Locomotion Control of a Biped Robot Using Nonlinear Oscillators

Recently, many experiments and analyses with biped robots have been carried out. Steady walking of a biped robot implies a stable limit cycle in the state space of the robot. In the design of a locomotion control system, there are primarily three problems associated with achieving such a stable limit cycle: the design of the motion of each limb, interlimb coordination, and posture control. In addition to these problems, when environmental conditions change or disturbances are added to the robot, there is the added problem of obtaining robust walking against them. In this paper we attempt to solve these problems and propose a locomotion control system for a biped robot to achieve robust walking by the robot using nonlinear oscillators, each of which has a stable limit cycle. The nominal trajectories of each limb's joints are designed by the phases of the oscillators, and the interlimb coordination is designed by the phase relation between the oscillators. The phases of the oscillators are reset and the nominal trajectories are modified using sensory feedbacks that depend on the posture and motion of the robot to achieve stable and robust walking. We verify the effectiveness of the proposed locomotion control system, analyzing the dynamic properties of the walking motion by numerical simulations and hardware experiments. Shinya Aoi received the B.E. and M.E. degrees from the Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan in 2001 and 2003, respectively. He is a Ph.D. candidate in the Department of Aeronautics and Astronautics, Kyoto University. Since 2003, he has been a research fellow of the Japan Society for the Promotion of Science (JSPS). His research interests include dynamics and control of robotic systems, especially legged robots. He is a member of IEEE, SICE, and RSJ. Kazuo Tsuchiya received the B.S., M.S., and Ph.D. degrees in engineering from Kyoto University, Kyoto, Japan in 1966, 1968, and 1975, respectively. From 1968 to 1990, he was a research member of Central Research Laboratory in Mitsubishi Electric Corporation, Amagasaki, Japan. From 1990 to 1995, he was a professor at the Department of Computer Controlled Machinery, Osaka University, Osaka, Japan. Since 1995, he has been a professor at the Department of Aeronautics and Astronautics, Kyoto University. His fields of research include dynamic analysis, guidance, and control of space vehicles, and nonlinear system theory for distributed autonomous systems. He is currently the principal investigator of “Research and Education on Complex Functional Mechanical Systems” under the 21st Century Center of Excellence Program (COE program of the Ministry of Education, Culture, Sports, Science and Technology, Japan).     

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。     

Robot Dynamic Modeling Using a Power Flow Approach with Application to Biped Locomotion

In this paper, we present a method for robots modeling called bidirectional dynamic modeling. This new method takes into account the gear efficiency and the direction of power transmission in the gears. Epicyclic gearboxes have often different efficiencies in the two directions of power transmission. The characteristics of the chain of transmission must then be taken into consideration in order to describe the dynamic behavior of robots. The two directions of power flow can indeed occur in robot motions. Depending on that direction the dynamic model is different. The bidirectional dynamic modeling is experimentally applied to a bipedal walking robot. Our method exhibits a better accuracy over classical modeling. Moreover, when applied to computed torque control, the bidirectional model increases the tracking performances.     

Design and Quasi-Static Locomotion Analysis of the Rolling Disk Biped Hybrid Robot

Motivated by the need for greater speed, efficiency, and adaptability in climbing and walking robots, we have developed a bipedal planar robot that complements its walking and climbing capabilities with rolling. Rolling capabilities are provided by an innovative morphology, without the need for additional resources beyond those required by walking and climbing. Herein, we present the design of this robot, the development of a quasi-static rolling controller, and a comparison of experimentally obtained speed and energy data for walking versus rolling locomotion. We show that rolling can significantly improve energy efficiency over walking—as much as a factor of 5.5. We also demonstrate the ability to roll up slopes and roll over obstacles.      

小型双足步行机器人的机构设计及其运动仿真

小型双足步行机器人具有多关节、多驱动器、多自由度的特点,本文以人体全身17个主要关节及其运动特性为研究对象,利用三维设计软件CATIA设计出小型双足步行机器人的全身机构,根据ZMP理论,以正常人行走的“X”形交叉动作为原则,规划出其各关节转角,在ADAMS下对其虚拟样机进行运动仿真,确保实现机器人的稳定步行和做舞蹈动作。     

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.      

Dynamic Modeling and Hydrodynamic Performance of Biomimetic Underwater Robot Locomotion

We developed a dynamic model of a Nitinol artificial muscle activated biomimetic robot. The robot was reverse engineered from the American lobster and built in the Biomimetic Underwater Robot Program at Northeastern University. It is intended for autonomous remote-sensing operations in shallow waters. An experimentally based Nitinol artificial muscle model was integrated into the robot dynamic model. The hydrodynamic characteristics of the robot were determined experimentally. The muscle control signals were generated by utilizing a readily available biomimetic control architecture. The effects of the timing parameters were investigated. Simulations indicate that the developed robot is able to locomote with high stability. It can walk against constant currents and surge.     

基于ADAMS的双足机器人拟人行走动态仿真

在双足机器人HEUBR_1的设计中,下肢采用了一种新的串并混联的仿人结构,并在足部增加了足趾关节.为验证该仿人结构设计的合理性及拟人步态规划的可行性,在ADAMS虚拟环境中建立了双足机器人HEUSR_1的仿真模型.通过拟人步态规划生成了运动仿真数据,在ADAMS虚拟环境中实现了具有足趾运动的拟人稳定行走,经仿真分析,获得了双足机器人HEUBR_1拟人行走步态下的运动学和动力学特性,仿真结果表明:双足机器人HEUBR_1的串并混联的仿人结构设计能够满足行走要求,且拟人步态规划方法可行,有足趾运动的拟人行走具有运动平稳、能耗低、足底冲击力小的特点.稳定行走的仿真步态数据可为下一步双足机器人HEUBR_1样机行走实验提供参考数据.     

Control of a Biped Walking Robot during the Double Support Phase

This paper discusses the control problem of a biped walking robotduring the double-support phase. Motion of a biped robot during thedouble-support phase can be formulated as motion of robotmanipulators under holonomic constraints. Based on the formulation,the walking gait is generated by controlling the position of thetrunk of the robot to track a desired trajectory, referenced in theworld frame. Constrained forces at both feet were controlled suchthat firm contact is preserved between the feet and ground by using asimplified model of the double-support phase. The control scheme wasevaluated experimentally.     

仿生双足机器人步态轨迹自适应控制方法研究

仿生双足机器人的步态控制具有高阶、高耦合,以及不完整约束等复杂特征,为了使其行走性能更接近人体,基于模型分析提出了一种步态轨迹自适应控制方法.首先在人体步态变化对质心投影位置与质心角动量影响的基础上,引入倒立摆建立步态模型来模拟人体行走状态,同时推导出质心投影点位置与速度公式.然后为了实现步态轨迹自适应控制,对影响步态...     

Development of a Complete Dynamic Model of a Planar Five-Link Biped and Sliding Mode Control of Its Locomotion During the Double Support Phase

This paper presents a complete dynamic model of a planar five-link biped walking on level ground. The single support phase (SSP), double support phase (DSP) and double impact occurring at the heel strike are included in the model. By modifying the conventional definition of certain physical parameters of the biped system, it is shown that the procedure of the derivation of the dynamic equations and their final forms are significantly simplified. For motion regulation during the DSP, our dynamic model is formulated as the motion of biped system under holonomic constraints, and the hip position and the trunk orientation are selected as the independent generalized coordinates to describe the constraint system and to eliminate the constraint forces from the equations of motion. Based on the presented dynamic formulation, we develop a sliding mode controller for motion regulation during the DSP where the biped is treated as a redundant manipulator. The stability and the robustness of the controller are investigated, and its effectiveness is demonstrated by computer simulations. To the best of our knowledge, it is the first time that a sliding mode controller is developed for biped walking during the DSP. This work makes it possible to provide robust sliding mode control to a full range of biped walking and to yield dexterity and versatility for performing specific gait patterns.     

Robot Motion Planning in Dynamic Uncertain Environments

In the real world, mobile robots often operate in dynamic and uncertain environments. Therefore, it is necessary to develop a motion planner capable of real-time planning that also addresses uncertainty concerns. In this paper, a new algorithm, Dynamic AO* (DAO*), is developed for navigation tasks of mobile robots. DAO* not only performs a good anytime behavior and offers a fast replanning framework, but also considers the motion uncertainty. Moreover, by incorporating DAO* with D* Lite, a new planning architecture, DDAO*, is represented to efficiently search in large state spaces. Finally, simulations and experiments are shown to verify the efficiency of the proposed algorithms.     

双足机器人跨越动态障碍物在线控制系统设计

在双足机器人跨越动态障碍物的在线控制问题中,脚步规划和步态控制的学习时间是关键问题;提出了一种将机器人的步态控制和脚步规划分别独立设计的控制策略;步态控制目的是产生关节点轨迹并控制对理想轨迹的跟踪,考虑到双足机器人关节点轨迹的不连续性,应用小脑模型连接控制CMAC记忆特征步态的关节点轨迹;脚步规划的控制目标是通过对环境的视觉感知预测机器人的运动路径,算法是基于无需对动态环境精确建模的模糊Q学习算法;仿真结果表明该控制策略的可行性,并且可以有效缩短在线学习时间。     

A Simplified CPGs Network with Phase Oscillator Model for Locomotion Control of a Snake-like Robot

CPG (Central pattern generator) is a dynamical system of coupled nonlinear oscillators or neural networks inspired by a control mechanism in animal bodies. Without any rhythmic inputs, the CPG has the ability to produce oscillatory patterns. This paper presents a novel structure of a CPG network which can produce rhythmic motion that imitates movement of animals such as snake and lamprey. The focus is on the locomotion control of a snake-like robot, where phase oscillator has been adopted as the dynamical model to control the harmonic motion of the CPG network. There are two main points addressed in this paper: (1) simple network structure of unidirectional coupling oscillators, and (2) a single parameter to control the body shape and to control the forward and backward movement of the snake-like robot. The proposed CPG network is designed to have a simple structure with less complexity, less mathematical computation, fast convergence speed and exhibit limit cycle behavior. In addition, a new parameter, τ is introduced to control the smoothness of the CPG output as well as the speed of the snake-like robot. Simulation and experimental results show that the proposed CPG network can be used to control the serpentine locomotion of a snake-like robot.     

A Biologically Inspired Biped Locomotion Strategy for Humanoid Robots: Modulation of Sinusoidal Patterns by a Coupled Oscillator Model

Biological systems seem to have a simpler but more robust locomotion strategy than that of the existing biped walking controllers for humanoid robots. We show that a humanoid robot can step and walk using simple sinusoidal desired joint trajectories with their phase adjusted by a coupled oscillator model. We use the center-of-pressure location and velocity to detect the phase of the lateral robot dynamics. This phase information is used to modulate the desired joint trajectories. We do not explicitly use dynamical parameters of the humanoid robot. We hypothesize that a similar mechanism may exist in biological systems. We applied the proposed biologically inspired control strategy to our newly developed human-sized humanoid robot computational brain (CB) and a small size humanoid robot, enabling them to generate successful stepping and walking patterns.     

Adaptive Gait Control of a Biped Robot Based on Realtime Sensing of the Ground Profile

In this paper, realtime control of dynamic biped locomotion usingsensor information is investigated. We used an ultrasonic rangesensor mounted on the robot to measure the distance from the robot tothe ground surface. During the walking control, the sensor data isconverted into a simple representation of the ground profile inrealtime. We also developed a control architecture based on theLinear Inverted Pendulum Mode which we proposed previously fordynamic walking control. Combining the sensory system and thecontrol system enabled our biped robot, Meltran II, to walk overground of unknown profile successfully.     

Real-Time Motion Tracking of Robot Manipulators Using Adaptive Genetic Algorithms

The paper presents a genetic algorithm approach to real-time motion tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve real time tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position level rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic Research arm that demonstrate good tracking accuracy and reasonable joint velocities.     

Simulating Adaptive Human Bipedal Locomotion Based on Phase Resetting Using Foot-Contact Information

Humans generate bipedal walking by cooperatively manipulating their complicated and redundant musculoskeletal systems to produce adaptive behaviors in diverse environments. To elucidate the mechanisms that generate adaptive human bipedal locomotion, we conduct numerical simulations based on a musculoskeletal model and a locomotor controller constructed from anatomical and physiological findings. In particular, we focus on the adaptive mechanism using phase resetting based on the foot-contact information that modulates the walking behavior. For that purpose, we first reconstruct walking behavior from the measured kinematic data. Next, we examine the roles of phase resetting on the generation of stable locomotion by disturbing the walking model. Our results indicate that phase resetting increases the robustness of the walking behavior against perturbations, suggesting that this mechanism contributes to the generation of adaptive human bipedal locomotion.     

Realization of Dynamic Stair Climbing for Biped Humanoid Robot Using Force/Torque Sensors

This paper proposes a control algorithm for the dynamic stair climbing of a human-sized biped humanoid robot. Dynamic stair climbing can cause more instability than dynamic biped walking on the ground because stair climbing requires an additional vertical motions and a large step length. We assume that stair configuration is already known and only use force/torque sensors at ankle joint to achieve a control algorithm for a stable dynamic stair climbing. We describe a stair climbing pattern generation and stair climbing stages, and then propose a real-time balance control algorithm which is composed of several online controllers. Each online controller is addressed in detail with experimental results. Finally, the effectiveness and performance of the proposed control algorithm are verified through a dynamic stair climbing experiment of KHR-2.     

双手爪爬杆机器人对杆件的位姿检测与自主抓夹

为实现5自由度平面构型的双手爪爬杆机器人Climbot对目标杆件的自主抓夹,提出一种基于2D激光扫描测距仪的杆件位姿检测和自主抓夹方法.首先根据Climbot的平面构型,给出了机器人在两圆杆间过渡时的特殊位姿约束条件.再摆动夹持器使得安装在上面的激光传感器可以用扫描的方式获取目标杆件上若干中心点位置,并将其拟合出杆件的空间直线方程,即杆件位姿.并基于直线方程,规划出了满足过渡约束条件的自主抓夹运动.最后通过实验分析了杆件中心点位置的检测误差,以及所求杆件位姿相对于实际杆件和Climbot夹持器坐标系的角度误差.相对于杆件尺寸以及夹持器张合度,上述误差均可接受.本文方法能够准确地检测目标杆件的位置信息,并给出合理的抓夹运动规划.