An Approach to Design MIMO FO Controllers for Unstable Nonlinear Plants

This paper develops an approach to control unstable nonlinear multi-inputs multi-output (MIMO) square plants using MIMO fractional order (FO) controllers. The controller design uses the linear time invariant (LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix (TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function (TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D (Derivative) TF is related to a FO TF of the form Dδ, δ = [0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.      

A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model

In this article, a nonlinear dynamic model of a flexible manipulator is derived through finite element method associated with Lagrange approach. The flexible manipulator is modeled as an Euler-Bernoulli beam driven by a motor at its base and with a point mass tip payload. The generalized coordinates of the system are selected to be the displacements and rotations of the nodes on the considered flexible beam, and such that a state space model is obtained with all the state variables having physical meanings. Based on this model, an effective nonlinear feedback controller is developed to control the tip position. Furthermore, an efficient algorithm is developed to calculate the inverse of the system's inertia matrix for real-time implementation. Numerical simulation results are given to show the effectiveness of the controller and its robustness in handling payload variations. © 1997 John Wiley & Sons, Inc.     

Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks

This paper mainly focuses on designing a sliding mode boundary controller for a single flexible-link manipulator based on adaptive radial basis function (RBF) neural network. The flexible manipulator in this paper is considered to be an Euler-Bernoulli beam. We first obtain a partial differential equation (PDE) model of single-link flexible manipulator by using Hamiltons approach. To improve the control robustness, the system uncertainties including modeling uncertainties and external disturbances are compensated by an adaptive neural approximator. Then, a sliding mode control method is designed to drive the joint to a desired position and rapidly suppress vibration on the beam. The stability of the closed-loop system is validated by using Lyapunov’s method based on infinite dimensional model, avoiding problems such as control spillovers caused by traditional finite dimensional truncated models. This novel controller only requires measuring the boundary information, which facilitates implementation in engineering practice. Favorable performance of the closed-loop system is demonstrated by numerical simulations.     

Trajectory control of a two DOF rigid–flexible space robot by a virtual space vehicle

Model based control schemes use inverse dynamics of the robot arm to produce the main torque component necessary for trajectory tracking. For a model-based controller one is required to know the model parameters accurately. This is a very difficult job especially if the manipulator is flexible. This paper presents a control scheme for trajectory control of the tip of a two arm rigid–flexible space robot, with the help of a virtual space vehicle. The flexible link is modeled as an Euler–Bernoulli beam. The developed controller uses the inertial parameters of the base of the space robot only. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy. The efficacy of the controller is shown through simulated and animation results.     

Collision‐free control of robotic manipulators in the task space

This paper addresses the problem of position control of robotic manipulators in the task space with obstacles. A computationally simple class of task space regulators consisting of a transpose Jacobian controller plus an integral term including the task error and the gradient of a penalty function generated by obstacles is proposed. The Lyapunov stability theory is used to derive the control scheme. Through the use of the exterior penalty function approach, collision avoidance of the robot with obstacles is ensured. The performance of the proposed control strategy is illustrated through computer simulations for a direct‐drive arm of a SCARA type manipulator operating in both an obstacle‐free task space and a task space including obstacles. © 2005 Wiley Periodicals, Inc.     

A new controller design for a flexible one-link manipulator

A novel controller design for noncollocated flexible one-link manipulator arm tip position control based on variable structure sliding mode control is presented. Using the assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncollocated manipulator tip position control is then designed. The position state variables are obtained directly from the inversion of the output submatrix multiplied by the sensor measurements. The velocity state variables are estimated through decoupled estimators-a separate first-order observer for each of the system's modes under consideration. Different sampling periods are used for the estimator and the controller. The performance of the controller is evaluated through a series of simulations, followed by an analysis of the designed control system     

An Adaptive Regulator of Robotic Manipulators in the Task Space

This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.     

Query based model learning and stable tracking of a robot arm using radial basis function network

In the context of a robot manipulator, a generalized neural emulator over the complete workspace is very difficult to obtain because of dimensionally insufficient training data. A query based learning algorithm is proposed in this paper that can generate new examples where control inputs are independent of states of the system. This algorithm is centered around the concept of network inversion using an extended Kalman filtering based algorithm. This is a novel idea since robot manipulator is an open loop unstable system and generation of control input independent of state is a research issue for neural model identification. Two trajectory independent stable control schemes have been designed using the neural emulator. One of the control schemes uses forward-inverse-modeling approach to update the controller parameters adaptively following Lyapunov function synthesis technique. The proposed scheme is trajectory independent unlike the back-propagation scheme. The second type of controller predicts the minimum variance estimate of control action using recall process (network inversion) and the control law is derived following a Lyapunov function synthesis approach so that the closed loop system consisting of controller and neural emulator remains stable. The simulation experiments show that the model validation approach is efficient and the proposed control schemes guarantee stable accurate tracking.     

Set-valued observers and optimal disturbance rejection

A set-valued observer (also called guaranteed state estimator) produces a set of possible states based on output measurements and models of exogenous signals. We consider the guaranteed state estimation problem for linear time-varying systems with a priori magnitude bounds on exogenous signals. We provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l^∞-induced norm sense. We then consider the utility of set-valued observers for disturbance rejection with output feedback and derive the following general separation structure. An optimal controller can consist of a set-valued observer followed by a static nonlinear function on the observed set of possible states. A general construction of this function is provided in the scalar control case. Furthermore, in the special case of full-control, i.e., the number of control inputs equals the number of states, optimal output feedback controllers can take the form of an optimal estimate of the full-state feedback controller     

Belief-Driven Manipulator Visual Servoing for Less Controlled Environments

This paper presents the architecture of a feedforward manipulator control strategy based on a belief function that may be appropriate for less controlled environments. In this architecture, the belief about the environmental state, as described by a probability density function, is maintained by a recursive Bayesian estimation process. A likelihood is derived from each observation regardless of whether the targeted features of the environmental state have been detected or not. This provides continuously evolving information to the controller and allows an inaccurate belief to evolve into an accurate belief. Control actions are determined by maximizing objective functions using non-linear optimization. Forward models are used to transform control actions to a predicted state so that objective functions may be expressed in task space. The first set of examples numerically investigates the validity of the proposed strategy by demonstrating control in a two dimensional scenario. Then a more realistic application is presented where a robotic manipulator executes a searching and tracking task using an eye-in-hand vision sensor.     

Position and force tracking of a two‐manipulator system manipulating a flexible beam

This article discusses the issue of hybrid position and force control of a two‐manipulator system manipulating a flexible beam in trajectory tracking. Unlike our previous approach of set‐point position control in the trajectory tracking, the system coordinates are hard to be regulated to the desired states with nonzero tracking velocities under continuous feedback control. In this study, we design a hybrid position and force tracking controller while using saturation control to compensate for the effect of beam vibration dynamics on the tracking performance. All parameters and states used in the controller are readily available so that the proposed method is feasible to implement. Under the proposed controller, the tracking error asymptotically converges to a predetermined boundary. Simulation results demonstrate the validity of the proposed approach. © 2001 John Wiley & Sons, Inc.     

Partially decoupled approach of extended non-minimal state space predictive functional control for MIMO processes

This paper presents a partially decoupled design of the state space predictive functional control for MIMO processes. The multivariable process is first treated into MISO process by a simple Cramer's rule solution to linear equations which provides a balance between model complexity and control system design, and then the derived MISO process based extended state space predictive functional control is presented. The overall design of the controller enables the controller to consider both the process state dynamics and the output dynamics, thus improved control performance for tracking set-points and disturbance rejection is resulted. The proposed controller is tested on both model match and model mismatch cases to demonstrate its superiority. In addition, a closed-form of transfer function representation that facilitates frequency analysis of the control system is provided to give further insight into the proposed method.     

Task space control of a welding robot using a fuzzy coordinator

This paper introduces a fuzzy coordinator as a novel application of fuzzy controller. A control transformation from the task space to the joint space is required to control a robot manipulator in the task space. Because the actuators operate in the joint space while the manipulator is controlled in the task space. A conflict between two spaces is produced due to using an imprecise transformation. Fuzzy coordinator coordinates two spaces by modifying the control transformation affected by uncertainties. The fuzzy coordinator is designed simply and operates as a robust controller. The role of fuzzy coordinator is analyzed and illustrated in the robust control of a welding robot in the task space. A circular trajectory is planned for a welding task performed by a SCARA robot. The fuzzy coordinator is then used to improve the performance of control system affected by imprecise transformations including the imprecise path transformation and the approximated feedback linearization.     

基于CAN总线控制系统的航天特种机械臂设计

航天特种机械臂具备精确操作和视觉识别的能力,在载人航天领域中广泛应用,为了在复杂环境中精准完成陆基装配任务,设计基于CAN总线控制系统的航天特种机械臂。从关节、连杆、驱动电机、锁紧制动器等方面,组装航天特种机械臂结构元件。装设航天特种机械臂控制器,在控制器中加设一个串行通信接口,将控制器连接到CAN总线中,配置CAN总线控制系统的通信协议,完成航天特种机械臂硬件结构设计。利用航天特种机械臂中传感器设备,检测航天特种机械臂实时位姿,补偿航天特种机械臂重力负载。根据机械臂工作任务,规划移动轨迹,在控制器的支持下,通过控制量的计算与通信,实现航天特种机械臂的控制功能。性能测试实验表明,设计基于CAN总线控制系统的航天特种机械臂平均位置和关节姿态角的控制误差分别为3.0m和0.32°,平均形变量为2.64m2,具有较好的控制性能和抗压性能。     

Motion Control of a Nonholonomic Mobile Manipulator in Task Space

In this paper, the motion control of a mobile manipulator subjected to nonholonomic constraints is investigated. The control objective is to design a computed‐torque controller based on the coupled dynamics of the mobile manipulator. The proposed controller achieves the capability of simultaneous tracking of a reference velocity for the mobile base and a reference trajectory for the end‐effector. The aforementioned reference velocity and trajectory are defined in the task space, such task setting imitates the actual working conditions of a mobile manipulator and thus makes the control problem practical. To solve this tracking problem, a steering velocity is firstly designed based on the first‐order kinematic model of the nonholonomic mobile base via dynamic feedback linearization. The main merit of the proposed steering velocity design is that it directly utilizes the reference velocity set in the task space without requiring the knowledge of a reference orientation. A torque controller is subsequently developed based on a proposed Lyapunov function which explicitly considers the coupled dynamics of the mobile manipulator to ensure the mobile base and end‐effector track the reference velocity and trajectory respectively. This proposed computed‐torque controller is able to realize asymptotic stability of both the base velocity tracking error and the end‐effector motion tracking error. Simulations are conducted to demonstrate the effectiveness of the proposed controller.     

Sliding Mode Adaptive Neural-Network Control for Nonholonomic Mobile Modular Manipulators

A general mobile modular manipulator can be defined as a m-wheeled holonomic/nonholonomic mobile platform combining with a n-degree of freedom modular manipulator. This paper presents a sliding mode adaptive neural-network controller for trajectory following of nonholonomic mobile modular manipulators in task space. Dynamic model for the entire mobile modular manipulator is established in consideration of nonholonomic constraints and the interactive motions between the mobile platform and the onboard modular manipulator. Multilayered perceptrons (MLP) are used as estimators to approximate the dynamic model of the mobile modular manipulator. Sliding mode control and direct adaptive technique are combined together to suppress bounded disturbances and modeling errors caused by parameter uncertainties. Simulations are performed to demonstrate that the dynamic modeling method is valid and the controller design algorithm is effective.     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

机械手臂的多模型预测控制

针对机械手臂的非线性特点,提出了基于隶属度函数的多模型预测控制方法。该方法首先根据机械手臂的特点,选择合适的调度变量,将机械手臂的工作空间划分为若干个工作子空间,在每个子空间内的平衡点处对机械手臂进行线性化处理,得到相应的线性子模型,从而得到机械手臂的多模型表示;其次针对每个线性子模型设计局部预测控制器,使其在相应的子空间内达到控制要求;最后选择梯形隶属度函数与局部预测控制器进行加权求和,获得全局多模型预测控制器,以对机械手臂进行控制。仿真结果表明,当机械手臂的工作条件在大范围内变化时,全局多模型预测控制器的控制性能远优于常规PD控制器,达到了预期的控制目的。     

基于扩张状态观测的机器人分散鲁棒跟踪控制

针对模型不确定性多关节机器人的轨迹跟踪控制问题, 提出一种基于扩张状态观测补偿的关节独立分散鲁棒控制方法. 设计多个并联的扩张状态观测器, 分别对每个独立关节的未知模型动态与外部扰动进行动态估计和补偿, 采取非线性状态反馈控制以提高系统的控制性能. 各个关节的控制完全独立, 因而控制器结构简单、可靠、易于实现. 对所设计的关节分散鲁棒控制器的 Lyapunov 稳定性进行了分析, 证明系统是指数收敛全局一致最终有界稳定的. 对 PUMA560 机械手的大量控制仿真验证了本文方法的有效性.