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.     

Global tracking for underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable. It has been designed using a 3 degrees of freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method.     

Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

The full‐state stabilization scheme is proposed for the control of an underactuated surface vessel with unknown modeling parameters. By knowing only the upper/lower bounds of model parameters, the designed controller is the first one able to globally uniformly asymptotically stabilize all the states of the vessel to zero. The virtual surge velocity control law is first derived, which makes the Lyapunov function at the kinematic level non‐increasing, irrelevant to the yaw velocity, leaving a freedom for choosing the virtual yaw velocity control law to stabilize the other state variables. After finishing the design of virtual velocity law, the back‐stepping approach and the Lyapunov redesign technique are combined to obtain the actual force/torque control law despite parameter uncertainties. Simulation examples are given to illustrate the effectiveness of the proposed control law, showing that all the states and the control inputs are globally uniformly asymptotically convergent to zero under parameter uncertainties and are globally bounded under unknown external bounded disturbances. Copyright © 2013 John Wiley & Sons, Ltd.     

On estimation of the domain of attraction for sliding mode control of underactuated nonlinear systems

A system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed‐loop system trajectory reaches the surface, it moves along the surface while converging to the origin. In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using sliding mode control in the presence of system uncertainties is presented. Specifically, it is shown that the closed‐loop system trajectories reach the sliding surface in finite time, and a constructive methodology to determine exponential stability of the closed‐loop system on the sliding surface is developed, which ensures asymptotic stability of the overall closed‐loop system. Furthermore, the aforementioned framework provides the basis to determine an estimate of the domain of attraction for the closed‐loop system with uncertainties. Finally, the results developed in the paper are experimentally validated using a linear inverted pendulum testbed to show a good match between the actual domain of attraction of the upward equilibrium state of the pendulum and its analytical estimate.Copyright © 2012 John Wiley & Sons, Ltd.     

舵减摇控制系统的开环增益成形设计

针对船舶航向/舵减横摇控制系统的特点,提出了一种新的设计方案.对舵减横摇控制回路,基于开环增益成形的思想,通过指定闭环灵敏度函数的幅频特性形状,得到相应的舵减横摇控制器.在设计过程中不但考虑了对象的非最小相位特性,还分析了Bode积分定理对性能的约束条件,在系统的性能和控制输出之间进行了折衷,给出了一组优化设计结果.对航向控制回路,应用混合灵敏度问题设计了H∞航向控制器.设计指标是在保证船舶能很好的跟踪航向指令的前提下尽可能的减小艏摇控制回路和横摇控制回路之间的耦合作用.仿真结果表明,所设计的舵减摇控制系统满足性能要求,取得了较高的减摇率,而且横摇运动对航向的影响很小.通过对摄动后的对象进行仿真,进一步验证了系统具有很好的鲁棒性.     

A New Approach for Vehicle Lateral Velocity and Yaw Rate Control with Uncertainty

In order to attain excellent stability and maneuverability to ensure safety and ride‐comfort, the lateral velocity and yaw rate of a vehicle are expected to be controlled at any desired values simultaneously. A basic manipulation model of a vehicle with two degrees of freedom which requires two independent control inputs (front and rear steering angle) is constructed. In this model, we consider the mass and the moment of inertia of the vehicle are the uncertain parameters which are (possibly) fast‐varying. However, no further information, except that the uncertainties are bounded, is assumed. Furthermore, the bound is unknown. An adaptive robust control methodology based on the Udwadia and Kalaba approach which guarantees uniform boundedness and uniform ultimate boundedness is proposed to drive the system to follow the pre‐specified constraints approximately. The adaptive law is of leakage type which can adjust itself based on the tracking error. The numerical simulation results conducted by MATLAB demonstrate the ease and effectiveness of implementation.     

基于级联方法的欠驱动AUV全局K指数3 维直线跟踪控制

采用非线性系统级联方法,提出一种欠驱动自主水下航行器的3维直线跟踪控制算法,首先将3维直线跟踪误差模型分解为水平面运动受垂直面运动扰动的级联结构;然后分别设计俯仰角指令和航向角指令,进一步将平面直线跟踪模型分解为位置跟踪误差受俯仰角/航向角跟踪误差扰动的级联结构,并设计了俯仰角和航向角的跟踪控制律,通过逐级应用级联系统稳定性理论证明了3维直线跟踪误差的全局κ指数稳定性;最后通过数学仿真验证了所提出跟踪控制算法的有效性。     

Nonlinear dynamic model identification methodology for real robotic surface vessels

This paper presents a methodology for identifying the nonlinear dynamic model of underactuated surface vessels for the purpose of model-based controller design. The methodology outlines the required tests that need to be performed and the formulations that need to be used for sequentially identifying the model parameters one by one. The identification methodology is performed on a robotic vessel by testing in outdoor environments and the accuracy of the dynamic model is verified. The physical control inputs to the vessel are a propeller rotational speed and a rudder angle. 3 degrees of freedom are assumed for the nonlinear dynamic model of the surface vessel. Finally, an approach is proposed that discusses how the identified full nonlinear dynamic model can be used for control design. Results of typical closed-loop control tests are presented.     

欠驱动船舶的运动规划和全局指数跟踪控制

针对目前欠驱动船舶航迹跟踪控制难以实现跟踪任意可行航迹问题,提出一种运动规划方法。利用多项式拟合,并结合船舶动力学模型,通过离散期望点规划出操作性可实现的全部期望姿态。同时,为实现欠驱动船舶的航迹快速跟踪控制,提出一种全局指数航迹跟踪控制律。引入微分同胚变换,建立两个级联的子系统构成的航迹跟踪误差动态方程;基于反步法的设计原理,运用Lyapunov直接方法对变换后的误差系统设计了全局指数航迹跟踪控制律。仿真结果验证了所提出的全局指数航迹跟踪控制律能够有效实现跟踪任意可行航迹。     

Robust Position Stabilization of Underactuated Surface Vessels With Unknown Modeling Parameters Via Simple P/D‐Like Feedback: The Center Manifold Approach

In this work, two smooth time‐invariant control laws are proposed to achieve asymptotic position stabilization of underactuated surface vessels despite modeling parameter uncertainties. The proposed control laws take a strikingly simple linear proportional derivative (PD)‐like feedback form or just a simplest proportional (P)‐like one, where the former relies on measuring the relative position error and surge/yaw velocity and the latter relies on measuring only the relative position error, decreasing or minimizing the sensing cost. The stabilities of the closed‐loop systems for the both control laws are strictly proved via the center manifold approach despite the unknown model parameters. The effectiveness of the proposed control laws is verified by simulation examples.     

基于核相关滤波的无人机偏航角跟踪控制系统设计

针对非线性自抗扰控制技术设计的系统、线性自抗扰技术设计的系统受到噪声影响,导致信号传输受到阻碍,出现偏航角跟踪控制结果精准度低的问题,提出了基于核相关滤波的无人机偏航角跟踪控制系统设计;在系统总体架构支持下,采用STM32F407型号主控芯片,保证无人机控制系统稳定性;在方向盘下安装有转向角传感器,为ESP电子控制单元提供方向盘;使用频率为2.4 GHz遥控器接收机生成具有不同脉冲宽度PWM信号,通过控制旋翼偏航控制器,推动旋翼在不同角度指令下旋转;利用核相关滤波器过滤目标图像,通过滤波器的输运来估计目标运动位置,并确定地面参考坐标系与无人机机体坐标系,构成无人机在空间中六个自由度,由此设计偏航角跟踪控制软件流程,跟踪控制无人机偏航角;由实验结果可知,该系统滚转角与实际值轨迹一致,误差为0;俯仰角与实际值轨迹有偏差,误差为0.05°,为无人机向不同方向精准飞行提供系统支持.     

Experimental test of a robust formation controller for marine unmanned surface vessels

Experiments with two formation controllers for marine unmanned surface vessels are reported. The formation controllers are designed using the nonlinear robust model-based sliding mode approach. The marine vehicles can operate in arbitrary formation configurations by using two leader-follower control schemes. For the design of these controller schemes 3 degrees of freedom (DOFs) of surge, sway, and yaw are assumed in the planar motion of the marine surface vessels. Each vessel only has two actuators; therefore, the vessels are underactuated and the lack of a kinematic constraint puts them into the holonomic system category. In this work, the position of a control point on the vessel is controlled, and the orientation dynamics is not directly controlled. Therefore, there is a potential for an oscillatory yaw motion to occur. It is shown that the orientation dynamics, as the internal dynamics of this underactuated system, is stable, i.e., the follower vehicle does not oscillate about its control point during the formation maneuvers. The proposed formation controller relies only on the state information obtained from the immediate neighbors of the vessel and the vessel itself. The effectiveness and robustness of formation control laws in the presence of parameter uncertainty and environmental disturbances are demonstrated by using both simulations and field experiments. The experiments were performed in a natural environment on a lake using a small test boat, and show robust performance to parameter uncertainty and disturbance. This paper reports the first experimental verification of the above mentioned approach, whose unique features are the use of a control point, the zero-dynamic stability analysis, the use of leader-follower method and a nonlinear robust control approach.     

Three‐Dimensional Constrained Tracking Control Via Exact Differentiation Estimator of a Quadrotor Helicopter

In this paper, a constructive method is presented to design a three dimensional trajectory tracking controller that forces a quadrotor helicopter to track a bounded and sufficiently smooth reference trajectory asymptotically in the presence of constant force disturbances. The quadrotor helicopter under consideration has fewer independent thrusters than degrees of freedom to be controlled. Motivated by the vehicle's steering practices, the roll and pitch angles are regarded as virtual controls along with four control forces to fulfill the task of position and yaw angle reference tracking. To prevent position constraint violation, the barrier Lyapunov function (BLF) is employed in the vectorial backstepping procedure to guarantee that the position and attitude constraints are not violated. The backstepping procedure employs an exact and robust sliding mode differentiator of order two to facilitate the implementation of the attitude command signal without calculating the virtual control signal derivative analytically.     

一种基于前馈－反馈复合控制方式的制动稳定性控制方法

设计了一种前馈—反馈复合控制结构，将直接横摆力矩控制和主动前轮转向控制相结合以提高制动稳定性．控制器将前轮转向角视为输入，将外部侧向干扰力和力矩作用视为扰动，通过前馈校正补偿转向角引起的状态变化；同时建立扰动状态观测器，采用反馈控制校正消除外部扰动引起的状态误差．仿真试验证实这种控制方法在提高制动稳定性方面有良好的效果．     

Optimal setpoint chasing in dynamic positioning of deep‐water drilling and intervention vessels

Conventional controller designs for dynamic positioning of ships and floating marine structures have so far been based on the principle on automatic positioning in the horizontal‐plane about desired position and heading co‐ordinates defined by the operator. A three degrees‐of‐freedom multivariable controller either of linear or nonlinear type, normally with feedback signals from surge, sway and yaw position and velocities, has been regarded as adequate for the control objective. For floating structures with small waterplane area such as semi‐submersibles, feedback from roll and pitch angular rotation velocity may also be included to avoid thrust‐induced roll and pitch motions that are caused by the hydrodynamic and the geometrical couplings between the horizontal and vertical planes. However, for certain marine operations this control philosophy may not be the most appropriate approach ensuring safety and cost effectiveness. For drilling and work‐over operations the main positioning objective is to minimize the bending stresses along the riser and the riser angle magnitudes at the well head on the subsea structure, and at the top joint as well. A positioning control strategy solely based on manual setting of the desired position co‐ordinates may not be the most optimal solution for these applications. In this paper a new hybrid dynamic positioning controller, that also accounts for riser angle offsets and bending stresses is proposed. It is shown that a significant reduction in riser angle magnitude can be achieved. Simulations with a drilling semi‐submersible demonstrate the effect of the proposed control strategy. Copyright © 2001 John Wiley & Sons, Ltd.     

The control point concept for nonlinear trajectory-tracking control of autonomous helicopters with fly-bar

An alternative approach for automatic trajectory-tracking control of small unmanned helicopters with fly-bar is proposed. This approach uses the spatial three-dimensional coordinates of a point on the helicopter's local coordinate frame other than its centre of gravity, called the control point, and the helicopter's yaw angle as four control outputs. The helicopter is assumed to have four independent control inputs. With this choice of control outputs, the helicopter's input–output model becomes a square control system, which opens the possibility of implementation of many robust nonlinear control methods that are suitable for such systems. The helicopter, which has six rigid body degrees of freedom (DOFs), has two underactuated DOFs (UA-DOFs). It is proved that the zero-dynamics of the UA-DOFs are inherently stable, leading to a stable control system. A sliding mode controller is designed for trajectory-tracking of the outputs. It is verified via simulations that the response of the control outputs and UA-DOFs are in fact stable.     

欠驱动自主水面船的非线性路径跟踪控制

基于级联方法提出一种欠驱动自主水面船的全局K指数稳定路径跟踪控制算法.采用以自由路径参考点为原点的Serret-Frenet坐标系建立路径跟踪误差的动态模型,以路径参数的变化率为附加控制输入,克服了以正交投影点为坐标原点时的奇异值问题.设计路径跟踪航向角指令,将路径跟踪模型分解为位置跟踪子系统和航向角、前向速度跟踪子系统两个子系统级联的形式,设计航向角和前向速度的全局指数稳定跟踪控制器,应用级联系统理论证明了路径跟踪误差的全局K指数稳定性.数学仿真和自主水面船湖上实验结果验证了该路径跟踪控制算法的有效性.     

Global asymptotic tracking of asymmetrical underactuated surface vessels with parameter uncertainties

In this work, we investigate the tracking control problem of asymmetrical underactuated surface vessels with parameter uncertainties. The tracking error model is first derived via appropriate coordinate transformations, and is considered as a cascade structure composed of two subsystems. The Lyapunov redesign approach is employed to construct the control laws separately to stabilize the two subsystems with unknown model parameters. The cascade system theory is applied to prove the global uniform asymptotic convergence of the state trajectory to the reference one provided the desired yaw velocity is not vanishing. The effectiveness of the proposed control laws is verified by simulation examples.     

Two approaches for feedforward control and optimal design of underactuated multibody systems

An underactuated multibody system has less control inputs than degrees of freedom. For trajectory tracking, often a feedforward control is necessary. Two different approaches for feedforward control design are presented. The first approach is based on a coordinate transformation into the nonlinear input–output normal-form. The second approach uses servo-constraints and results in a set of differential algebraic equations. A comparison shows that both feedforward control designs have a similar structure. The analysis of the mechanical design of underactuated multibody systems might show that they are nonminimum phase, i.e., they have unstable internal dynamics. Then the feedforward control cannot be computed by time integration and output trajectory tracking becomes a very challenging task. Therefore, based on the two presented feedforward control design approaches, it is shown that through the use of an optimization procedure underactuated multibody systems can be designed in such a way that they are minimum phase. Thus, feedforward control design using the two approaches is significantly simplified.     

Dynamics and control of a class of underactuated mechanical systems

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable