Quantized-states-based adaptive control against unknown slippage effects of uncertain mobile robots with input and state quantization

An adaptive tracking design strategy based on quantized state feedback is developed for uncertain nonholonomic mobile robots with unknown wheel slippage effects. All state variables and control torques are assumed to be quantized by the state and input quantizers, respectively, in a network control environment. Thus, the quantized state feedback information is only available for the tracking control design. An approximation-based adaptive controller using quantized states is recursively designed to ensure the robust adaptive tracking against unknown wheel slippage effects where the quantized-states-based adaptive mechanism is derived to compensate for unknown wheel slippage effects, system nonlinearities, and quantization errors. The boundedness of the quantization errors and estimated parameters in the closed-loop system is analyzed by presenting some theoretical lemmas. Based on these lemmas, we prove the uniform ultimate boundedness of closed-loop signals and the convergence of the trajectory tracking error in the presence of wheel slippage effects. Simulations verify the effectiveness of the resulting tracking scheme.     

Quantized feedback stabilization for a class of linear systems with nonlinear disturbances

The quantized feedback stabilization problem for a class of linear system with nonlinear disturbances is addressed, in which the system and controller are connected via a communication channel. In this case, the effect of quantization errors is studied. A practical quantized scheme is designed such that the transmission error decays to zero exponentially. Meanwhile, a sufficient condition in terms of linear matrix inequality for input-to-state stability (ISS) of the system is presented with regard to the transmission error. Therefore, a quantized stabilization of the system is guaranteed based on the ISS property. A simulation example for the single-link flexible joint robot is presented to demonstrate the effectiveness of the result.     

Adaptive control of kinematically redundant robots

A redundant robot has more degrees of freedom than those neededto position the Robert end-effector uniquely. In a usual robotictask, only end-effector position trajectory is specified. Thejoint position trajectory is unknown, and it must be selectedfrom a self-motion manifold for a specified end-effector. Inmany situations, the robot dynamic parameters such as the linkmass, inertia, and joint viscous friction are unknown. The lackof knowledge of the joint trajectory and the dynamic parametersmake it difficult to control redundant robots. In this paper we show, through careful formulation of the problem,that the adaptative control of redundant robots can be addressedas a reference-velocity traking problem in the joint space.A control law ensures bounded estimation of the unknown dynamicparameters of the robot, and the convergence to zero of thevelocity traking error is derived. To ensure the joint motionon the self-motion manifold remains bounded, a homeomorphictransformation is found. This transformation decomposes thedynamics of the velocity tracking error into a cascade systemconsisting of the dynamics in the end-effector error coordinatesand the dynamics on the self-motion manifold. The dynamics onthe self-motion manifold is shown to be related to the conceptof zero dynamics. In the shown that, if the reference jointtrajectory is selected to optimize a certain type of objectivefunction, then stable dynamics on the self-motion manifold result.This ensures the overall stability of the adaptive system. Detailedsimulations are given to test the theoretical developments.The proposed adaptive scheme does not require measurements ofthe joint acceleration or the inversion of the inertia matrixof the robot.     

Optimization of the Internal Dynamics of Underactuated Robots

A robot is underactuated if it possesses less control inputs than degrees of freedom, e.g. due to passive joints. The analysis of the mechanical design of these kinds of underactuated robots often shows that they are non-minimum phase, i.e. they have an internal dynamic which is not asymptotically stable. Therefore, feedback linearization is not possible, and output trajectory tracking becomes a very challenging task. It is shown that through an optimization procedure the mechanical design of an underactuated robot can be altered in such a way that the internal dynamics becomes stable. Thus feedback linearization of the underactuated robot becomes possible. In the optimization procedure, the design parameters are additional masses which are added to defined locations at different un-actuated links of the robot. The optimization criteria is two-stage and firstly requires that all eigenvalues of the linearized zero-dynamics are in the left half-plane and secondly that initial errors in the zero-dynamics decay rapidly. Due to the two-stage criteria computation the optimization problem is discontinuous. Also there might be many local minima. Therefore a particle swarm optimization procedure is used. The efficiency of this optimization approach is demonstrated by simulation of an underactuated robot. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results.     

Novel design of adaptive neural network controller for a class of non-affine nonlinear systems

The tracking control problem is studied for a class of uncertain non-affine systems. Based on the principle of sliding mode control (SMC), using the neural networks (NNs) and the property of the basis function, a novel adaptive design scheme is proposed. A novel Lyapunov function, which depends on both system states and control input variable, is used for the development of the control law and the adaptive law. The approach overcomes the drawback in the literature. In addition, the lumped disturbances are taken in account. By theoretical analysis, it is proved that tracking errors asymptotically converge to zero. Finally, simulation results demonstrate the effectiveness of the proposed approach.     

Distributed subgradient method for multi‐agent optimization with quantized communication

This paper focuses on a distributed optimization problem associated with a time‐varying multi‐agent network with quantized communication, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on subgradient methods, we propose a distributed algorithm to solve this problem under the additional constraint that agents can only communicate quantized information through the network. We consider two kinds of quantizers and analyze the quantization effects on the convergence of the algorithm. Furthermore, we provide explicit error bounds on the convergence rates that highlight the dependence on the quantization levels. Finally, some simulation results on a l₁‐regression problem are presented to demonstrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

航天器编队飞行多目标姿态快速跟踪鲁棒控制

研究了航天器编队飞行多目标姿态跟踪鲁棒控制问题．主航天器装有一个快速机动天线和一个星载相机．考虑相机对地面目标跟踪,同时考虑天线与从航天器通信的空间任务．通过引入角速度约束和姿态角约束,分别推导了相机和天线的参考姿态角、角速度和角加速度．提出期望逆系统的概念,将三维空间姿态跟踪问题转化为调节问题,简化了控制器的设计．考虑存在参数摄动和外部干扰力矩的情况,基于期望逆系统和滑模控制,设计了鲁棒姿态跟踪控制器,并利用Liapunov稳定性理论证明了控制系统的渐近稳定性．以两航天器编队飞行多目标跟踪为例进行数值仿真,结果表明所设计的控制器具有良好的鲁棒性和优越的跟踪性能．     

自适应模糊变结构控制的研究

本文主要研究一类具有未知常数控制增益的非线性系统的自适应模糊控制问题,提出了一种能够利用专家的语言信息和数字信息的自适应模糊变结构控制器的设计方案。通过理论分析,证明了模糊变结构控制系统是全局稳定的,跟踪误差可收敛到零的一个邻域内     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.     

A velocity observer design for tracking task-based motions of unicycle type mobile robots

The paper presents a design of a nonlinear velocity observer and its application within a model-based tracking control strategy for tracking task-based motions of unicycle type mobile robots. The strategy is the model reference tracking control strategy for programmed motion and it enables switching between controllers employed in it to improve a tracking precision as well as switching between coordinates used for modeling based on a type of a nonholonomic system. The strategy benefits by adding the velocity observer to its architecture due to the reduction of a number of measurements needed for feedback tracking.     

Quasi-projective and finite-time synchronization of delayed fractional-order BAM neural networks via quantized control

This paper deals with the problems of quasi-projective synchronization (QPS) and finite-time synchronization (FTS) for a kind of delayed fractional-order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite-time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols.     

力觉临场感遥操作机器人系统的鲁棒控制

力觉临场感遥操作机器人系统的通信通道中存在通信时延,而且在机器人和环境建模中,系统参数存在不确定性,以致可能造成系统不稳定和操作性能降低.针对通信时延和系统不确定性,建立系统的状态方程,利用鲁棒控制理论,提出用力、位置和速度反馈的控制方法.分析与实验表明,用该方法设计的控制器能使系统鲁棒渐近稳定,而且能使系统完全透明.     

基于Udwadia-Kalaba方法的并联机器人鲁棒伺服约束控制

针对2自由度冗余驱动并联机器人轨迹跟踪控制问题,提出了一种基于Udwadia Kalaba方程的鲁棒伺服控制方法.在负载、外部干扰以及制造误差的影响下,无法得到机器人精确、完整的运动模型,导致机器人控制性能变差.为解决这类不确定性带来的影响,提出了一种鲁棒控制方法.该方法通过保证系统的一致有界性和一致最终有界性,使系统能够精确跟踪理想约束轨迹.此外,该方法采用Udwadia Kalaba方程,求解控制过程中满足系统理想约束所需要的约束力.Udwadia Kalaba方程不需要Lagrange乘子或伪广义速度等辅助变量,可以同时处理完整约束和非完整约束,且可以获得满足轨迹约束的约束力解析解.利用Lyapunov函数对该鲁棒控制方法的稳定性进行了理论证明,并且通过仿真实验,验证了该鲁棒控制方法能够在非理想条件下实现给定轨迹的高精度跟踪控制.     

Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters

This paper deals with the problem of adaptive robust synchronization of chaotic systems based on the Lyapunov theory. A controller is designed for a feedback linearizable error system with matched uncertainties. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system as time tends to infinity. Since this approach does not require any information about the bound of uncertainties, this information is not needed in advance. In order to prevent the frequent switching phenomenon in the control signal, the method is modified such that the norm of tracking error is bounded. Numerical simulations on two uncertain Rossler systems with matched uncertainties show fast responses of tracking error, while the errors are Uniformly Ultimately Bounded, and the control signal is reasonably smooth.     

Adaptive tuning of the fuzzy controller for robots

An adaptive tuning algorithm of the fuzzy controller is developed for a class of serial-link robot arms. The algorithm can on-line tune parameters of premise and consequence parts of fuzzy rules of the fuzzy basis function (FBF) controller. The main part of the fuzzy controller is a fuzzy basis function network to approximate unknown rigid serial-link robot dynamics. Under some mild assumptions, a stability analysis guarantees that both tracking errors and parameter estimate errors are bounded. Moreover, a robust technique is adopted to deal with uncertainties including approximation errors and external disturbances. Simulations of the proposed controller on the PUMA-560 robot arm demonstrate the effectiveness.     

Controlling of a mobile robot with a trailer and its nilpotent approximation

This work studies a number of approaches to solving the motion planning problem for a mobile robot with a trailer. Different control models of car-like robots are considered from the differential-geometric point of view. The same models can also be used for controlling a mobile robot with a trailer. However, in cases where the position of the trailer is of importance, i.e., when it is moving backward, a more complex approach should be applied. At the end of the article, such an approach, based on recent works in sub-Riemannian geometry, is described. It is applied to the problem of reparking a trailer and implemented in the algorithm for parking a mobile robot with a trailer.     

Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.     

Locally oriented potential field for controlling multi-robots

In this paper, we present an extension of the boundary value problem path planner (BVP PP) to control multiple robots in a robot soccer scenario. This extension is called Locally Oriented Potential Field (LOPF) and computes a potential field from the numerical solution of a BVP using local relaxations in different patches of the solution space. This permits that a single solution of the BVP endows distinct robots with different behaviors in a team. We present the steps to implement LOPF as well as several results obtained in simulation.