题和发展方向进行深入研究,最终目标是将欠驱动控制策略应用于两足步行机器人的行走过程控制,以提高其运动性能。     

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.