仿人机器人相似性运动轨迹跟踪控制研究

提出一种基于带观测器的条件状态反馈控制的仿人机器人相似性运动轨迹跟踪控制方法.首先,分析了7连杆双足机器人动力学模型,阐述了其运动能量方程与动力学特征方程; 其次,基于带观测器的状态反馈控制器原理,构建起三维倒立摆平衡控制模型; 最后,由线性二次型调节器确定状态反馈增益矩阵,使机器人轨迹跟踪误差最小化,以复现出较高相似度的双足步行运动效果.实验验证了该方法的有效性.     

Time-variant feedback controller based on capture point and maximal output admissible set of a humanoid

This paper formulates the maximal output admissible (MOA) set of a capture point (CP) feedback controller for adaptive humanoid balancing. In previous studies where the MOA set was employed, an adaptive strategy-switching control was proposed. In general, the MOA set requires iterative computation; however, this study has proven that the MOA set of the CP feedback controller can be obtained analytically. This result was applied to a continuous switching feedback gain, which was regarded as a time-variant feedback controller realizing an adaptive response to external disturbances. The validity of the proposed time-variant controller was verified by a whole-body dynamics simulation.     

A real-time optimal energy-saving walking pattern generator based on gradient descent method and linear quadratic control

Many recent approaches have successfully generated a stable walking pattern for biped robots, but discussions about its optimization are relatively few. In this paper, a Center of Gravity (COG) trajectory optimization method is proposed to minimize the cost function of joint torque, joint limit, and joint speed limit. The linear quadratic control-based inverted pendulum controller optimizes the COG trajectories in sagittal and lateral directions with the COG height trajectory. The COG height trajectory is optimized by finding the derivative of the cost function with respect to the COG height offline. Then the proposed walking pattern generator builds the COG height trajectory database of different walking steps for online connection of a walking pattern. The walking pattern generator is verified by experiments and simulations of different step cycles with our humanoid robot, NINO, and it can clearly reduce the required joint torque of the robot while walking. In addition, compared with the fixed COG height trajectory, the energy consumption is reduced by 14% from the experimental results. Thus, the method succeeds in generating a more energy-saving walking pattern.     

一级倒立摆状态反馈控制系统设计

倒立摆控制系统是一个复杂的、不稳定的、非线性系统,对倒立摆系统的研究能有效的反映控制中的许多典型问题。对一级直线型倒立摆,首先运用牛顿运动定律建立倒立摆系统的运动方程,进而求出系统的状态空间表达式,建立数学模型。其次运用状态反馈极点配置法,以小车的位移、速度,摆杆与竖直向上的偏角、摆角变化速度作为四个状态变量,由给定的控制要求求出状态反馈增益矩阵,将极点配置在控制要求的位置。另外考虑到系统的某些状态如小车速度和摆杆角速度不容易直接测量等,本文分别基于小车和摆杆子系统设计了两个全维观测器,分别对状态量进行了重构并给出了仿真结果分析。     

Wheeled inverted pendulum type assistant robot: design concept and mobile control

This paper describes the design concept of the human assistant robot I-PENTAR (Inverted PENdulum Type Assistant Robot) aiming at the coexistence of safety and work capability and its mobile control strategy. I-PENTAR is a humanoid type robot which consists of a body with a waist joint, arms designed for safety, and a wheeled inverted pendulum mobile platform. Although the arms are designed low-power and lightweight for safety, it is able to perform tasks that require high power by utilizing its self-weight, which is the feature of a wheeled inverted pendulum mobile platform. I-PENTAR is modeled as a three dimensional robot; with controls of inclination angle, horizontal position, and steering angle to achieve high mobile capability. The motion equation is derived considering the non-holonomic constraint of the two-wheeled mobile robot, and a state feedback control method is applied for basic mobile controls wherein the control gain is calculated by the LQR method. Through several experiments of balancing, linear running, and steering, it was confirmed that the robot could realize stable mobile motion in a real environment by the proposed controller.     

基于ODE 引擎的开放式仿人机器人仿真

为了获得灵活、开放、简洁的仿真功能,提出了一种基于ODE（open dynamics engine）的仿人机器人 仿真平台集成方案．将基于ODE 的仿人机器人仿真系统开发过程定义为两类运算：变换叠加和关节叠加,并设计 了这两类叠加的ODE 算法．将仿人机器人结构描述为一个设计者和计算机都可以理解的结构表,将该结构表翻译 为ODE 基本元素实现仿真．设计并实现了一个基于所提出方案的仿人机器人仿真平台,根据基于倒立摆的步态规 划思想,设计并在仿真平台上实现了双足步行的仿真实验．实验证明了文中方法的有效性．     

Active balance of humanoids with foot positioning compensation and non-parametric adaptation

To maintain human-like active balance for a humanoid robot, this paper proposes a novel adaptive non-parametric foot positioning compensation approach that can modify predefined step position and step duration online with sensor feedback. A constrained inverted pendulum model taking into account of supporting area to CoM acceleration is used to generate offline training samples with constrained nonlinear optimization programming. To speed up real-time computation and make online model adjustable, a non-parametric regression model based on extended Gaussian Process model is applied for online foot positioning compensation. In addition, a real-time and sample-efficient local adaptation algorithm is proposed for the non-parametric model to enable online adaptation of foot positioning compensation on a humanoid system. Simulation and experiments on a full-body humanoid robot validate the effectiveness of the proposed method.     

Observer based biped walking control, a sensor fusion approach

In humanoid walking research, the prevailing approach is to utilize an abstraction of the robot to a single center of mass (3D linear inverted pendulum mode). Smaller disturbances or an oscillation of the body are typical for a walking robot and must be addressed by an appropriate sensor feedback. To this end, this paper proposes a novel observer fusing joint angle sensors and force sensing resistors. This new method of sensor feedback in a preview control system balances the walk by damping those disturbances and oscillations of the body. Moreover, novel stabilizing methods for defining reference trajectories for the zero moment point and limbs are examined.     

State-incremental optimal control of 3D COG pattern generation for humanoid robots

Many researchers have proposed walking pattern generation methods with zero moment point – center of gravity (ZMP–COG) constraints. Some of the researchers used a neural-networks (NN), a central pattern generator (CPG), or a genetic algorithm (GA) for ZMP–COG pattern generation. However, the parameters used in those methods are too many, and the procedure to learn or to search them costs too much computation time. Other researchers designed controllers or used analytical solution method to generate COG trajectories. These methods generate the ZMP-COG pattern very quickly, but the COG height is limited to a constant to linearize the inverted pendulum model of the robot. Due to this limitation, the robots cannot walk freely on surfaces that change in height. To solve this problem, researchers start to use the original nonlinear inverted pendulum model to make the COG height changeable such as using a numerical method or a feedback controller. In this paper, an optimal control-based pattern generator that can allow COG height change is proposed. It can solve sagittal and lateral COG patterns with arbitrarily assigned COG height and ZMP trajectories in real time. Thus, dynamic walking on height-changing surfaces can be achieved.     

Non-linear stable inversion-based output tracking control for a spherical inverted pendulum

We design an exact output tracking control law for a four degree of freedom spherical inverted pendulum based on the non-linear stable inversion tool proposed by Devasia et al. (1989). The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that the pendulum can be steered to track some smooth desired translational trajectories while keeping the pendulum tightly around the upright position. The design proceeds in three steps: 1. identification of the internal dynamics; 2. feedforward control design for achievable trajectories; 3. feedback design to stabilize the achievable trajectories. The computer simulations show that the proposed controller can deliver excellent tracking performance.     

不确定平面二级倒立摆的鲁棒自适应控制

为提高倒立摆控制系统的抗扰动能力,降低其对未建模动态等的敏感度,研究了不确定平面二级倒立摆的鲁棒自适应控制器的设计方法。把倒立摆动力学模型分解为确定和不确定两部分,用一个非线性参数化模糊逻辑系统逼近平面二级倒立摆的不确定动态,采用李雅普诺夫稳定性理论推导出使平面二级倒立摆的状态误差渐近收敛的鲁棒控制器及自适应律。理论分析和仿真结果表明所提出的控制算法是有效的。     

基于模糊加权的倒立摆混合控制

针对小车倒立摆系统,提出了一种线性状态反馈控制和滑模控制模糊加权的控制方法.滑模控制器的作用是将摆角控制在零的一个邻域内,在此邻域内首先采用近似的线性化模型来描述倒立摆系统,然后采用基于极点配置的方法设计系统的线性状态反馈控制器以使系统的状态稳定在给定值,两个控制器的输出通过加权求和作为倒立摆的控制作用.仿真结果证实了该方法的有效性.     

二级直线倒立摆系统的实物控制

针对二级直线倒立摆系统,采用拉格朗日方程法建立其理论模型,分别使用线性二次最优控制（Linear Quadratic Regulator,LQR）及基于趋近律的滑模控制（Sliding Mode Control,SMC）算法来实现干扰存在情况下倒立摆的平衡控制。对于LQR算法,研究了矩阵[Q]和矩阵[R]与反馈控制矩阵[K]的定性关系,并经过反复多次实验,不断试凑,得到一组良好的控制参数,实现了倒立摆的稳定控制。SMC算法采用基于指数趋近律的控制方法进行了滑模变结构控制器的设计,并利用边界层法来进一步削弱抖振。最后通过仿真及实验,实现了倒立摆的实物平衡控制。     

Linear controller for an inverted pendulum having restricted travel: A high-and-low gain approach

The problem of balancing an inverted pendulum has been a benchmark example in demonstrating and motivating various control design techniques. In this paper, we provide a linear state feedback design technique for balancing an inverted pendulum. The pivot of this pendulum is mounted on a carriage that has limited horizontal travel. For any given (arbitrarily small) allowable travel of the carriage, our design yields a linear state feedback controller that balances the pendulum with an infinite amount of gain margin in the sense that, if the feedback gain is perturbed by any multiplying factor greater than one, the controller will still balance the pendulum without requiring greater traveling distance than the maximum allowable.     

基于Lie理论的倒立摆系统的控制算法研究

该文通过能量反馈和最优控制相结合的方法实现倒立摆系统的自摆起和稳定控制。在摆起阶段采用能量反馈方法实现快速摆起，而在平衡稳定控制阶段，采用一种非线性系统微分几何方法一李理论，对倒立摆系统进行近似线性化，此种线性化方法使模型更多包含原系统主要的非线性部分，更能逼近实际系统，针对采用李理论得到的近似线性化模型，对倒立摆系统进行最优稳定控制设计。仿真和实时控制试验结果表明，文中提出的李理论近似模型线性化方法对于控制器设计结果是有效的，而且采用的能量反馈和最优控制相结合的联合控制策略能够成功实现倒立摆系统的自摆起和稳定控制过程。     

Local stabilization for linear discrete-time systems with bounded controls and norm-bounded time-varying uncertainty

The problem of the local stabilization of linear discrete-time systems subject to bounded controls and suffering from uncertainty of the norm-bounded time-varying type is addressed. From the solution of a certain discrete Riccati equation, a control gain and a set of safe initial conditions are obtained. The asymptotic stability of the saturated closed-loop system is then locally guaranteed for all admissible uncertainties. It is also shown how the control problem can be translated into L.M.I. conditions. The connections between local stability results and disturbance rejection problem are investigated. In the presence of control saturation, it is thus shown that it is possible to reject a certain class of perturbations. Finally, a discretized model of the inverted pendulum allows us to illustrate the results. © 1998 John Wiley & Sons, Ltd.     

Structural design of composite nonlinear feedback control for linear systems with actuator constraint

The performance of the composite nonlinear feedback (CNF) control law relies on the selection of the linear feedback gain and the nonlinear function. However, it is a tough task to select an appropriate linear feedback gain and appropriate parameters of the nonlinear function because the general design procedure of CNF control just gives some simple guidelines for the selections. This paper proposes an operational design procedure based on the structural decomposition of the linear systems with input saturation. The linear feedback gain is constructed by two linear gains which are designed independently to stabilize the unstable zero dynamics part and the pure integration part of the system respectively. By investigating the influence of these two linear gains on transient performance, it is flexible and efficient to design a satisfactory linear feedback gain for the CNF control law. Moreover, the parameters of the nonlinear function are tuned automatically by solving a minimization problem. The proposed design procedure is illustrated by applying it to design a tracking control law for the inverted pendulum on a cart system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stabilization of a 3D axially symmetric pendulum

Stabilizing controllers are developed for a 3D pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry. This assumption allows development of a reduced model that forms the basis for controller design and global closed-loop analysis; this reduced model is parameterized by the constant angular velocity component of the 3D pendulum about its axis of symmetry. Several different controllers are proposed. Controllers based on angular velocity feedback only, asymptotically stabilize the hanging equilibrium. Then controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. These problems can be viewed as stabilization of a Lagrange top. Finally, if the angular velocity about the axis of symmetry is assumed to be zero, controllers are introduced, based on angular velocity and reduced attitude feedback, that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium. This problem can be viewed as stabilization of a spherical pendulum.     

Modeling of an inverted pendulum based on fuzzy clustering techniques

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enough information or dynamics of the system. This can be overcome by designing a feedback controller, which stabilize the system before identification can takes place. Recently Takagi–Sugeno (T–S) fuzzy modeling based on clustering techniques have shown great progress in identification of nonlinear systems. Hence in this paper, Takagi–Sugeno (T–S) model is proposed for an inverted pendulum based on fuzzy c-means, Gustafson–Kessel (G–K) and Gath–Geva clustering techniques. Simulation results show that Gustafson–Kessel (G–K) clustering technique produces satisfactory performance.     

Fractional Control of a Humanoid Robot Reduced Model with Model Disturbances

There is an open discussion between those who defend mass-distributed models for humanoid robots and those in favor of simple concentrated models. Even though each of them has its advantages and disadvantages, little research has been conducted analyzing the control performance due to the mismatch between the model and the real robot, and how the simplifications affect the controller’s output. In this article we address this problem by combining a reduced model of the humanoid robot, which has an easier mathematical formulation and implementation, with a fractional order controller, which is robust to changes in the model parameters. This controller is a generalization of the well-known proportional–integral–derivative (PID) structure obtained from the application of Fractional Calculus for control, as will be discussed in this article. This control strategy guarantees the robustness of the system, minimizing the effects from the assumption that the robot has a simple mass distribution. The humanoid robot is modeled and identified as a triple inverted pendulum and, using a gain scheduling strategy, the performances of a classical PID controller and a fractional order PID controller are compared, tuning the controller parameters with a genetic algorithm.