Adaptive splitbelt treadmill walking of a biped robot using nonlinear oscillators with phase resetting

To investigate the adaptability of a biped robot controlled by nonlinear oscillators with phase resetting based on central pattern generators, we examined the walking behavior of a biped robot on a splitbelt treadmill that has two parallel belts controlled independently. In an experiment, we demonstrated the dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. The robot produced stable walking on the splitbelt treadmill at various belt speeds without changing the control strategy and parameters, despite a large discrepancy between the belt speeds. This is due to modulation of the locomotor rhythm and its phase through the phase resetting mechanism, which induces the relative phase between leg movements to shift from antiphase, and causes the duty factors to be autonomously modulated depending on the speed discrepancy between the belts. Such shifts of the relative phase and modulations of the duty factors are observed during human splitbelt treadmill walking. Clarifying the mechanisms producing such adaptive splitbelt treadmill walking will lead to a better understanding of the phase resetting mechanism in the generation of adaptive locomotion in biological systems and consequently to a guiding principle for designing control systems for legged robots.     

An approach to analyzing biped locomotion dynamics and designing robot locomotion controls

An approach to analyzing biped locomotion problems is presented. This approach applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls. A robot model which has no knee joints or feet and is constrained to motion in the sagittal plane is chosen as a sufficiently simple model of a biped to illustrate the approach. A goal of the analysis is the design of a locomotion control for the robot which produces a walking gait having a velocity and stride length similar to those of a human walking gait. The principle feature of the approach is a much deeper understanding of the dynamics of biped locomotion than previous approaches have provided.     

正弦驱动与传感反馈结合的双足机器人仿生行走控制

提出了一种正弦驱动与传感反馈结合的双足机器人仿生行走控制方法．所有关节由正弦振荡器驱动, 较之相互耦合的神经元振荡器更加简单;控制参数具有明晰的物理意义,便于对运动模式进行调节．传感反馈表征 了机器人的运动状态,对于保证机器人的稳定行走起着至关重要的作用．将机器人碰地、碰膝等关键运动状态作为 相位反馈,对控制力矩进行相位重置,协调各关节动作,进而实现控制器、机器人、环境的耦合．同时,从节省能量 和仿生的角度,考虑了关节运动的被动特性,确定了各关节力矩的作用区间．仿真结果表明,该控制方法能实现机 器人稳定行走,并具有良好的能效性和自稳定性.     

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.

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。     

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.     

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.     

Central pattern generators based on Matsuoka oscillators for the locomotion of biped robots

Biologically inspired control approaches based on central pattern generators (CPGs) with neural oscillators have been drawing much attention for the purpose of generating rhythmic motion for biped robots with human-like locomotion. This article describes the design of a neural-oscillator-based gait-rhythm generator using a network of Matsuoka oscillators to generate a walking pattern for biped robots. This includes the proper consideration of the oscillator’s parameters, such as a time constant for the adaptation rate, coupling factors for mutual inhibitory connections, etc., to obtain a stable and desirable response from the network. The article examines the characteristics of a CPG network with six oscillators, and the effect of assigning symmetrical and asymmetrical coupling coefficients among oscillators within the network structure under different possible inhibitions and excitations. The kinematics and dynamics of a five-link biped robot have been modeled, and its joints are actuated through simulation by the torques output from the neural rhythm generator to generate the trajectories for hip, knee, and ankle joints. The parameters of the neural oscillators are tuned to achieve flexible trajectories. The CPG-based control strategy is implemented and tested through a simulation. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

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。     

基于GCIPM行走的步行机器人路径规划

介绍了利用重力补偿倒立摆方式（GCIPM）提高步行机器人行走的稳定性。该方法与以往利用线性倒立摆方式（IPM）控制的机器人相似,但是考虑了期望轨迹上机器人的迈步腿力。当基于IPM的路径规划应用到实际的步行机器人上,依据ZMP控制理论从预固定点移动时,被忽略的迈步腿力的变化在实际中使稳定性得不到保证。由于GCIPM考虑了迈步腿力的影响,仿真表明,应用GCIPM的步行机器人,稳定性得到优化提高。     

Learning CPG-based biped locomotion with a policy gradient method

In this paper, we propose a learning framework for CPG-based biped locomotion with a policy gradient method. We demonstrate that appropriate sensory feedback to adjust the rhythm of the CPG (Central Pattern Generator) can be learned using the proposed method within a few hundred trials in simulations. We investigate linear stability of a periodic orbit of the acquired walking pattern considering its approximated return map. Furthermore, we apply the controllers acquired in numerical simulations to our physical 5-link biped robot in order to empirically evaluate the robustness of walking in the real environment. Experimental results demonstrate that the robot was able to successfully walk using the acquired controllers even in the cases of an environmental change by placing a seesaw-like metal sheet on the ground and a parametric change of the robot dynamics with an additional weight on a shank, which was not modeled in the numerical simulations.     

Pseudo-passive dynamic walkers designed by coupled evolution of the controller and morphology

In this paper we investigated the morphology and controller of biped robots. We viewed them as design components that together can induce dynamically stable bipedal locomotion. We conducted coupled evolution of the morphology and controller of a biped robot, consisting of nine links and eight joints, actuated by oscillators without sensor feedback in three-dimensional simulation. As a result, both pseudo-passive dynamic walkers and active-control walkers emerged, but the pseudo-passive dynamic walkers showed more dynamic stability than the active-control walkers. This is because compliant components in morphology function as noise filters and passive oscillators. Analysis on this latter class of walkers revealed that this was achieved by two novel functions: self-stabilization and self-regulation. Because these functions were handled by the passive dynamics induced in the robot morphology, due to its compliance, we concluded that a computational trade-off between the controller and morphology occurs in these devices. Finally, we have concluded that appropriate compliance is a key to achieving dynamical stability during locomotion.     

基于深度强化学习的双足机器人斜坡步态控制方法

为提高准被动双足机器人斜坡步行稳定性, 本文提出了一种基于深度强化学习的准被动双足机器人步态控制方法. 通过分析准被动双足机器人的混合动力学模型与稳定行走过程, 建立了状态空间、动作空间、episode过程与奖励函数. 在利用基于DDPG改进的Ape-X DPG算法持续学习后, 准被动双足机器人能在较大斜坡范围内实现稳定行走. 仿真实验表明, Ape-X DPG无论是学习能力还是收敛速度均优于基于PER的DDPG. 同时, 相较于能量成型控制, 使用Ape-X DPG的准被动双足机器人步态收敛更迅速、步态收敛域更大, 证明Ape-X DPG可有效提高准被动双足机器人的步行稳定性.     

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.     

A closed-loop approach for tracking a humanoid robot using particle filtering and depth data

Humanoid robots introduce instabilities during biped march that complicate the process of estimating their position and orientation along time. Tracking humanoid robots may be useful not only in typical applications such as navigation, but in tasks that require benchmarking the multiple processes that involve registering measures about the performance of the humanoid during walking. Small robots represent an additional challenge due to their size and mechanic limitations which may generate unstable swinging while walking. This paper presents a strategy for the active localization of a humanoid robot in environments that are monitored by external devices. The problem is faced using a particle filter method over depth images captured by an RGB-D sensor in order to effectively track the position and orientation of the robot during its march. The tracking stage is coupled with a locomotion system controlling the stepping of the robot toward a given oriented target. We present an integral communication framework between the tracking and the locomotion control of the robot based on the robot operating system, which is capable of achieving real-time locomotion tasks using a NAO humanoid robot.     

仿人预测控制在双足机器人步行控制中的应用

基于零力矩点(ZMP)的预测控制是目前双足机器人步行控制中最先进的方法,但是预测控制需要比较精确的预测模型,在环境扰动导致模型失配时,预测控制的性能下降较快。为了解决这个问题,利用仿人智能控制对环境误差具有较强抑制的特点改进预测控制。探讨了在步行控制中引入仿人智能控制的必要性和仿人智能控制改进预测控制的可行性,并设计了仿人预测控制器。最后通过仿真实验验证了新的控制器对双足机器人步行控制的有效性。     

Adaptive walking pattern generation and balance control of the passenger-carrying biped robot,HUBO FX-1, for variable passenger weights

A passenger-carrying biped robot is a practical robot capable of carrying a passenger for both entertainment purposes and disabled transport by means of biped walking. In the walking controls of the biped walking robot, changes in the payload are not generally considered. However, in the case of a passenger-carrying biped robot, the range of possible payloads for passenger weight is relatively wide, from zero to approximately one hundred kgf. In the authors’ previous research pertaining to passenger-carrying biped robots, the robot was modeled using a specific passenger weight; hence, the control parameters were tuned for it and kept to be constant. However, the previous method’s weakness was a decrease in the walking performance and walking stability of the robot when the passenger’s weight was much heavier or lighter than the predefined passenger weight. Therefore, in this paper, the walking pattern generation and balance control methods are developed to adaptively cope with variable passenger weights. These methods are then experimentally verified to ensure that the walking performance could be preserved uniformly for a variation of passenger weights.     

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.     

Realization of a hydraulic actuated biped robot walking without double support phase

This paper introduced a new walking pattern generation method for biped robots without active roll joint at the ankle and described a simple walking pattern generation method for the robot without using ZMP (Zero Moment Point) information directly. Firstly, the paper introduced a hydraulic actuated biped robot with eight degrees of freedom, which had payload capacity. Secondly, the paper provided a dynamic balance control method in the lateral plane. Not as the inverted pendulum model, this control method was also available for biped robot without active roll joint at the ankle. Thirdly, in order to decrease the vibration, the paper tried to keep the robot walking with an approximate constant speed in the frontal direction. Finally, weight loading experiments in the MD.DAMS simulation environment and physical prototype empty load experiments were used to verify the effectiveness of the proposed walking pattern methods.