Toward a human-like biped robot with compliant legs

Conventional models of bipedal walking generally assume rigid body structures, while elastic material properties seem to play an essential role in nature. On the basis of a novel theoretical model of bipedal walking, this paper investigates a model of biped robot which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is evaluated in simulation and a physical robotic platform by analyzing the kinematics and ground reaction force. The experimental results show that, with a proper leg design of passive dynamics and elasticity, an attractor state of human-like walking gait patterns can be achieved through extremely simple control without sensory feedback. The detailed analysis also explains how the dynamic human-like gait can contribute to adaptive biped walking.     

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.     

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.     

Experimental Study of Dynamic Bipedal Walking Based on the Principle of Parametric Excitation with Counterweights

This paper reports some interesting results from our experimental study of parametrically excited dynamic bipedal walking. We describe the details of the walking machine that has telescopic legs, semicircular feet, free hip joint and counterweights. The walker can sustain stable dynamic walking on level ground based on mechanical energy restoration in accordance with the principle of parametric excitation utilizing the effects of semicircular feet and counterweights. Results of numerical analysis on the effect of the counterweights on the gait efficiency are also described.     

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.      

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.     

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.     

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。     

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.     

The motion control of a statically stable biped robot on an unevenfloor

This work studies the motion control of a statically stable biped robot having seven degrees of freedom. Statically stable walking of the biped robot is realized by maintaining the center-of-gravity inside the convex region of the supporting foot and/or feet during both single-support and double-support phases. The main points of this work are framing the stability in an easy and correct way, the design of a bipedal statically stable walker, and walking on sloping surfaces and stairs.     

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.     

双足机器人在动态环境中步态规划研究

在双足机器人跨越迎面而来的动态障碍物的问题中,由于障碍物的高度,和速度是不可预测等因素,机器人的迈步步长和迈步高度决定了其能否实现成功跨越.介绍一种双足机器人步态规划方法,应用模糊Q学习算法对迈步高度进行学习,将迈步的起始点、落点和迈步高度作为特征点,利用三次样条对特征点进行插值得到摆动腿运动轨迹,最后通过摆动角间的几何关系得出各关节处摆动角的变化规律,控制机器人跨越动态障碍物.仿真结果表明,通过进行的步态规划,机器人可以成功跨越动态障碍物,并且各关节处的摆动角变化曲线平缓无畸变.     

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 framework for the control of stable aperiodic walking in underactuated planar bipeds

This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.     

Construction of a Gait Adaptation Model in Human Split-Belt Treadmill Walking Using a Two-Dimensional Biped Robot

A number of studies have measured kinematics, dynamics and oxygen uptake while a person walks on a treadmill. In particular, during walking on a split-belt treadmill, in which the left and right belts have different speeds, remarkable differences in kinematics are observed between normal subjects and subjects with cerebellar disease. In order to construct a gait adaptation model of such human split-belt treadmill walking, we proposed a simple control model and developed a new two-dimensional biped robot walk on a split-belt treadmill. We combined the conventional limit-cycle-based control consisting of joint PD control, cyclic motion trajectory planning and a stepping reflex with a newly proposed adjustment of P-gain at the hip joint of the stance leg. The data obtained in experiments on the robot (normal subject model and cerebellum disease subject model) have highly similar ratios and patterns to data obtained in experiments on normal subjects and subjects with cerebellar disease carried out by Bastian et al. We also showed that the P-gain at the hip joint of the stance leg was the control parameter of adaptation for symmetric gaits in split-belt walking and that P-gain adjustment corresponded to muscle stiffness adjustment by the cerebellum. Consequently, we successfully proposed a gait adaptation model for human split-belt treadmill walking, and confirmed the validity of our hypotheses and the proposed model using the biped robot.     

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。     

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.     

3D walking biped: optimal swing of the arms

A ballistic walking gait is designed for a 3D biped with two identical two-link legs, a torso, and two identical one-link arms. In the single support phase, the biped moves due to the existence of a momentum, produced mechanically, without applying active torques in the interlink joints. This biped is controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the seven interlink joints. Then an infinity of solutions exists to find the impulsive torques. An effort cost functional of these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, there is an optimal swinging amplitude of the arms. For this optimal motion of the arms, the cost functional is minimum.     

脉冲推力作用下半被动双足机器人的行走动力学分析

为了提高半被动双足机器人在水平地面上行走的稳定性,研究一种脉冲推力作用下半被动双足机器人的行走动力学行为.以最简单的特殊行走模型为动力学模型,采用支撑腿脚后跟脉冲推力作为双足机器人行走动力源.鉴于系统模型的高度非线性,将连续阶段的非线性微分方程线性化;利用角动量守恒和脉冲推力构造一个二维离散映射;采用离散映射的不动点及其特征值分析系统周期步态的存在性和稳定性;接着讨论系统的倍周期分岔.在理论分析的基础上,通过Matlab软件对半被动双足机器人的行走动力学进行仿真实验. 仿真结果表明,在水平地面上行走的半被动双足机器人具有稳定的周期-1步态和周期-2步态.