A nonholonomic control method for stabilizing an X4-AUV

A nonholonomic control method is considered for stabilizing all attitudes and positions (x, y, or z) of an underactuated X4 autonomous underwater vehicle (AUV) with four thrusters and six degrees of freedom (DOF), in which the positions are stabilized according to the Lyapunov stability theory. A dynamic model is first derived, and then a sequential nonlinear control strategy is implemented for the X4-AUV which is composed of translational and rotational subsystems. A controller for the translational subsystem stabilizes one position out of the x-, y-, and z-coordinates, whereas controllers for the rotational subsystems generate the desired roll, pitch, and yaw angles. Thus, the rotational controllers stabilize all the attitudes of the X4-AUV at the desired (x-, y-, or z-) position of the vehicle. Some numerical simulations are conducted to demonstrate the effectiveness of the proposed controllers.     

欠驱动船舶的光滑时变指数镇定

船舶水平面运动的欠驱动特性使船舶运动控制的研究具有了新的内涵．本文在船舶水平面运动的运动学及动力学模型基础上,将其演化为二阶系统方程组．针对其欠驱动的特性,借助微分同胚变换及控制输入变换将其转化为两个子系统,分别设计状态反馈控制律,从而得到了原系统的具有指数收敛速率的时变光滑反馈镇定律,实现闭环系统所有状态全局指数收敛至平衡点．该方法可用于欠驱动船舶动力定位或自动泊位控制．最后的仿真试验验证表明本方法是有效的．     

Time-varying exponential stabilization of the position and attitudeof an underactuated autonomous underwater vehicle

The paper considers feedback stabilization of the position and attitude of an autonomous underwater vehicle (AUV) with a reduced number of actuators. A nonlinear model describing both the dynamics and the kinematics of an AUV is studied. The paper shows that previous results on attitude stabilization of a spacecraft can be applied to exponentially stabilize both the position and attitude of an AUV using only four, possibly three, actuators. Simulation results are presented     

Exponential stabilization of an underactuated autonomous surface vessel

This paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters. It is first shown that although the system is not asymptotically stabilizable to a given configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium. Time-invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates. A simulation example is included to demonstrate the results.     

Global uniform asymptotic stabilization of an underactuated surface vessel

Explicit formulas of smooth time-varying state feedbacks, which make the origin of an underactuated surface vessel globally uniformly asymptotically stable, are proposed. The construction of the feedback extensively relies on the backstepping approach. The feedbacks constructed are time-periodic functions.     

Asymptotic stabilization of some equilibria of an underactuated underwater vehicle

The stabilization problem for selected relative equilibria of an underactuated rigid body, modelling a simple underwater vehicle, moving in an ideal fluid is addressed. State feedback control laws achieving local asymptotic stability of a forward motion and of a diving/rising with forward/reverse motion are proposed. The control design exploits the Hamiltonian nature of the system to be controlled and it is based on the so-called interconnection and damping assignment (IDA) procedure. Simulation results complete the work.     

Switched seesaw control for the stabilization of underactuated vehicles

This paper addresses the stabilization of a class of nonlinear systems in the presence of disturbances, using switching controllers. To this effect we introduce two new classes of switched systems and provide conditions under which they are input-to-state practically stable (ISpS). By exploiting these results, a methodology for control systems design—called switched seesaw control—is obtained that allows for the development of nonlinear control laws yielding input-to-state stability. The range of applicability and the efficacy of the methodology proposed are illustrated via two nontrivial design examples. Namely, stabilization of the extended nonholonomic double integrator (ENDI) and stabilization of an underactuated autonomous underwater vehicle (AUV) in the presence of input disturbances and measurement noise.     

Universal controllers for stabilization and tracking of underactuated ships

We examine the problem of universal control for underactuated surface ships with only surge force and yaw moment. Namely, a single controller is to be designed to achieve stabilization and tracking simultaneously. We propose, in this paper, the first universal controller of which the synthesis is based on Lyapunov's direct method and backstepping technique. Our result is extendible to the input-saturation when the surge and yaw velocities are considered as the controls. Numerical simulations are provided to validate the effectiveness of the proposed controller and to demonstrate its sensitivity with respect to model parameters.     

A simple robust control for global asymptotic position stabilization of underactuated surface vessels

Global asymptotic stabilization of underactuated surface vessels is generally achieved only by designing complicated controllers. This paper proposes a very simple control law that globally asymptotically stabilizes the position of underactuated surface vessel to a desired constant location and its velocities to zero. The proposed controller is independent of velocity signals and is robust to model parameters. It neither includes an observer nor an adaptive/sliding‐mode law. Controller development and stability analysis rely on a novel Lyapunov function and LaSalle's theorem. Furthermore, by extending the proposed control strategy, a saturated control law is also obtained ensuring the semiglobal asymptotic stability of position error system. Effectiveness of the proposed control schemes is demonstrated by simulation examples. Copyright © 2017 John Wiley & Sons, Ltd.     

A switching algorithm for global exponential stabilization of uncertain chained systems

This note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances. The objective is to design a robust nonlinear state feedback law such that the closed-loop system is globally Kexponentially stable. We propose a novel switching control strategy involving the use of input/state scaling and integrator backstepping. The new features of our controllers include the ability to achieve Lyapunov stability, exponential convergence, and robustness to a set of uncertain drift terms.     

欠驱动水面机器人变周期全局渐近镇定控制

为了实现欠驱动水面机器人的全局渐近镇定,首先借助微分同胚变换,将欠驱动水面机器人的镇定问题转化成对由两个串级子系统构成的二阶欠驱动系统的镇定问题.针对转换后的系统,本文提出一种光滑的变周期控制方法,以实现对该系统的全局渐近镇定.与已有文献中控制律使用常数周期的方法相比,本文方法根据系统状态实时调整控制律周期,从而提高系统在原点附近的收敛速率.随后,基于上述方法,给出了水面机器人变周期控制算法,实现原系统的全局渐近镇定.最后,仿真对比结果验证所提变周期控制方法的有效性.     

A global output-feedback controller for stabilization and tracking of underactuated ODIN: A spherical underwater vehicle

This paper presents a method to design an output-feedback controller that simultaneously solves global asymptotic stabilization and tracking of an underactuated omni-directional intelligent navigator—a spherical underwater vehicle moving in a horizontal plane (i.e. at a constant depth). The vehicle does not have a sway actuator and has only position and orientation measurements available. The control development is based on Lyapunov's direct method, backstepping technique and use of interconnected structure of the vehicle dynamics. Numerical simulations demonstrate the results.     

Robust exponential stabilization for network-based switched control systems

It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A network-based switched control system, as a special case of networked control systems, is studied. Such a system is represented with network-induced delays and packet dropout as a switched delay system. Sufficient conditions for robust exponential stability are derived for a class of switching signals with average dwell time. A stabilization design for continuous-time, linear switched plant with nonlinear perturbation under a given communication network via a hybrid state feedback controller is proposed. A hybrid controller design is network-dependent and given in terms of linear matrix inequalities.     

On optimal control law implementations for exponential performanceindex

An alternate implementation is established, under certain conditions, for previously obtained solution to the linear-exponential-Gaussian stochastic optimal control problem. The implementation allows the current control to be specified without using future values of the measurement process parameters, which are often unavailable in practice     

Global asymptotic stabilization of the attitude and the angular rates of an underactuated non-symmetric rigid body

The paper deals with the global stabilization of both the attitude and the angular velocities of an underactuated rigid body. First a stability theorem is proven for a class of systems; subsequently, the equations describing the physics of the rigid body are presented, showing that the rigid body belongs to the considered class of systems, and a sufficient condition for the application of the theorem to the stability of the rigid body equilibrium is pointed out. Finally, some simulation results are reported showing the effectiveness of the proposed methodology.     

Adaptive exponential stabilization for a class of nonlinear retarded processes

This paper considers the problem of adaptive exponential stabilization for a class of single-input single-output nonlinear retarded processes. The class includes certain linear retarded systems which are subject to sector-bounded actuator and sensor nonlinearities. It is shown that there is a wide range of high-gain adaptive compensators which achieve exponential stability for the class of processes under consideration. This work was supported by SERC under Grant No. GR/D/45710.     

A Lyapunov approach to exponential stabilization of nonholonomicsystems in power form

In this paper a continuous feedback control law with time-periodic terms is derived for the control of nonholonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector fields are homogeneous of degree zero     

欠驱动桥式吊车系统自适应控制

针对桥式吊车这类非线性欠驱动系统, 提出了一种基于耗散理论的自适应控制器. 它能够有效地抑制运输过程中负载的摆动, 并将其快速准确地运送到指定的位置. 相比其他吊车控制系统, 这种控制器无需准确测量台车和负载质量以及吊绳长度, 可以根据系统响应情况来对这些参数进行在线估计, 这将极大地方便控制器在实际吊车系统中的推广应用. 对于闭环系统的稳定性, 文中通过李雅普诺夫理论及拉塞尔不变性原理进行了证明, 仿真结果也证实了这种自适应控制器能够对吊车系统进行良好的控制.     

Control of an exoskeleton robot arm with sliding mode exponential reaching law

Robots are now working not only in human environments but also interacting with humans, e.g., service robots or assistive robots. A 7DoFs robotic exoskeleton MARSE-7 (motion assistive robotic-exoskeleton for superior extremity) was developed as an assistive robot to provide movement assistance and/or ease daily upper-limb motion. In this paper, we highlight the nonlinear control of MARSE-7 using the modified sliding mode exponential reaching law (mSMERL). Conventional sliding control produces chattering which is undesired for this kind of robotic application as it causes damage to the mechanical structure. Compared to conventional sliding control, our approach significantly reduces chattering and delivers a high dynamic tracking performance. The control architecture was implemented on a field-programmable gate array (FPGA) in conjunction with a RT-PC. In experiments, trajectory tracking that corresponds to typical passive arm movement exercises for single and multi joint movements were performed to evaluate the performance of the developed robot and the controller. Experimental results demonstrate that the MARSE-7 can effectively track the desired trajectories.     

Feedback stabilization for a class of discontinuous systems driven by integrator

This paper investigates the feedback stabilization problem for a class of discontinuous systems which is characterized by Filippov differential inclusion. Lyapunov-based backstepping design method is generalized with nonsmooth Lyapunov functions to solve the control problem. A set-valued time derivative is introduced first for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with nondifferentiable Lyapunov function. Conditions for designing a virtual control law which is shown nondifferentiable in general in the recursive design problem are proposed. Finally, as a special case, piecewise linear system is discussed to demonstrate the application of the presented design approach.