Stabilization of bipedal walking based on compliance control

The embodiment of physical compliance in humanoid robots, inspired by biology, improves the robustness of locomotion in unknown environments. The mechanical implementation using elastic materials demands a further combination together with controlled compliance to make the intrinsic compliance more effective. We hereby present an active compliance control to stabilize the humanoid robots for standing and walking tasks. Our actively controlled compliance is achieved via admittance control using closed-loop feedback of the six axis force/torque sensors in the feet. The modeling and theoretical formulation are presented, followed by the simulation study. Further, the control algorithms were validated on a real humanoid robot COMAN with inherent compliance. A series of experimental comparisons were studied, including standing balancing against impacts, straight walking, and omni-directional walking, to demonstrate the necessity and the effectiveness of applying controlled compliance on the basis of physical elasticity to enhance compliant foot-ground interaction for the successful locomotion. All data from simulations and experiments related with the proposed controller and the performance are presented, analyzed, and discussed.     

Real-time continuous ZMP pattern generation of a humanoid robot using an analytic method based on capture point

This paper introduces an analytic method to generate a continuous ZMP pattern based on a capture point (CP). When a target CP is decided in real-time, the pattern generator makes the CP, ZMP, which it is within convex hull of the supporting feet area, and CoM patterns without discontinuity by closed-form solutions for a single step. Therefore, the proposed pattern generation method does not need a ZMP pattern modification, numerical iterations, and future ZMPs. The method is employed to treat applications such as step length change while walking and push recovery during walking in place. Furthermore, since compliant characteristics such as body oscillation appear in the humanoid robot, we introduce a system model, a double inverted pendulum model with flexible joints for the model-based control. Finally, the real-time walking pattern generation method and the walking control scheme are verified by experiments with the humanoid robot HUBO2.     

Walking in the resonance with the COMAN robot with trajectories based on human kinematic motion primitives (kMPs)

Research in humanoid robotics aims to develop autonomous systems that are able to assist humans in the performance of everyday tasks. Part of the robotics community claims that the best solution to guarantee the maximum adaptability of robots to the majority of human tasks is mimicry. Based on this premise both the structure of the human body and human behavior have been the focus of studies, with the aim of imitating and reproducing on robotic systems the results of millennia of human evolution. The research presented in this paper aims (i) at transferring the features of human locomotion to the COmpliant huMANoid (COMAN) robot, by means of kinematic motion primitives (kMPs) extracted from human subjects, and (ii) at improving the energetic performance of the walk of COMAN by exploiting its intrinsic compliance: it will be shown that, when the robot is walking at a gait frequency that is close to one of the main resonance frequencies of the mechanism, the springs contribute to tracking the human-like kMPs-based trajectories imposed, providing at the right time about 15 % of the energy required for locomotion, and that was previously stored.     

Multi-physics modelling of a compliant humanoid robot

We present a multibody simulator being used for compliant humanoid robot modelling and report our reasoning for choosing the settings of the simulator’s key features. First, we provide a study on how the numerical integration speed and accuracy depend on the coordinate representation of the multibody system. This choice is particularly critical for mechanisms with long serial chains (e.g. legs and arms). Our second contribution is a full electromechanical model of the inner dynamics of the compliant actuators embedded in the COMAN robot, since joints’ compliance is needed for the robot safety and energy efficiency. Third, we discuss the different approaches for modelling contacts and selecting an appropriate contact library. The recommended solution is to couple our simulator with an open-source contact library offering both accurate and fast contact modelling. The simulator performances are assessed by two different tasks involving contacts: a bimanual manipulation task and a squatting tasks. The former shows reliability of the simulator. For the latter, we report a comparison between the robot behaviour as predicted by our simulation environment, and the real one.     

A reflexive neural network for dynamic biped walking control

Biped walking remains a difficult problem, and robot models can greatly facilitate our understanding of the underlying biomechanical principles as well as their neuronal control. The goal of this study is to specifically demonstrate that stable biped walking can be achieved by combining the physical properties of the walking robot with a small, reflex-based neuronal network governed mainly by local sensor signals. Building on earlier work (Taga, 1995; Cruse, Kindermann, Schumm, Dean, & Schmitz, 1998), this study shows that human-like gaits emerge without specific position or trajectory control and that the walker is able to compensate small disturbances through its own dynamical properties. The reflexive controller used here has the following characteristics, which are different from earlier approaches: (1) Control is mainly local. Hence, it uses only two signals (anterior extreme angle and ground contact), which operate at the interjoint level. All other signals operate only at single joints. (2) Neither position control nor trajectory tracking control is used. Instead, the approximate nature of the local reflexes on each joint allows the robot mechanics itself (e.g., its passive dynamics) to contribute substantially to the overall gait trajectory computation. (3) The motor control scheme used in the local reflexes of our robot is more straightforward and has more biological plausibility than that of other robots, because the outputs of the motor neurons in our reflexive controller are directly driving the motors of the joints rather than working as references for position or velocity control. As a consequence, the neural controller and the robot mechanics are closely coupled as a neuromechanical system, and this study emphasizes that dynamically stable biped walking gaits emerge from the coupling between neural computation and physical computation. This is demonstrated by different walking experiments using a real robot as well as by a Poincaré map analysis applied on a model of the robot in order to assess its stability.     

基于模型预测—中枢模式发生器的六足机器人轨迹跟踪控制

为了模仿动物卓越的运动能力和环境适应能力,提出了六足仿生机器人的轨迹跟踪控制方法。首先建立了机器人的运动学模型,接着通过转向参数将机器人的速度和角速度与中枢模式发生器（CPG）参数结合起来,设计了转换函数。然后通过转换函数将模型预测控制器和CPG网络结合起来,提出了基于CPG的模型预测控制器（MPC-CPG）,并证明了其稳定性。最后对机器人跟踪圆周轨迹和直线轨迹进行了仿真和实验。实验表明,在有初始误差的条件下,机器人在MPC-CPG控制器的作用下能够快速地消除位置误差和航向角误差,跟踪上参考轨迹。轨迹跟踪的位置误差始终保持在-0.1～0.1 m,航向角误差保持在-27?～20?。在MPC-CPG控制器的作用下,机器人不仅具有较高的轨迹跟踪精度,同时还表现出良好的运动平滑性和协调性,进一步验证了所提出的MPC-CPG控制器的有效性。     

Control of a robotic orthosis for gait rehabilitation

Robot assisted gait training may help in producing rapid improvements in functional gait parameters. This paper presents new experimental results with an intrinsically compliant robotic gait training orthosis. The newly developed robotic orthosis has 6 degrees of freedom (DOFs). A trajectory tracking controller based on the boundary layer augmented sliding control (BASMC) law was implemented to guide the subject’s limbs on physiological gait trajectories. The compliance of the robotic orthosis sagittal plane hip and knee joints was also controlled, independently of the trajectory tracking control. The robotic orthosis and the control scheme were evaluated on three neurologically intact subjects walking on a treadmill. A maximum trajectory tracking error of 10° was recorded at the hip and knee sagittal plane joints. The results showed that subjects can walk in the robotic orthosis with comfort and the BASMC law was able to guide the subject’s limbs on reference physiological trajectories.     

矢量场逐次逼近的康复机器人柔顺交互控制

为了实现康复机器人的主动柔顺交互,提出了一种基于矢量场逐次逼近的控制模型;设计了矢量场逐次逼近系统,可输出机器人关节期望位移,该输出能与输入的扭矩、表面肌电及脑电等信号在振幅、频率和相位上保持同步,且通过调节遗忘因子参数值,可改变主动柔顺交互的积极性;利用自行设计的穿着型下肢康复机器人样机进行柔顺辅助实验,以验证所提出控制模型的有效性;通过FFT（Fast Fourier transformation）频谱对机器人关节扭矩的组成成分进行了分析,并采用基于最小二乘法的参数辨识方法实施了重力补偿,以便康复机器人实时控制.实验结果表明,该控制模型对于实现康复机器人与人之间的柔顺交互是有效的.     

Adaptive Task-Space Control of Flexible-Joint Manipulators

This paper considers the motion control and compliance control problemsfor uncertain rigid-link, flexible-joint manipulators, and presents newadaptive task-space controllers as solutions to these problems. The motioncontrol strategy is simple and computationally efficient, requires littleinformation concerning either the manipulator or actuator/transmissionmodels, and ensures uniform boundedness of all signals and arbitrarilyaccurate task-space trajectory tracking. The proposed compliant motioncontrollers include an adaptive impedance control scheme, which isappropriate for tasks in which the dynamic character of theend-effector/environment interaction must be controlled, and an adaptiveposition/force controller, which is useful for those applications thatrequire independent control of end-effector position and contact force. Thecompliance control strategies retain the simplicity and model independenceof the trajectory tracking scheme upon which they are based, and are shownto ensure uniform boundedness of all signals and arbitrarily accuraterealization of the given compliance control objectives. The capabilities ofthe proposed control strategies are illustrated through computer simulationswith a robot manipulator possessing very flexible joints.     

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.     

Overview of the Lucy Project: Dynamic Stabilization of a Biped Powered by Pneumatic Artificial Muscles

This paper gives an overview of the Lucy project. What is special is that the biped is not actuated with the classical electrical drives, but with pleated pneumatic artificial muscles. In an antagonistic setup of such muscles both the torque and the compliance are controllable. From human walking there is evidence that joint compliance plays an important role in energy-efficient walking and running. To be able to walk at different walking speeds and step lengths, a trajectory generator and joint trajectory tracking controller are combined. The first generates dynamically stable trajectories based on the objective locomotion parameters which can be changed from step to step. The joint trajectory tracking unit controls the pressure inside the muscles so the desired motion is followed. It is based on a computed torque model and takes the torque–angle relation of the antagonistic muscle setup into account. With this strategy the robot is able to walk at a speed up to 0.15 m/s. A compliance controller is developed to reduce the energy consumption by combining active trajectory control with the exploitation of the natural dynamics. A mathematical formulation was developed to find an optimal compliance setting depending on the desired trajectory and physical properties of the system. This strategy is experimentally evaluated on a single pendulum structure and not implemented on the real robot because the walking speed of the robot is currently too slow. At the end a discussion is given about the pros and cons of building a pneumatic biped, and the control architecture used.     

Guaranteeing prescribed performance and contact maintenance via an approximation free robot force/position controller

In this paper, we consider the problem of force/position tracking for a robot with revolute joints in compliant contact with a kinematically known planar surface. A novel controller is designed capable of guaranteeing, for an a priori known nonsingular initial robot condition, (i) certain predefined minimum speed of response, maximum steady state error as well as overshoot concerning the force/position tracking errors, (ii) contact maintenance and (iii) bounded closed loop signals. No information regarding either the robot dynamic model or the force deformation model is required and no approximation structures are utilized to estimate them. As the tracking performance is a priori guaranteed irrespectively of the control gains selection, the only concern is to adopt those values that lead to reasonable input torques. Finally, a comparative simulation study on a 6-DOF robot illustrates the performance of the proposed controller.     

Gait planning for quadruped robot based on dynamic stability: landing accordance ratio

In this article, the method for increasing dynamic stability of quadruped robot is proposed. Previous researches on dynamic walking of quadruped robots have used only walking pattern called central pattern generator (CPG). In this research, different from walking generation with only CPG, a instinctive stability measure called landing accordance ratio, is proposed and used for increasing dynamic stability. In addition, dynamic balance control and control to adjust walking trajectory for increasing dynamic stability measure is also proposed. Proposed methods are verified with dynamic simulation and a large number of experiments with quadruped robot platform.     

一种基于迭代的质心逆运算的方法

通过已知质心精确反解计算仿人机器人各关节的角度是一个经常遇到的问题。在双足行走,平衡控制等领域都很常见。但对于自由度高的仿人机器人系统,质心逆运算比较困难,尤其在双足支撑情况下,问题变为一个多自由度的并联机构,此时需要额外的约束和限制条件,使得计算非常复杂。本文基于Levenberg-Marquardt算法来解决复杂关节的逆解问题,研究在给定踝关节的情况下,用假定质心固定身体上的简化模型来使得真实质心逼近目标点,然后通过重复逼近缩小误差。我们通过NAO仿人机器人模型上的模拟验证了该算法实现了较高的准确性和计算效率。     

Real-time compliance control of an assistive joint using QNX operating system

An assistive robot is a novel service robot, playing an important role in the society. For instance, it can amplify human power not only for the elderly and disabled to recover/rehabilitate their lost/impaired musculoskeletal functions but also for healthy people to perform tasks requiring large forces. Consequently, it is required to consider both accurate position control and human safety, which is the compliance. This paper deals with the robot control compliance problem based on the QNX real-time operating system. Firstly, the mechanical structure of a compliant joint on the assistive robot is designed using Solidworks. Then the parameters of the assistive robot system are identified. The software of robot control includes data acquisition and processing, and control to meet the compliance requirement of the joint control. Finally, a Hogan impedance control experiment is carried out. The experimental results prove the effectiveness of the method proposed.     

Robust tracking control of an electrically driven robot: adaptive fuzzy logic approach

This paper is concerned with the robust tracking control of an electrically driven robot with the model uncertainties in the robot dynamics and the motor dynamics. The motors driving the joints of the robot are assumed to be equipped with only the joint position and the current measurement devices. Adaptive fuzzy logic and adaptive backstepping method are employed to provide the solution to the control problem. The suggested method does not require the measurement of the velocity nor the acceleration. Simulation results from a two-link electrically driven robot show the satisfactory performance of the proposed control scheme even in the presence of internal model uncertainties in both the robot and motor dynamics and external disturbances.     

Decoupling and tracking control for elastic joint robots with coupled joint structure

The paper deals with the modeling, identification, and control of a flexible joint robot developed for medical applications at the German Aerospace Center (DLR). In order to design anthropomorphic kinematics, the robot uses a coupled joint structure realized by a differential gearbox, which however leads to strong mechanical couplings inside the coupled joints and must be taken into account. Therefore, a regulation MIMO state feedback controller based on modal analysis is developed for each coupled joint pair, which consists of full state feedback (motor position, link side torque, as well as their derivatives). Furthermore, in order to improve position accuracy and simultaneously keep good dynamic behavior of the MIMO state feedback controller, a cascaded tracking control scheme is proposed, based on the MIMO state feedback controller with additional feedforward terms (desired motor velocity, desired motor acceleration, derivative of the desired torque), which are computed in a computed torque controller and take the whole rigid body dynamics into account. Stability analysis is shown for the complete controlled robot. Finally, experimental results with the DLR medical robot are presented to validate the practical efficiency of the approaches.     

A biologically inspired active compliant joint using local positive velocity feedback (LPVF).

Starting from studies which revealed that positive feedback is found in the control system for walking in arthropods, we have constructed a new positive feedback driven joint that can be used for solving compliant motion tasks. We propose two different joint constructions each of which shows passive compliance. Based on these joints we introduce three different local positive velocity feedback (LPVF) controllers and discuss their properties in the context of motion generation in closed kinematic chains. The third circuit named undelayed dLPVF is used for the control of a compliant planar manipulator which turns a crank. Our concept is of highly decentralized nature and follows the idea of embodiment. In our case this means that a process which is controlled by LPVF controllers reveals its nature when the controllers interact with this process.     

Development of flexible joints for a humanoid robot that walks on an oscillating plane

In this study, we develop flexible joints for a humanoid robot that walks on an oscillating plane and discuss their effectiveness in compensating disturbances. Conventional robots have a rigid frame and are composed of rigid joints driven by geared motors. Therefore, disturbances, which may be caused by external forces from other robots, obstacles, vibration and oscillation of the surface upon which the robot is walking, and so on, are transmitted directly to the robot body, causing the robot to fall. To address this problem, we focus on a flexible mechanism. We develop flexible joints and incorporate them in the waist of a humanoid robot; the experimental task of the robot is to walk on a horizontally oscillating plane until it reaches the desired position. The robot with the proposed flexible joints, reached the goal position despite the fact that the controller was the same as that used for a conventional robot walking on a static plane. From these results, we conclude that our proposed mechanism is effective for humanoid robots that walk on an oscillating plane.     

Position/torque hybrid control of a rigid,high-gear ratio quadruped robot

In this study, we introduce position/torque hybrid control for a newly designed rigid and high-gear ratio quadruped robot. The Experimental results indicated that the use of this control strategy allows the quadruped robot to maintain its stability while walking, and foot contact can be stabilized with only knee torque control and other joints are position controlled, without contact force feedback. Additionally, we suggested a smooth pattern connection method within or from preview control to the center of mass natural dynamics, and vice versa. We validated the proposed control strategies by conducting experiments.