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.     

基于PNDSC 的欠驱动AUV编队控制器设计

针对含有模型不确定与未知海洋环境扰动下的欠驱动自主水下航行器(AUV)的编队控制问题, 提出一种基于预估器的神经网络动态面(PNDSC) 控制算法. 将动态面法引入控制器的设计中, 采用神经网络逼近AUV模型中的不确定项与海洋环境的扰动, 并结合预估器设计了神经网络权值的离散迭代更新率. Lyapunov 稳定性分析表明, 闭环系统所有信号是一致最终有界的. 仿真结果验证了所提出方法的有效性.

     

Non-linear model predictive formation control for groups of autonomous surface vessels

Designing non-linear model predictive control (NMPC) laws for controlling multiple autonomous surface vessels in arbitrary formations in environments containing obstacles are reported in this paper. Two leader-follower decentralized geometrical control schemes that are required for defining a unique two-dimensional formation are considered. A three-degree-of-freedom dynamic model of surface vessels has been used for the controller design. It is assumed that the surface vessels are under-actuated and obstacles are present in the vessels' work environment. The real-time optimization abilities of the NMPC method has been used to improve the response of the unactuated DOF of the vessels and to directly incorporate the local obstacle avoidance into the formation control eliminating the need for an external local obstacle avoidance algorithm. This leads to more effective obstacle avoidance decisions based on the dynamics of the vehicle. The effectiveness the developed control law, even in the presence of model uncertainty and external disturbances are demonstrated via computer simulations.     

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.     

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．     

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.     

A new formation control of multiple underactuated surface vessels

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.     

基于模糊不确定观测器的四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性的四旋翼飞行器,提出了一种基于模糊不确定观测器（Fuzzy uncertainty observer,FUO）的自适应动态面轨迹跟踪控制方法.通过将四旋翼飞行器系统分解为位置、姿态角和角速率三个动态子系统,使得各子系统虚拟控制器能够充分考虑欠驱动约束;采用一阶低通滤波器重构虚拟控制信号及其一阶导数,实现四旋翼跟踪控制设计的迭代解耦;设计了一种模糊不确定观测器,用以估计和补偿未知外界扰动与系统不确定性,从而确保闭环系统的稳定性和跟踪误差与其他系统信号的一致有界性.仿真研究验证了所提出的控制方法的有效性和优越性.     

Dynamic and stable reconfiguration of self-reconfigurable planar parallel robots

This paper discusses dynamic and stable reconfigurations of self-reconfigurable planar parallel robots that can be done by coupling and decoupling of two underactuated robots on a horizontal plane. The limbs of the parallel robots are 2R open kinematic chains with their second joints unactuated. Two types of self-reconfigurable parallel robots are considered. One is formed by two limbs, and the other is by a limb and an underactuated robot consisting of two limbs and a platform. Uncertainty singularities enable them to self-reconfigure without additional actuators at their coupling mechanism. In this paper, we propose dynamic contact motion control to move them from an initial contact configuration to an uncertainty singular configuration while maintaining their contact. This paper also considers dynamic stability at their uncertainty singularities as equilibrium and shows that there exist geometrically stable configurations without feedback control, which are useful for decoupling. Experiments with real robots are carried out to verify the effectiveness of the dynamic contact motion control and stability analysis.     

基于扩张观测器的欠驱动船舶轨迹跟踪低频学习自适应动态面输出反馈控制

针对速度不可测的三自由度欠驱动船舶轨迹跟踪控制问题,考虑船舶存在模型参数不确定项以及外界环境干扰未知情况,提出一种基于扩张观测器的欠驱动船舶轨迹跟踪低频学习自适应动态面输出反馈控制策略.该策略构造扩张观测器估计船舶速度向量,利用神经网络算法逼近模型参数不确定项,然后采用动态面控制技术避免对虚拟控制律直接求导,简化控制律计算过程,并引入低频增益学习技术消除外界扰动导致控制信号产生高频振荡,最后选取李雅普诺夫函数证明该控制律能够保证船舶跟踪闭环系统中所有误差信号一致最终有界.仿真结果表明,本文所设计控制器对船舶模型参数不确定项及外界环境干扰具有较强的鲁棒性,能够实现对船舶轨迹的有效跟踪.     

Stabilization And Tracking Of Underactuated Surface Vessels In Random Waves With Fin Based On Adaptive Hierarchical Sliding Mode Technique

Trajectory tracking and roll stabilization are both vital practices in ship motion control. Trajectory tracking is a kind of low‐frequency control, while roll stabilization by means of fins is a kind of high‐frequency control. However, they have been studied separately previously; most tracking control of underactuated surface vessels in the previous studies do not account for roll stabilization by means of fins. In reality, however, they are an integral system. In this paper, a simple control strategy is proposed to achieve trajectory tracking and fin roll stabilization simultaneously. Four degrees of freedom derived from a six degrees of freedom mathematical model of a surface vessel is considered, including surge, sway, roll and yaw. Surge force, roll moment and yaw moment are considered as control inputs, while position, yaw angle and roll angle are controlled. The number of control inputs is fewer than the outputs to be controlled. Therefore, we are dealing with an underactuated problem. An adaptive hierarchical sliding mode control technique is employed to deal with the underactuation. Stabilization of underactuated surface vessels is studied as a special case. Random waves are applied to test the robustness of the designed controllers. Lyapunov stability theory is used to show the stability of closed‐loop system. The simulation results verify the effectiveness of the proposed strategy.     

Robust adaptive path following of underactuated ships

Robust path following is an issue of vital practical importance to the ship industry. In this paper, a nonlinear robust adaptive control strategy is developed to force an underactuated surface ship to follow a predefined path at a desired speed, despite the presence of environmental disturbances induced by wave, wind and ocean-current. The proposed controller is scalable and is designed using Lyapunov's direct method and the popular backstepping and parameter projection techniques. Along the way of proving closed-loop stability, we obtain a new stability result for nonlinear cascade systems with non-vanishing uncertainties. Interestingly, it is shown in this paper that our developed control strategy is easily extendible to situations of practical importance such as parking and point-to-point navigation. Numerical simulations using the real data of a monohull ship are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated ships.     

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.     

四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性集总未知非线性的四旋翼飞行器,提出了一种采用自适应不确定性补偿器的自适应动态面轨迹跟踪方法.通过将四旋翼飞行器系统分解为位置、欧拉角和角速率3个动态子系统,使各子系统虚拟控制器设计能充分考虑欠驱动约束;结合动态面控制技术,通过采用一阶低通滤波器,避免对虚拟控制信号求导;进而设计自适应不确定性补偿器,处理未知外界扰动和系统不确定性,最终确保闭环控制系统的稳定性、跟踪误差一致最终有界和系统所有状态信号有界.仿真研究和实验结果验证了本文提出控制方法的有效性和优越性.     

Nonlinear robust adaptive sliding mode control design for miniature unmanned multirotor aerial vehicle

This paper addresses the stability and tracking control problem of miniature unmanned multirotor aerial vehicle (MUMAV) in the presence of bounded uncertainty. The uncertainty may appear from unmodeled dynamics, underactuated property, input disturbance and flying environment. Nonlinear robust adaptive sliding mode control algorithm is designed by using Lyapunov function. Robust adaptation laws are designed to learn and compensate the bounded parametric uncertainty. Lyapunov analysis shows that the proposed algorithms can guarantee asymptotic stability and tracking control property of the linear and angular dynamics of MUMAV system. Compared with other existing control methods, the proposed design is very simple and easy to implement as it does not require multiple design steps, augmented auxiliary signals and exact bound of the uncertainty. Experimental results on a miniature unmanned quadrotor aerial vehicle are presented to illustrate of effectiveness of the proposed design for real-time applications.     

风浪流干扰及参数不确定欠驱动船舶航迹跟踪的滑模鲁棒控制

针对欠驱动船舶的模型参数不确定和外界风浪流干扰问题,为实现水平面的航迹跟踪控制,提出了一种基于上下界的滑模控制方法.首先利用反步法将控制器的设计分解为运动学回路和动力学回路.其次,在运动学回路中为实现位置跟踪误差的收敛,根据期望航迹与当前位置信息,设计船舶的纵向与侧移参考速度,并视为镇定位置误差的虚拟控制律;在动力学回路中,将虚拟控制律作为新的跟踪目标,利用滑模方法设计实际控制律实现对参考速度的跟踪控制,最终实现了欠驱动船舶的跟踪控制.最后对有无干扰下的欠驱动船模分别进行了仿真实验,仿真结果证明了控制律的有效性.     

A self-propelled robotic system with a visco-elastic joint: dynamics and motion analysis

This paper studies the dynamics and motion generation of a self-propelled robotic system with a visco-elastic joint. The system is underactuated, legless and wheelless, and has potential applications in environmental inspection and operation in restricted spaces which are inaccessible to human beings, such as pipeline inspection, medical assistance and disaster rescue. Locomotion of the system relies on the stick–slip effects, which interacts with the frictional force of the surface in contact. The nonlinear robotic model utilizes combined tangential-wise and normal-wise vibrations for underactuated locomotion, which features a generic significance for the studies on self-propelled systems. To identify the characteristics of the visco-elastic joint and shed light on the energy efficacy, parameter dependences on stiffness and damping coefficients are thoroughly analysed. Our studies demonstrate that the dynamic behaviour of the self-propelled system is mainly periodic and desirable forward motion is achieved via identification of the variation laws of the control parameters and elaborate selection of the stiffness and damping coefficients. A motion generation strategy is developed, and an analytical two-stage motion profile is proposed based on the system response and dynamic constraint analysis, followed by a parameterization procedure to optimally generate the trajectory. The proposed method provides a novel approach in generating self-propelled locomotion, and designing and computing the visco-elastic parameters for energy efficacy. Simulation results are presented to demonstrate the effectiveness and feasibility of the proposed model and motion generation approach.     

基于反步法的欠驱动UUV的3维路径跟踪控制

研究了欠驱动无人水下航行器(unmanned underwater vehicle,UUV)在3维空间中的路径跟踪控制器设计及其稳定性分析问题.首先建立2阶积分器形式的欠驱动UUV空间6自由度运动模型和动力学模型.针对该运动模型,以位置误差作为虚拟控制变量,基于反步法(backstepping)设计路径跟踪控制器.根据李亚普诺夫理论,在理论上证明了所设计的路径跟踪控制系统是稳定的.该控制器实现了欠驱动UUV 3维空间的路径跟踪控制.仿真结果验证了控制器的有效性.     

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.     

多自主船协同路径跟踪的自适应动态面控制

为实现多自主船含模型不确定与未知风浪流干扰下的协同路径跟踪控制,提出了一种基于神经网络自适应动态面控制的协同路径跟踪算法.该算法采用单隐层(SHL)神经网络逼近模型不确定性以及海洋环境干扰,所引入的动态面设计技术显著降低了控制算法的复杂性.同时将网络通信约束考虑在内,通过设计分散式协同控制律有效地降低了信息通讯量.Lyapunov稳定性分析证明了闭环系统所有的状态和信号是有界的,并且通过选择合适的设计参数可使跟踪误差为任意小.对比仿真结果验证了所提方法的有效性.