一种双足机器人变结构控制的ZMP补偿优化方法

针对双足机器人系统,设计了一种变结构轨迹跟踪控制器。基于双足机器人系统ZMP(zero moment point)方程和实际ZMP信息,提出一种ZMP补偿优化方法,通过在线实时调整机器人躯体重心竖直方向上的位置来补偿回复稳定姿态所必需的力矩,最终产生修正的ZMP轨迹。12自由度的双足机器人动力学仿真验证了所提出优化方法的鲁棒性和适用性,而且机器人能在一定范围外力的干扰下回复稳定姿态步行。     

Trajectory generation and dynamic control of planar biped robots with curved soles

This paper proposes a locomotion pattern and a control method for biped robots with curved soles. First, since the contact point of a supporting leg may arbitrarily move back and forth on the ground, we derived the desired trajectory from a model called the Moving Inverted Pendulum Model (MIPM) where the Zero Moment Point (ZMP) exists at the supporting point and can be moved intentionally. Secondly, a biped robot with curved soles is an under-actuated system since the supporting point contacting with a point on the ground has no actuator during the single supporting phase. Therefore, this paper proposes a computed-torque control for this under-actuated system using decoupled dynamic equations. A series of computer simulations with a 7-DOF biped robot with curved soles shows that the proposed walking pattern and control method are effective and allow the biped robot to walk fast and stably, and move more like human beings. Also, it is shown that the curved sole shape has superior energy consumption compared to flat soles, and greater efficiency in ascending and descending the stairs.     

两足机器人步行运动参数对单足支撑期ZMP点影响的研究

在两足步行机器人的研究中,一般将零力矩点(ZMP点)的位置与支撑范围的关系作为判别其步行稳定性的依据.提出一种通用的方法,来分析两足机器人的步行运动参数对ZMP点位置的影响,并通过对机器人单足支撑期运动的计算机仿真,试图得到步行运动参数的变化对稳定性影响的规律,以期对机器人动态步行的稳定性设计提供实用的参考.     

Energy dissipation rate control and parallel equations solving method for planar spined quadruped bouncing robot

This paper continues our investigation into Energy dissipation rate control (EDRC) and Parallel equations solving method (PESM). Our previous works showed how EDRC enables us to provide stable walking or running gaits for legged robots via controlling robot’s loss of energy rate during Impact phases (IP). This is while PESM facilitates the trajectory designing process of the robot’s active joints during each Single support phase (SSP) by solving the robot’s inverse kinematic and inverse dynamic equations in parallel. Even though PESM is very powerful and suitable for both quadruped robot, and despite the under actuation problem at the ankle joint, and biped robots, despite the presence of Zero momentum point criteria (ZMP) at the ankle joint, still, this method is limited to robots just with three and five DoFs. Therefore, the main purpose hereis to show how it is possible to extend the application of PESL to a spined quadruped robot with four DoFs by employment of the Central pattern generator (CPG) controller units and finding a connection among CPG’s output, PESM and the robot’s foot placement. Besides, as EDRC is employed to realize a stable bouncing gait for the robot, a whole numerical study is performed on the robot’s impact dynamic equations to evaluate the effect of spine joint on the robot’s impact dynamics.

     

基于弹簧小车模型和预观控制的双足快速步行研究

针对机器人的滑动和滑转,补充了机器人稳定步行的修正条件;利用三阶泰勒公式引入舒适度的概念,推导出基于舒适度的ZMP公式;提出一种用于动力学分析的三维弹簧平台-小车模型,通过简化的舒适度ZMP公式推导出该模型的运动规律;基于三维弹簧平台-小车模型,结合预观控制理论生成步行样本;最后,进行了机器人虚拟样机快速步行仿真,步速达到2.088km/h。     

基于变长倒立摆模型的双足机器人爬楼梯步态规划

能在复杂环境中持续稳定地行走是双足机器人的一个重要性能,比如平地、楼梯.针对双足机器人爬楼梯的步态规划问题,提出了一种运用变长倒立摆模型来实现双足机器人爬楼梯步态规划的方法,并运用虚拟样机进行动态步行仿真.仿真结果表明,运用该步态规划方法可以得到可行的机器人爬楼梯轨迹.     

多关节双足步行机器椅行走步态规划

根据多关节双足步行机器椅的结构特点,采用D-H法建立系统运动学模型。从构造多关节双足步行机器椅行走姿态和过程零力矩点(Zero moment point,ZMP)评价考虑,提出基于优化方法的多关节双足步行机器椅行走步态的离散化模型和方法,实现过程优化向有限变量优化的转变。基于过程稳定性评价的优化计算,结合动态步行仿真,完成双足步行机器椅的开环多连杆执行机构行走步态的合理规划。解决多关节双足步行机器椅行走步态过程稳定性评价与其开环多连杆执行机构的多变量泛函问题。提出的离散化模型对求解开环连杆机构的时空多变量泛函规划问题具有重要参考价值。     

两足步行椅机器人的稳定性研究

文章针对两足步行椅机器人介绍了其步态规划中步行稳定性的计算方法。以前向运动为例，详细讨论了先进行姿态规划并计算出机器人各部分位姿，然后利用ZMP理论求出其步行的稳定裕度的方法，通过计算机仿真验证了这一计算方法的有效性。     

两足步行椅机器人及其稳定性计算研究

两足步行椅机器人是一种为残疾人设计,用来替代轮椅和假肢的助残机器人.本文介绍了两足步行椅机器人的整体机构设计,并以前向运动为例,详细讨论了利用ZMP理论进行步行稳定性计算的方法,最后通过计算机仿真验证了这一计算方法的有效性.     

基于ZMP点的两足机器人步态优化

采用身高、速度和步长等六个参数描述两足机器人动态步行 ,并进行了定量分析 ;然后利用面向对象思想完成牛顿 -欧拉算法的计算机实现 ,进而求出机器人动态行走时的 ZMP点 ;最后 ,以 ZMP点为目标函数用遗传算法对步态进行了优化 ,其结果证明算法的有效性。     

Energy efficient walking control for biped robots using interval type-2 fuzzy logic systems and optimized iteration algorithm

An energy efficient approach is proposed for the walking control of bipedal robots. To compensate the ZMP error caused by model uncertainties and external disturbances, we design a new walking controller in this paper. Different from currently available control schemes for cancelling ZMP error, our newly proposed one additionally incorporates a fuzzy logic systems(FLSs) mechanism and an iterative mechanism. By employing FLSs to deduce Center of Mass(CoM) correction according to ZMP error and designing iterative mechanism to compute the optimal joint position, the newly proposed controller exhibits an excellent performance. To tackle the control difficulties arising from physical constraints of actuators and hard-to-stabilization of biped robot, an optimized control algorithm is included in the iterative mechanism to guarantee the convergence to the optimal solution. Moreover, the interval type-2 FLSs are adopted to handle the uncertainties. Finally, the experiment results are provided to validate the proposed control scheme.     

双足欠驱动机器人能量成型控制

研究欠驱动双足机器人在3D空间稳定行走控制器。建立双足机器人的3D动力学模型,通过构建概循环拉格朗日函数,把欠驱动双足机器人的3D动态系统解耦成前向和侧向部分。针对前向2D欠驱动部分设计势能成型和动能成型控制器,为了求解能量成型控制器,将匹配方程分解成分别与角度和角速度相关的两个子条件,再将非线性偏微分方程变为线性偏微分方程,求解出能量成型控制器对前向行走进行控制,使前向行走获得稳定且具有仿生特点。对侧向部分采用零动态控制,在保证侧向稳定同时,还满足系统的动态解耦条件。对不同步长行走进行仿真试验,仿真结果表明,动态步行收敛于稳定的极限环,步态符合仿生规律,验证了所提出理论的可行性和有效性。     

Biped walking robot based on a 2-UPU+2-UU parallel mechanism

Existing biped robots mainly fall into two categories： robots with left and right feet and robots with upper and lower feet. The load carrying capability of a biped robot is quite limited since the two feet of a walking robot supports the robot alternatively during walking. To improve the load carrying capability, a novel biped walking robot is proposed based on a 2-UPU＋2-UU parallel mechanism. The biped walking robot is composed of two identical platforms（feet） and four limbs, including two UPU（universal-prismatic-universal serial chain） limbs and two UU limbs. To enhance its terrain adaptability like articulated vehicles, the two feet of the biped walking robot are designed as two vehicles in detail. The conditions that the geometric parameters of the feet must satisfy are discussed. The degrees-of-freedom of the mechanism is analyzed by using screw theory. Gait analysis, kinematic analysis and stability analysis of the mechanism are carried out to verify the structural design parameters. The simulation results validate the feasibility of walking on rugged terrain. Experiments with a physical prototype show that the novel biped walking robot can walk stably on smooth terrain. Due to its unique feet design and high stiffness, the biped walking robot may adapt to rugged terrain and is suitable for load-carrying.     

Optimal trajectory generation for biped robots walking up-and-down stairs

This paper proposes an optimal trajectory generation method for biped robots for walking up-and-down stairs using a Real-Coded Genetic Algorithm (RCGA). The RCGA is most effective in minimizing the total consumption energy of a multi-dof biped robot. Each joint angle trajectory is defined as a 4-th order polynomial of which the coefficients are chromosomes or design variables to approximate the walking gait. Constraints are divided into equalities and inequalities. First, equality constraints consist of initial conditions and repeatability conditions with respect to each joint angle and angular velocity at the start and end of a stride period. Next, inequality constraints include collision prevention conditions of a swing leg, singular prevention conditions, and stability conditions. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot model that consists of seven links in the sagittal plane. The optimal trajectory is more efficient than that generated by the Modified Gravity-Compensated Inverted Pendulum Mode (MGCIPM). And various trajectories generated by the proposed GA method are analyzed from the viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.     

Fabrication of four-point biped robot foot module based on contact-resistance force sensor and its evaluation

This paper presents the design of robot foot module of four-point biped walking robot and its fabrication. The foot module has four sensor units based on contact-resistance force sensor. The thin-film-type force sensor is fabricated by coating resistive ink on thin polyimide film using silk screening technique. The simple structure is devised and fabricated to assemble the thin force sensor rigidly. The unit force sensor module is evaluated by the calibration setup to obtain the characteristics of repeatability and hysteresis. The sensor module presents hysteresis error of about 5% and repeatability error of about 0.37%. The calculated zero moment point (ZMP) of the foot module is also compared with the measured position using static load of 50 N. The maximum location error of ZMP is less than 10%. The robot foot module shows the possibility of applying it to humanoid walking.     

教学型双足步行机器人直线行走步态稳定规划方法

通过对双足机器人行走步态的研究,利用多项式插值法对双足机器人直线行走步态进行规划,分析了踝关节轨迹和髋关节轨迹,通过调节单腿支撑期和双腿支撑期的比例系数来调整机器人的行走步态,使其实现稳定步行。再通过ADAMS建立虚拟样机仿真实验,验证了这种步态规划方法的正确性与可行性。     

A hybrid controller based on CPG and ZMP for biped locomotion

Biped locomotion has attracted much attention in recent years. The most successful implemented methods in this area are based on two approaches, central pattern generator (CPG) and zero moment point (ZMP). Unfortunately, neither of these concepts can solely solve the movement challenge completely. In this study, we introduce a hybrid controller to combine the advantages of these methods. The proposed controller is based on two major approaches, CPG and ZMP. This hybrid controller is composed of a trajectory control system and a trajectory generator system. The trajectory control system applied to keep the robot stable uses ZMP as a real time control feedback. The trajectory generator system, which is composed of nonlinear oscillators, generates stable motions. The parameters of CPG are tuned by a new two-stage approach using differential evolution (DE) and bees algorithm (BA). Furthermore, performance of the proposed controller is verified using the robotic simulation software Webots.     

基于过程ZMP的双足步行机器椅步态规划

解决了多关节双足步行机器椅行走步态过程稳定性评价与其开环多连杆执行机构的多变量泛函问题.从构造多关节双足步行机器椅行走姿态和过程ZMP(Zero Moment Point,零力矩点)评价考虑,提出了基于优化方法的多关节双足步行机器椅行走步态的离散化模型和方法,实现了基于过程稳定性评价的双足步行机器椅的开环多连杆执行机构行走步态的合理规划.文中提出的离散化模型对求解开环连杆机构的多变量泛函规划问题具有重要的参考价值.     

双足机器人的鲁棒自适应复合控制器设计

针对复杂机器人对象,充分考虑系统的各种不确定因素,在不确定保守上界己知情况下,设计了全局稳定的鲁棒自适应复合控制器。控制器设计在确保高品质控制的同时,避免或减少了参数漂移、保守鲁棒增益及控制系统抖振等问题,从理论与实际的角度提高了控制器的鲁棒性和实用性。仿真实验验证了提出优化方法的有效性,而且机器人能在一定范围外力的干扰下回复稳定姿态步行。     

Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot

In this paper, operation analysis of a Chebyshev-Pantograph leg mechanism is presented for a single degree of freedom (DOF) biped robot. The proposed leg mechanism is composed of a Chebyshev four-bar linkage and a pantograph mechanism. In contrast to general fully actuated anthropomorphic leg mechanisms, the proposed leg mechanism has peculiar features like compactness, low-cost, and easy-operation. Kinematic equations of the proposed leg mechanism are formulated for a computer oriented simulation. Simulation results show the operation performance of the proposed leg mechanism with suitable characteristics. A parametric study has been carried out to evaluate the operation performance as function of design parameters. A prototype of a single DOF biped robot equipped with two proposed leg mechanisms has been built at LARM (Laboratory of Robotics and Mechatronics). Experimental test shows practical feasible walking ability of the prototype, as well as drawbacks are discussed for the mechanical design.