Universal Practical Tracking Control of a Planar Underactuated Vehicle

In this article, a universal controller is proposed for a planar underactuated vehicle to track arbitrary trajectories including feasible/non‐feasible ones and fixed points. The controller design relies on several coordinate/input transformations, auxiliary trajectory design and the back‐stepping technique. The stability analysis shows that the position and orientation tracking errors are uniformly globally practically asymptotically convergent (UGPAC), and the velocity tracking errors are uniformly globally asymptotically convergent (UGAC) to a ball of origin. Moreover, if the tracked target is in uniform rectilinear motion or motionless, the whole closed‐loop tracking error system is uniformly globally practically asymptotically stable (UGPAS). The effectiveness of proposed control law is verified by simulation examples.     

Adaptive control of first-order systems with nonlinearparameterization

In this paper, an adaptive control method is presented for a class of first-order systems with nonlinear parameterization. The main features of the scheme are that a novel integral-type Lyapunov function is developed for constructing an asymptotically stable adaptive controller, and output tracking error bounds are provided to evaluate the control performance of the adaptive system. The design procedure and the effectiveness of the proposed controller are illustrated through an example study     

基于节能考虑的全向移动机器人鲁棒补偿轨迹跟踪控制

针对全向移动机器人在跟踪目标的过程中存在跟踪误差以及产生能量损耗的问题,首先构建一种新型机器人能耗模型,该模型能够有效预测机器人运行过程中各种能量消耗;其次,基于该能耗模型设置兼顾轨迹跟踪误差和能耗最小的性能指标函数,在其约束下,提出一种基于干扰鲁棒补偿的反馈节能控制器;然后,引入不确定性及干扰估计观测法,构建鲁棒补偿项,在满足能耗最优的前提下实现对外界干扰的有效抑制;最后,基于Lyapunov稳定性理论证明所提出的节能干扰鲁棒补偿控制系统是渐近稳定的.通过将所提出的控制器与比例微分控制器、$H_\infty$控制以及节能补偿控制进行比较,仿真结果表明,所提出的控制方法其控制精度更高、能量损耗更低、具有更强的鲁棒性.     

Velocity observer-based iterative learning control for robot manipulators

This article addresses the problem of designing an iterative learning control for trajectory tracking of rigid robot manipulators subject to external disturbances, and performing repetitive tasks, without using the velocity measurement. For solving this problem, a velocity observer having an iterative form is proposed to reconstruct the velocity signal in the control laws. Under assumptions that the disturbances are repetitive and the velocities are bounded, it has been shown that the whole control system (robot plus controller plus observer) is asymptotically stable and the observation error is globally asymptotically stable, over the whole finite time-interval when the iteration number tends to infinity. This proof is based upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed observer–controller schemes.     

Guaranteed cost non-fragile tracking control for omnidirectional rehabilitative training walker with velocity constraints

In this study, a new nonlinear tracking control method with velocity constraints performance is proposed for omnidirectional rehabilitative training walker. The aim of the study is to design an asymptotically stable nonfragile controller that can guarantee the safety of the rehabilitee and ensure tracking on a training trajectory planned by a physical therapist. According to Lyapunov theory, the guaranteed cost non-fragile controller can be designed to maintain stability in terms of solutions of linear matrix inequalities. The concept of safety velocity is given and the sufficient conditions for the existence of such a controller with safety velocity constraints performance are derived. As an application, simulation results confirm the effectiveness of the proposed method and verify that the walker can provide safe training velocity.     

Adaptive tracking with saturating input and controller integralaction

The authors consider the problem of controlling stable linear plants subject to input saturation constraints and parametric uncertainties. A globally stable adaptive controller which performs well in the presence of such constraints is designed, using a specific pole placement that accounts for the saturation constraint, an integral action to deal with the tracking problem, and an adaptive control law with an ad hoc excitation capability together with a parameter adaptation to cope with the parametric uncertainty. The proposed controller allows one to track slowly varying reference sequences. Particularly, in the case of a constant reference, the output tracking error vanishes asymptotically and the control input does stop saturating after a finite time     

Global asymptotic stability of a tracking sectorial fuzzy controller for robot manipulators.

This paper shows that fuzzy control systems satisfying sectorial properties are effective for motion tracking control of robot manipulators. We propose a controller whose structure is composed by a sectorial fuzzy controller plus a full nonlinear robot dynamics compensation, in such a way that this structure leads to a very simple closed-loop system represented by an autonomous nonlinear differential equation. We demonstrate via Lyapunov theory, that the closed-loop system is globally asymptotically stable. Experimental results show the feasibility of the proposed controller.     

Motion control of an omnidirectional mobile platform for trajectory tracking using an integral sliding mode controller

In this paper, a new tracking controller that integrates a kinematic controller (KC) with an integral sliding mode dynamic controller (ISMC) is designed for an omnidirectional mobile platform (OMP) to track a desired trajectory at a desired velocity. First, a posture tracking error vector is defined, and a kinematic controller (KC) is chosen to make the posture tracking error vector convergent to zero asymptotically. Second, an integral sliding surface vector is defined based on the angular velocity tracking error vector and its integral term. An integral sliding mode dynamic controller (ISMC) is designed to make the integral sliding surface vector and the angular velocity tracking error vector convergent to zero asymptotically. The above controllers are obtained based on the Lyapunov stability theory. To implement the designed tracking controller, a control system is developed based on PIC18F452. A scheme for measuring the posture tracking error vector using a camera sensor combined with an angular sensor is introduced. The simulation and experimental results are presented to illustrate the effectiveness and applicability of the proposed tracking controller.     

Redundant input guaranteed cost non-fragile tracking control for omnidirectional rehabilitative training walker

In this study, the problem of guaranteed cost non-fragile tracking control on the omnidirectional rehabilitative training walker is examined. The nonlinear redundant input method is proposed when one wheel actuator fault occurs. The aim of the study is to design an asymptotically stable controller that can guarantee the safety of the user and ensure tracking on a training path planned by a physical therapist. The guaranteed cost control and the asymptotically zero state detectable concept of the walker are presented, and the model of redundant degree is constructed. The cost performance index is defined to restrain initial oversize input forces. On the grounds of LMI, a controller with gain variations that can satisfy asymptotic stability is obtained using a common Lyapunov function for admissible uncertainties resulting from an actuator fault. Simulation results confirm the effectiveness of the proposed method and verify that the walker can provide safe sequential motion when one wheel actuator is at fault.

     

Passivity-based torque and flux tracking for induction motors with magnetic saturation

An observer-based, globally asymptotically stable torque and rotor flux magnitude tracking controller for induction motors under magnetic saturation is proposed. The controller is synthesized using the passivity-based techniques. The paper considers a magnetically saturated π-model of the motor without any simplifying assumptions. Motor fluxes are reconstructed by a closed-loop observer. Closed-loop stability of the overall scheme including the observer is demonstrated. Simulation results are given to illustrate the proposed scheme.     

Adaptive one-step-ahead control for non-minimum phase systems with input magnitude and rate constraints

The adaptive control design for linear stable plants with input magnitude and rate constraints is addressed. The proposed algorithm adopts the self-tuning regulator (STR) adaptive control principle with one-step-ahead control as its underlying control design. An important governing equation relating the prediction error to the 'input discrepancy' between adaptive control and the corresponding non-adaptive control is identified, independent of how the parameter estimates are attained. Together with the convergence property of least-square type estimation algorithm, the governing equation leads to a successful analysis on the convergence and tracking performance of the adaptive constrained one-step-ahead controller. Specifically, globally input matching property is maintained in the sense that the adaptive constrained control asymptotically matches its corresponding non-adaptive one. Furthermore, the desired tracking performance of the adaptive controller can be achieved asymptotically if the corresponding non-adaptive control is eventually out of the constraints. The proposed adaptive control is applicable to both minimum and non-minimum phase stable systems.     

Globally asymptotically stable tracking control for a trailer system

This article addresses a tracking controller design for a trailer system consisting of a steering tractor and a passive trailer linked with a rigid free joint and having nonholonomic constraints. We design the tracking controller using the Lyapunov direct method, for both forward and backward driving of the trailer system. Backward driving is unstable, and thus is more difficult than forward driving. In previous research, we proposed a globally asymptotically stable (GAS) tracking control for forward driving of a trailer system with nonholonomic constraints. In this article, we implement the GAS tracking controller for forward and backward driving, and perform experiments using visual feedback and remote control systems. The experimental results represent stable responses and demonstrate the effectiveness of our method. © 2002 Wiley Periodicals, Inc.     

Performance improvement using time delays in multivariable controller design

A new controller for linear multivariable ordinary systems is suggested in which distributed delays are included in the feedback loop. A general design approach to obtain this type of controller is suggested. It is shown that the resulting closed-loop system is asymptotically stable under some sufficient conditions. Sufficient conditions are derived under which the disturbance attenuation, the robustness against parameter variations, and the time-delay stability margins are improved by the proposed controller. The state feedback tracking controller and the dual-state observer are obtained by modification of the proposed controller.     

Distributed control of target cooperative encirclement and tracking using range-based measurements

This paper investigates a distributed coordinate-free control method of ground target cooperative encirclement and tracking for an unmanned aerial vehicle (UAV) formation. Different from the existing methods, the relevant information for the circumnavigation can be measured by the UAV sensors rather than directly from the tracked target. Based on these distance measurements, a multi-UAV encirclement guidance law that satisfies both target coordination and tracking is designed. According to the proposed lemma of interconnected system, the formation system under the guidance law is globally uniformly asymptotically stable. The effectiveness and advantages of the proposed controller are validated via simulations.     

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.     

Adaptive observer-based trajectory tracking control of nonholonomic mobile robots

In this paper, an adaptive observer-based trajectory tracking problem is solved for nonholonomic mobile robots with uncertainties. An adaptive observer is first developed to estimate the unmeasured velocities of a mobile robot with model uncertainties. Using the designed observer and the backstepping technique, a trajectory tracking controller is designed to generate the torque as an input. Using Lyapunov stability analysis, we prove that the closed-loop system is asymptotically stable with respect to the estimation errors and tracking errors. Finally, the simulation results are presented to validate the performance and robustness of the proposed control system against uncertainties.     

基于反步法的移动机器人鲁棒跟踪控制

以四轮移动机器人为研究对象,建立了机器人完整的数学模型,包括运动学模型、动力学模型以及驱动电机模型。在机器人数学模型的基础上,采用反步法的思想设计具有全局收敛特性的鲁棒轨迹跟踪控制器,设计中考虑了驱动电机模型使控制器更符合实际控制要求,并将其分解为运动学控制器、动力学控制器以及电机控制器三部分,降低了控制器设计的难度。构造了系统的李雅普诺夫函数,证明了该类型移动机器人在所得控制器作用下,能实现对给定轨迹的全局渐近追踪。仿真实验结果表明基于反步法的控制器是有效的。     

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     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

基于终端滑模的四旋翼飞行器非线性轨迹跟踪控制

考虑到四旋翼飞行器的传统内外环控制策略依赖时标分离假设,稳定性分析复杂,并且控制参数选取困难的缺点,提出了一种与传统内外环控制策略不同的轨迹跟踪控制器;首先将四旋翼飞行器数学模型进行相应的变换,以分解为高度、偏航角和纵横向三个级联的子系统,再使用终端滑模控制方法设计高度和偏航角子系统的控制器,使两个子系统的状态误差可以在有限时间内收敛到原点,之后基于变量非线性变换设计纵横向子系统的控制器,分析了闭环系统稳定性,证明了所设计的轨迹跟踪控制器可以保证闭环系统跟踪误差渐近稳定到原点,最后仿真实验的结果验证了所设计的控制器的有效性。