Adaptive stabilization of mobile manipulators

This paper considers the motion control problem for uncertain mobile manipulator systems comprised of a robotic arm mounted on a wheeled mobile platform. More specifically, we address the problem of stabilizing mobile manipulators in the presence of uncertainty regarding the system dynamic model. It is proposed that a simple and effective solution to this problem can be obtained by combining ideas from homogeneous system theory and adaptive control theory. Thus each of the proposed control systems consists of two subsystems: a (homogeneous) kinematic stabilization strategy, which generates a desired velocity trajectory for the mobile manipulator, and an adaptive control scheme, which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented without knowledge of the details of the system dynamic model. Moreover, it is demonstrated that exponential rates of convergence can be achieved with this methodology. The efficacy of the proposed stabilization strategies is illustrated through computer simulations with two mobile manipulators. © 1998 John Wiley & Sons, Inc.     

Adaptive control of nonholonomic robotic systems

This paper considers the problem of controlling the motion of nonholonomic robotic systems in the presence of uncertainty regarding the system model and state, and presents a class of adaptive controllers as a solution to this problem. The proposed control strategies provide simple and robust solutions to a number of important nonholonomic system control problems, including stabilization to an equilibrium manifold, motion control to an equilibrium point via trajectory tracking, and stabilization to an equilibrium point. All of the schemes are computationally efficient, are implementable without knowledge of the system dynamic model, and ensure uniform boundedness of all signals and accurate motion control; furthermore, most of the controllers can be implemented without rate measurements. The efficacy of the proposed approach is illustrated through extensive computer simulations with nonholonomic robotic systems arising from explicit constraints on the system kinematics and from symmetries of the system dynamics. © 1998 John Wiley & Sons, Inc.     

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.     

含未校准摄像机参数的非完整移动机器人自适应动态反馈跟踪控制

研究基于视觉伺服的不确定非完整移动机器人的跟踪控制问题.基于视觉反馈和状态输入变换,提出一类非完整运动学系统的不确定模型,并运用两个新的变换,对3种不同情况分别设计自适应动态反馈控制器来跟踪不确定系统的期望轨迹.利用李雅普诺夫方法和推广的Barbalat引理,严格证明了误差系统的收敛性.仿真结果验证了所提方法的有效性.     

一类非完整系统的全局镇定

当非完整系统只能局部转换为链式形式时, 由于存在变换奇异点集合, 针对链式系统所设计的全局反馈控制律只能局部镇定原非完整系统, 而且当期望状态接近奇异点时, 闭环系统的吸引区很小. 本文针对一类可局部转换为链式系统的非完整系统, 首先利用吸引区是状态空间中的一个不变集且与变换奇异点集不相交的条件导出了一个吸引区的不变子集, 然后给出了将系统状态从任意点驱动到吸引区不变子集内的开环控制算法, 最后结合开环控制和闭环控制得到一种混合控制算法. 该混合控制算法可以保证任意不在变换奇异点集合内的期望状态是全局渐近稳定的. 对平面两转动关节空间机器人的仿真结果证实了算法的有效性.     

On trajectory and force tracking control of constrained mobile manipulators with parameter uncertainty

This paper studies the trajectory and force tracking control problem of mobile manipulators subject to holonomic and nonholonomic constraints with unknown inertia parameters. Adaptive controllers are proposed based on a suitable reduced dynamic model, the defined reference signals and the mixed tracking errors. The proposed controllers not only ensure the entire state of the system to asymptotically converge to the desired trajectory but also ensure the constraint force to asymptotically converge to the desired force. A detailed numerical example is presented to illustrate the developed methods.     

From Trajectory Tracking Control to Leader–Follower Formation Control

Abstract

This work investigates the leader–follower formation control of multiple nonholonomic mobile robots. First, the formation control problem is converted into a trajectory tracking problem and a tracking controller based on the dynamic feedback linearization technique drives each follower robot toward its corresponding reference trajectory in order to achieve the formation. The desired orientation for each follower is selected such that the nonholonomic constraint of the robot is respected, and thus the tracking of the reference trajectory for each follower is feasible. An adaptive dynamic controller that considers the actuators dynamics in the design procedure is proposed. The dynamic model of the robots includes the actuators dynamics in order to obtain the velocities as control inputs instead of torques or voltages. Using Lyapunov control theory, the tracking errors are proven to be asymptotically stable and the formation is achieved despite the uncertainty of the dynamic model parameters. In order to assess the proposed control laws, a ROS-framework is developed to conduct real experiments using four ROS-enabled mobile robots TURTLEBOTs. Moreover, the leader fault problem, which is considered as the main drawback of the leader–follower approach, is solved under ROS. An experiment is conducted where in order to overcome this problem, the desired formation and the leader role are modified dynamically during the experiment.     

非完整移动机器人的轨迹跟踪控制

讨论基于运动学模型的非完整移动机器人的轨迹跟踪控制问题。在一定的假设条件下实现了全局指数跟踪，该假设允许参考模型角速度和平移速度均趋于零，并将该方法推广到 动力学模型。仿真例子证明了该方法的有效性。     

FEEDBACK STABILIZATION OF NONHOLONOMIC CONTROL SYSTEMS USING MODEL DECOMPOSITION

This paper presents a simple and systematic approach for feedback stabilization of nonholonomic control systems. Its effectiveness is tested on two different nonholonomic control systems such as: a front wheel drive car, and a mobile robot with trailer. The method relies on the decomposition of model into two subsystems. One subsystem is stabilized by using the trajectory interception approach and other subsystem is steered by using sinusoidal inputs. The mixture of both types of control stabilizes the actual system. This approach does not necessitate the conversion of the system model into a “chained form”, and thus does not rely on any special transformation techniques. The approach presented is general and can be employed to control a variety of mechanical systems with velocity constraints.     

Adaptive tracking control of uncertain nonholonomic dynamic system

This note considers the tracking problem of nonholonomic dynamic systems with unknown inertia parameters. A new controller is proposed relying on newly defined tracking errors and the passivity property of the nonholonomic dynamic system. The proposed controller ensures that the entire state of the system asymptotically tracks the desired trajectory. Simulation results show effectiveness of the proposed controller     

Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots

In this paper, we investigate the output consensus problem of tracking a desired trajectory for a class of systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters. The subsystems are allowed to have non-identical dynamics, whereas with similar structures and the same yet arbitrary system order. And the communication status among the subsystems can be represented by a directed graph. Different from the traditional centralized tracking control problem, only a subset of the subsystems can obtain the desired trajectory information directly. A distributed adaptive control approach based on backstepping technique is proposed. By introducing the estimates to account for the parametric uncertainties of the desired trajectory and its neighbors’ dynamics into the local controller of each subsystem, information exchanges of online parameter estimates and local synchronization errors among linked subsystems can be avoided. It is proved that the boundedness of all closed-loop signals and the asymptotically consensus tracking for all the subsystems’ outputs are ensured. A numerical example is illustrated to show the effectiveness of the proposed control scheme. Moreover, the design strategy is successfully applied to solve a formation control problem for multiple nonholonomic mobile robots.     

一类非完整约束动力学系统的人工场导向控制

对于一类具有轮式移动机构的非完整动力学系统,本文通过建立人工场的方法来实 现其位姿镇定、轨迹跟踪和路径跟踪等控制问题.人工场用于导向和控制方向角,而通过辅助 的线速度控制以获取最佳收敛路径. 控制器设计中同时兼顾动力学扰动及实际系统速度和输 出力矩的饱和限制,所得控制器对于跟踪问题仅需知道期望位姿,而且结构简单、鲁棒性强、 便于实现.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator

In this paper, a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model, the discontinuous coordinate transformation and the “reaching law method” in variable structure control design. The proposed approach converts the stabilization problem of an n-dimensional chained system into the pole-assignment problem of an (n−3)-dimensional linear time-invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems.     

Visual servoing tracking control of uncalibrated manipulators with a moving feature point

The paper is concerned with the problem of uncalibrated visual servoing robots tracking a dynamic feature point along with the desired trajectory. A nonlinear observer and a nonlinear controller are proposed, which allow the considered uncalibrated visual servoing robotic system to fulfil the desired tracking task. Based on this novel control method, a dynamic feature point with unknown motion parameters can be tracked effectively along with the desired trajectory, even with multiple uncertainties existing in the camera, the kinematics and the manipulator dynamics. By the Lyapunov theory, asymptotic convergence of the image errors to zero with the proposed control scheme is rigorously proven. Simulations have been conducted to verify the performance of the proposed control scheme. The results demonstrated good convergence of the image errors.     

非完整移动机器人的有限时间跟踪控制算法研究

对非完整移动机器人的有限时间轨迹跟踪控制问题进行讨论．与基于非连续状态反馈的传统有限时间控制算法相比，基于连续状态反馈的有限时间控制算法更适合于控制工程应用．利用该连续系统有限时间控制技术，设计一种连续的状态反馈跟踪控制算法．使得对角速度为非零常数的期望轨迹，非完整移动机器人能够实现全局跟踪，并能在有限时间内完全跟踪上期望轨迹．仿真结果表明了该方法的有效性．     

Decentralised consensus-based formation tracking of multiple differential drive robots

This article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Robust motion tracking control of partially nonholonomic mechanical systems

This paper proposes a stable motion tracking control law for mechanical systems subject to both nonholonomic and holonomic constraints. The control law is developed at the dynamic level and can deal with model uncertainties. The proposed control law ensures the desired trajectory tracking of the configuration state of the closed-loop system. A global asymptotic stability result is obtained in the Lyapunov sense. A detailed example is presented to illustrate the proposed method.     

Dynamic Modeling and Tracking Control of a Nonholonomic Wheeled Mobile Manipulator with Dual Arms

This paper presents methodologies for dynamic modeling and trajectory tracking of a nonholonomic wheeled mobile manipulator (WMM) with dual arms. The complete dynamic model of such a manipulator is easily established using the Lagrange’s equation and MATHEMATICA. The structural properties of the overall system along with its subsystems are also well investigated and then exploited in further controller synthesis. The derived model is shown valid by reducing it to agree well with the mobile platform model. In order to solve the path tracking control problem of the wheeled mobile manipulator, a novel kinematic control scheme is proposed to deal with the nonholonomic constraints. With the backstepping technique and the filtered-error method, the nonlinear tracking control laws for the mobile manipulator system are constructed based on the Lyapunov stability theory. The proposed control scheme not only achieves simultaneous trajectory and velocity tracking, but also compensates for the dynamic interactions caused by the motions of the mobile platform and the two onboard manipulators. Simulation results are performed to illustrate the efficacy of the proposed control strategy.