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).     

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.     

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。     

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.      

双足机器人逆运动学的模糊自适应算法

针对双足机器人逆运动学的数值解法中存在的雅可比矩阵奇异性和调节参数固定问题,提出了一种改 进的求解方法．运用微分运动方程的近似解避开雅可比矩阵求逆,利用能够减小跟踪误差的自适应模糊控制法,调 节自适应参数以使近似解任意逼近精确解,从而得到了精确性极高和强鲁棒性的模糊自适应算法．通过双足机器人 运动学的仿真分析,验证了该算法的有效性．而且整套算法的计算时间约为0.35 ms,可以用于实际双足机器人的实 时控制．     

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。     

动态步行双足机器人THR-I的设计与实现

为了既能验证动态步行的理论结果,又能满足经济性的要求,本文设计并实现了一种基于总线型伺服电机的平面无脚双足机器人THR-I．首先介绍了该机器人的系统构成,包括机械结构部分和控制系统部分;在建立步行动力学方程时,考虑了中心约束系统的耦合影响．然后,利用虚拟约束原理,设计了步行约束,并成功实现了步行周期为0     

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.     

基于自学习中枢模式发生器的仿人机器人适应性行走控制

为了克服传统中枢模式发生器(Central pattern generator, CPG)关节空间控制方法的复杂性和局限性, 本文基于自学习中枢模式发生器模型, 提出了一套在线调制和融合多传感器信息的仿人机器人环境自适应行走控制方法.算法难点在于如何在机器人的工作空间将自学习CPG用于工作空间轨迹生成, 并使CPG参数直接和步态模式相关联.本文提出了利用自学习CPG来学习和实时生成机器人质心轨迹和脚掌轨迹的方法, 在线调节机器人步长、抬腿高度和步行速度等关键参数.参考生物反射行为, 利用传感反馈信息激发CPG以产生具有环境适应性的工作空间轨迹, 提升行走质量. 控制系统的参数通过优化算法来进一步改善行走性能.相比于传统的CPG关节空间法, 本文所采用的自学习CPG工作空间法不仅极大简化了CPG网络结构而且提高了仿人机器人行走的适应性.最后, 通过仿人机器人坡面适应性行走的仿真和实验, 验证了所提出控制策略的可行性和有效性.     

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.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

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。     

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.     

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.     

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.