Gait generation for a biped robot with knees and torso via trajectory learning and state-transition estimation

The proposed method can generate an optimal feedforward control input and the corresponding optimal walking trajectory minimizing the \(L_2\) norm of the control input by iteration of laboratory experiments. Since a general walking motion involves discontinuous velocity transitions caused by the collision with the ground, the proposed method consists of the combination of a trajectory learning part and an estimation part of the discontinuous state transition mapping using the stored experimental data. We apply the proposed method to a kneed biped robot with a torso, where we also provide a technique to generate an optimal gait not only being energy-efficient but also avoiding the foot-scuffing problem.     

双足机器人自然ZMP轨迹生成方法研究

为了实现双足机器人类人行走,提出了一种基于自然ZMP轨迹的双足机器人步行模式生成方法。在单腿支撑相,根据基于三维线性倒立摆模型,在设定从脚跟到脚趾移动的自然ZMP轨迹后,得到质心轨迹方程;在双腿支撑相采用线性摆模型生成质心轨迹方程。同时给出了在统一坐标系中的多步规划质心轨迹方程。在RoboCup 3D仿真平台实现了采用自然ZMP轨迹的双足机器人类人稳定步行,实验和竞赛结果都验证了该方法的有效性。     

A gait study for a one-leg-disabled hexapod robot

—As a remarkably strong point of a hexapod walking robot, it is considered that even if one of the six legs is disabled, static walking may be maintained by the remaining five legs. However, to maintain the static stability at maximum, a gait study for five-legged walking is a necessary factor. Hence, this paper describes a method of gait study for such a situation. Since it is very difficult to find a suitable gait by use of an analytical method without any model, such as a model based on insects' walking, we employed a programming method with the help of recent powerful computers. Some devices are applied to reduce the number of computations. As a result, we have obtained two kinds of gaits which can maintain the gait stability margin at a high level for a duty factor in the range of 0.6β < 1.     

欠驱动双足机器人动态步态规划方法研究

以欠驱动双足机器人为对象研究其周期稳定的动态步态规划方法。首先建立欠驱动双足机器人的混杂动力学模型,然后采用时不变步态规划策略对机器人步态进行规划,并研究周期步态的收敛条件。步态参数直接决定周期步态的稳定性,采用遗传算法,以能耗最优为目标,以限制条件为约束对步态参数进行选择和优化。最后通过虚拟样机对机器人的行走过程进行动力学仿真。实验表明规划步态收敛于稳定的极限环,实现了高速动态步行,该规划方法是可行的。     

基于约束满足的多目标双足机器人动态步态参数优化*

目前的步态优化算法仅仅实现了对单一目标的优化,把双足机器人步态优化看做是多目标优化问题,构建了衡量稳定性、能量消耗、步行速度三个目标评价函数。考虑到直接对多个目标加权求和的方法不能很好地处理多目标问题,提出一种新的基于约束满足的多目标步态参数优化算法,其思想是把基于惩罚函数的SPEA2(strength Pareto evolutionary algorithm2 )应用到多目标双足机器人动态步态参数优化问题上,规划出了同时满足这三个目标的动态优化步态。通过仿真实验表明了算法的有效性。     

Sensory-based walking motion instruction for biped humanoid robot

This paper describes a sensory-based biped walking motion instruction strategy. Visual and auditory sensors are employed to generate walking patterns according to human orders and to memorize various complete walking patterns effectively and systematically. The motion of lower-limbs for locomotion is created by an online pattern generator based on the sensory information. At the same time, the motion of the trunk and the waist for stability is generated online by a balance control method. Combining these locomotive and balance motions, a complete walking pattern is hierarchically constructed and memorized on a database. The walking instruction is conducted through computer simulation, and its effectiveness is verified.     

无动力双足步行机器人控制策略与算法

本文研究无动力双足步行机器人的建模、分析与控制问题. 基于能量的控制增加了机器人行走极限环的稳定性、鲁棒性, 扩大了极限环的收敛域; 角度不变控制使机器人的稳定行走步态摆脱了地面倾斜角度的限制; 把基于能量的控制与角度不变控制结合起来, 可以实现在不同倾斜角度地面上行走模式的切换. 基于能量的行走平均速度控制方法在平均速度与目标能量之间建立了联系, 能使机器人的行走产生新的稳定步态. 最后, 对无动力双足步行机器人的研究前景做了展望.     

Quasi optimal sagittal gait of a biped robot with a new structure of knee joint

The design of humanoid robots has been a tricky challenge for several years. Due to the kinematic complexity of human joints, their movements are notoriously difficult to be reproduced by a mechanism. The human knees allow movements including rolling and sliding, and therefore the design of new bio-inspired knees is of utmost importance for the reproduction of anthropomorphic walking in the sagittal plane. In this article, the kinematic characteristics of knees were analyzed and a mechanical solution for reproducing them is proposed. The geometrical, kinematic and dynamic models are built together with an impact model for a biped robot with the new knee kinematic. The walking gait is studied as a problem of parametric optimization under constraints. The trajectories of walking are approximated by mathematical functions for a gait composed of single support phases with impacts. Energy criteria allow comparing the robot provided with the new rolling knee mechanism and a robot equipped with revolute knee joints. The results of the optimizations show that the rolling knee brings a decrease of the sthenic criterion. The comparisons of torques are also observed to show the difference of energy distribution between the actuators. For the same actuator selection, these results prove that the robot with rolling knees can walk longer than the robot with revolute joint knees.     

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。     

双足机器人自适应常值驱动与传感反馈结合的仿生行走控制

为了将双足机器人的混沌步态控制收敛到稳定的周期步态,提出一种控制策略。首先用庞卡莱截面法研究斜坡倾角变化对步态的影响,结果表明,坡度增大会导致倍周期步态到混沌步态的产生;然后以人类步行的生物力学为仿生依据,根据延迟反馈控制的基本思路,设计了自适应常值驱动与传感反馈相结合的仿生行走控制策略,并依据当前步和前两步初始状态对控制器参数进行逐步调节,最终将混沌步态控制收敛到周期步态。仿真结果表明了所提出算法的有效性。     

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。     

Stability analysis and time-varying walking control for an under-actuated planar biped robot

This paper presents two walking controllers for a planar biped robot with unactuated point feet. The control is based on the tracking of reference motions expressed as a function of time. First, the reference motions are adapted at each step in order to create a hybrid zero dynamic (HZD) system. Next, the stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the HZD. When the controlled outputs are selected to be the actuated coordinates, most periodic walking gaits for this robot are unstable, that is, the eigenvalues of the linearized Poincaré map (ELPM) is larger than one. Therefore, two control strategies are explored to produce stable walking. The first strategy uses an event-based feedback controller to modify the ELPM and the second one is based on the choice of controlled outputs. The stability analysis show that, for the same robot and for the same reference trajectory, the stability of the walking (or ELPM) can be modified by some pertinent choices of controlled outputs. Moreover, by studying some walking characteristics of many stable cases, a necessary condition for stable walking is proposed. It is that the height of swing foot is nearly zero at the desired moment of impact. Based on this condition, the duration of the step is almost constant in presence of initial error, so a method for choosing controlled outputs for the second controller is given. By using this method, two stable domains for the controlled outputs selection are obtained.     

Central pattern generator parameter search for a biped walking robot using nonparametric estimation based Particle Swarm Optimization

A parameter search for a Central Pattern Generator (CPG) for biped walking is difficult because there is no methodology to set the parameters and the search space is broad. These characteristics of the parameter search result in numerous fitness evaluations. In this paper, nonparametric estimation based Particle Swarm Optimization (NEPSO) is suggested to effectively search the parameters of CPG. The NEPSO uses a concept experience repository to store a previous position and the fitness of particles in a PSO and estimated best position to accelerate a convergence speed. The proposed method is compared with PSO variants in numerical experiments and is tested in a three dimensional dynamic simulator for bipedal walking. The NEPSO effectively finds CPG parameters that produce a gait of a biped robot. Moreover, NEPSO has a fast convergence property which reduces the evaluation of fitness in a real environment. Recommended by Editorial Board member Euntai Kim under the direction of Editor Jae-Bok Song. Jeong-Jung Kim received the B.S. degree in Electronics and Information Engineering from Chonbuk National University in 2006 and the M.S. degree in Robotics from Korea Advanced Institute of Science and Technology in 2008. He is currently working toward a Ph.D. at the Korea Advanced Institute of Science and Technology. His research interests include biologically inspired robotics and machine learning. Jun-Woo Lee received the B.S. degree in Electronics, Electrical and Communication Engineering from Pusan National University in 2007. He is currently working toward an M.S. in the Korea Advanced Institute of Science and Technology. His research interests include swarm intelligence and machine learning. Ju-Jang Lee was born in Seoul, Korea, in 1948. He received the B.S. and M.S. degrees from Seoul National University, Seoul, Korea, in 1973 and 1977, respectively, and the Ph.D. degree in Electrical Engineering from the University of Wisconsin, in 1984. From 1977 to 1978, he was a Research Engineer at the Korean Electric Research and Testing Institute, Seoul. From 1978 to 1979, he was a Design and Processing Engineer at G. T. E. Automatic Electric Company, Waukesha, WI. For a brief period in 1983, he was the Project Engineer for the Research and Development Department of the Wisconsin Electric Power Company, Milwaukee. He joined the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, in 1984, where he is currently a Professor. In 1987, he was a Visiting Professor at the Robotics Laboratory of the Imperial College Science and Technology, London, U.K. From 1991 to 1992, he was a Visiting Scientist at the Robotics Department of Carnegie Mellon University, Pittsburgh, PA. His research interests are in the areas of intelligent control of mobile robots, service robotics for the disabled, space robotics, evolutionary computation, variable structure control, chaotic control systems, electronic control units for automobiles, and power system stabilizers. Dr. Lee is a member of the IEEE Robotics and Automation Society, the IEEE Evolutionary Computation Society, the IEEE Industrial Electronics Society, IEEK, KITE, and KISS. He is also a former President of ICROS in Korea and a Counselor of SICE in Japan. He is a Fellow of SICE and ICROS. He is an Associate Editor of IEEE Transactions on Industrial Electronics and IEEE Transactions on Industrial Informatics.     

Neuro-fuzzy gait synthesis with reinforcement learning for a biped walking robot

 A reinforcement learning-based neuro-fuzzy gait synthesizer, which is based on the GARIC (Generalized Approximate Reasoning for Intelligent Control) architecture, is proposed for the problem of biped dynamic balance. We modify the GARIC architecture to enable it to generate the trunk trajectory in both sagittal and frontal plane. The proposed gait synthesizer is trained by reinforcement learning that uses a multi-valued scalar signal to evaluate the degrees of failure or success for the biped locomotion by means of the ZMP (Zero Moment Point). It can form the initial dynamic balancing gait from linguistic rules, which are obtained from human intuitive balancing knowledge and biomechanics studies, and accumulate dynamic balancing knowledge through reinforcement learning, and thus constantly improve its gait during walking. The feasibility of the proposed method is verified through a 5-link biped robot simulation.     

Optimal path generation for a simulated autonomous mobile robot

The paper deals with a set of algorithms including path planning, trajectory planning, and path tracking for a tricycle type wheeled mobile robot. Path planning is carried out with parametric polynomial interpolation using an optimization algorithm based on robot geometric constraints. Trajectory characteristics are then derived from the planned geometric path with time varying parameters. A sliding mode control algorithm combined with an adaptive control law are used to track the planned trajectory. The technique deals with an environment free of obstacles. However, it can be easily integrated in a piecewise non colliding path generation. Simulation results are presented to show the validity of the different algorithms.Bissé Emmanuel is a Ph.D. student at the École Polytechnique de Montréal, Department of Mechanical Engineering.Bentounes Mohamed is a Ph.D. student at the École Polytechnique de Montréal, Department of Mechanical Engineering.Boukas El-Kébir is a Professor at the École Polytechnique de Montréal, Department of Mechanical Engineering.     

Stability and control of dynamic walking for a five-link planar biped robot with feet

During dynamic walking of biped robots, the underactuated rotating degree of freedom (DOF) emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant.This paper addresses the asymptotic orbit stability for criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with flat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.     

Stability and control of dynamic walking for a five-link planar biped robot with feet

During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.     

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.     

基于离散化的六足机器人自由步态规划

为精细模仿生物步态,充分发挥六足机器人运动潜能,本文在离散化机器人足端轨迹的基础上,融合中枢模式发生器(central pattern generator,CPG)模型与反射模型的核心思想,建立了离散化步态模型,结合稳定性分析,构建了机器人稳定的位置状态空间,将复杂的步态规划问题转化为稳定的位置状态空间中位置状态间的排序问题,在此基础上,提出了一种新的自由步态生成算法,并基于平均稳定裕量对该算法进行了优化.样机步态实验结果表明,自由步态生成算法与自由步态优化算法均可生成在一定程度上符合生物运动特点的稳定步态,实现机器人运动过程中速度的动态调整,跨越宽度为步距的障碍,且基于平均稳定裕量的自由步态优化算法生成步态的稳定性要远大于自由步态生成算法.