A curve extension design for coordinated path following control of unicycles along given convex loops

This article utilises a dynamic model of unicycles to address the convergence of vehicle formation about closed convex curves. A novel curve extension method, extending the target loop along the vector from the loop centre to the point on the loop, is proposed to construct a family of level curves and the existence of a loop function on a tubular-like neighbourhood is proved by referring to the tubular neighbourhood theorem. Path following control is derived based on the loop function which incorporated into the arc-length function to propose the solution to coordinated formation control. We show how backstepping technique, Lyapunov-based theory and graph theory can be combined together to construct the coordinated path following controller under the bidirectional commutation topology. It is proved that the designed cooperative control system is asymptotically stable if the graph is connected. The proposed method is effective for a skewed superellipse, which is a type of curve that includes circles, ellipses and rounded parallelograms.     

基于虚拟领航者的船舶无源协调编队控制研究

随着海上任务越来越复杂,许多作业过程要求多艘船舶相互协调. 本文结合了虚拟领航者协调策略和无源性理论控制方法的各自优势,提出了一种基于虚拟领航者的无源协调控制方法,来解决多艘船舶的协调路径跟踪问题.通过对虚拟领航者设计路径跟踪控制器,使其领导作业船舶按着指定的路 径进行协调作业,同时定义每艘船舶的队形参考点,应用无源性理论设计同步 控制器使所有船舶的参考点趋于一致,最终实现多艘船舶按一定的队形进行协调路径跟踪.最后通过仿真实验验证了所提算法的有效性.     

Sensor allocation with guaranteed exponential stability for linear multi‐rate sampled‐data systems

This paper addresses sensor allocation with guaranteed exponential stability for linear multi‐rate sampled‐data systems. It is assumed that a continuous‐time linear plant is exponentially stabilized by a continuous‐time linear controller. Given sensors with incommensurate sampling rates, the objective is to allocate each state to a sensor such that the resulting multi‐rate sampled‐data system remains exponentially stable. The main contributions of this paper are twofold. First, we propose sufficient Krasovskii‐based conditions to partition the state vector among sensors such that exponential stability of the closed‐loop system is guaranteed. Second, the problem of finding a partition that guarantees exponential stability is cast as a mixed integer program subject to linear matrix inequalities. The theoretical results are successfully applied to two robotic problems: path‐following in unicycles and hovering in quadrotors. Copyright © 2015 John Wiley & Sons, Ltd.     

On the least restrictive control for collision avoidance of two unicycles

We give an explicit analytical characterization of the least restrictive control for collision avoidance of two unicycles. The controller is proved to be least restrictive using viability theory. Copyright © 2006 John Wiley & Sons, Ltd.     

A path following algorithm for mobile robots

This paper considers path following control for a robotic platform. The vehicle used for the experiments is a specially designed robotic platform for performing autonomous weed control. The platform is four-wheel steered and four-wheel driven. A diesel engine powers the wheels via a hydraulic transmission. The robot uses a Real Time Kinematic Differential Global Positioning System to determine both position and orientation relative to the path. The deviation of the robot to the desired path is supplied to two high level controllers minimizing the orthogonal distance and orientation to the path. Wheel angle setpoints are determined from inversion of the kinematic model. At low level each wheel angle is controlled by a proportional controller combined with a Smith predictor. Results show the controller performance following different paths shapes including a step, a ramp, and a typical headland path. A refined tuning method calculates controller settings that let the robot drive as much as possible along the same path to its setpoint, but also limit the gains at higher speeds to prevent the closed loop system to become unstable due to the time delay in the system. Mean, minimum and maximum orthogonal distance errors while following a straight path on a paving at a speed of 0.5 m/s are 0.0, −2.4 and 3.0 cm respectively and the standard deviation is 1.2 cm. The control method for four wheel steered vehicles presented in this paper has the unique feature that it enables control of a user definable position relative to the robot frame and can deal with limitations on the wheel angles. The method is very well practical applicable for a manufacturer: all parameters needed are known by the manufacturer or can be determined easily, user settings have an easy interpretation and the only complex part can be supplied as a generic software module.     

Passivity-based control of a class of Blondel-Park transformableelectric machines

Concerns the extension to the general rotating electric machine model of the passivity-based controller method for induction motors. The motor's passivity properties are used at 2 levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems (essentially, the electrical and mechanical dynamics). Then, we design a torque-tracking controller that preserves passivity for the electrical subsystem and leaves the mechanical part as a passive disturbance. This leads to the cascaded controller structure which is typically analyzed involving time-scale separation. Our aim is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque-tracking problem. The class consists of machines whose nonactuated dynamics are damped and whose dynamics can be decoupled. This requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions have a clear physical interpretation in terms of the couplings between its dynamics and are satisfied by many machines. The passivity-based controller presented reduces to the well-known indirect vector controller for current-fed induction machines. Our developments constitute an extension to voltage-fed machines of this de facto standard in industrial applications     

Asymptotically stable path following for lateral motion of an unmanned ground vehicle

This study proposes an asymptotically stable path following controller for autonomous navigation of an unmanned ground vehicle (UGV) using vector field and robust-integral-signum error (RISE) feedback. The path following controller is divided into two parts: one part generating a heading command and another part designing a robust control. To determine the reference heading command under various uncertainties, the vector field method is employed, and then the RISE feedback controller is designed to follow the heading command. Finally, experiments are conducted on paved and unpaved roads to validate the effectiveness of the proposed method.     

Globally Stable Adaptive Dynamic Surface Control for Cooperative Path Following of Multiple Underactuated Autonomous Underwater Vehicles

The cooperative path following problem of multiple underactuated autonomous underwater vehicles (AUVs) involves two tasks. The first one is to force each AUV to converge to the desired parameterized path. The second one is to satisfy the requirement of a cooperative behavior along the paths. In this paper, both of the tasks have been further studied. For the first one, a simplified path following controller is proposed by incorporating the dynamic surface control (DSC) technique to avoid the calculation of derivatives of virtual control signals. Besides, in order to handle the uncertain dynamics, a new type of neural network (NN) adaptive controller is derived, and then an NN based energy‐efficient path following controller is firstly proposed, which consists of an adaptive neural controller dominating in the neural active region and an extra robust controller working outside the neural active region. For the second one, in order to reduce the amount of communications between multiple AUVs, a distributed estimator for the reference common speed is firstly proposed as determined by the communications topology adopted, which means the global knowledge of the reference speed is relaxed for the problem of cooperative path following. The overall algorithm ensures that all the signals in the closed‐loop system are globally uniformly ultimately bounded (GUUB) and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. Simulation results validate the performance and robustness of the proposed strategy.     

Simplified parallel-damped passivity-based controllers for dc-dc power converters

The development of a simplified parallel-damped passivity-based controller for the dc-dc boost converter is presented. The controller design involves choosing an appropriate structure to satisfy the stability condition which leads to a simplified structure as compared to the full-blown parallel-damped passivity-based controller. Tuning guidelines to achieve a desired output response are proposed. Simulation results are also given to illustrate the features of the feedback control strategy.     

Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers

In this paper, we present a Lyapunov-based homogeneous controller for the stabilisation of a perturbed chain of integrators of arbitrary order r ≥ 1. The proposed controller is based on homogeneous controller for stabilisation of pure chain of integrators. The control of homogeneity degree is also introduced and various controllers are designed using this concept, namely a bounded-controller with minimum amplitude of discontinuous control and a controller with globally fixed-time convergence. The performance of the controller is validated through simulations.     

Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels

The problem of path following for marine surface vessels using the rudder angle is addressed in this paper. A four-degree-of-freedom nonlinear surface vessel model, together with the Serret-Frenet equations, is introduced to describe the ship dynamics and path following error dynamics. While similar models have been used and reported in the literature for path following control algorithm development, the novelty of the approach presented in this work lies in the following aspects. (a) The back-stepping nonlinear controller design is based on feedback dominance, instead of feedback linearization and nonlinearity cancelation; (b) additional design parameters are employed in the Lyapunov function that lead to simplification of the controller in the design procedure and normalization of different variables in the Lyapunov function to improve the controller performance; (c) relying on feedback dominance and the introduction of the additional parameters in the Lyapunov function, the resulting controller is almost linear, with very benign nonlinearities allowing for analysis and evaluation; and (d) the performance of the nonlinear controller, in terms of path following, is analyzed for robustness in the presence of model uncertainties. The simulation results are presented to verify and illustrate the analytic development and the effectiveness of the resulting control against rudder saturation and rate limits, and delays in the control execution, as well as measurement noises. Furthermore, the control design is validated by experimental results conducted in a tank using a model ship.     

On transient performance improvement of adaptive control architectures

While adaptive control theory has been used in numerous applications to achieve given system stabilisation or command following criteria without excessive reliance on mathematical models, the ability to obtain a predictable transient performance is still an important problem – especially for applications to safety-critical systems and when there is no a-priori knowledge on upper bounds of existing system uncertainties. To address this problem, we present a new approach to improve the transient performance of adaptive control architectures. In particular, our approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimisation procedure to minimise the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. We provide a detailed stability analysis of the proposed approach, discuss the practical aspects of its implementation, and illustrate its efficacy on a numerical example.     

Stabilisation of nonlinear chemical processes via dynamic power-shaping passivity-based control

It is well known that energy-balancing passivity-based control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, some authors have used power-shaping techniques, where stabilisation is achieved by shaping a function akin to power instead of energy. Some extensions of the techniques to general nonlinear systems, yielding static state-feedback control laws, have also been reported. In this article, we extend these techniques to dynamic feedback control and apply them to nonlinear chemical processes. The stability analysis is carried out using the shaped power function as Lyapunov function. The proposed technique is illustrated with two nonlinear chemical process examples.     

Asymptotic stabilization via control by interconnection of port-Hamiltonian systems

We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium. We propose two different ways to overcome this restriction, one based on adaptation ideas, and the other one adding an extra damping injection to the controller. The analysis and design principles are illustrated through an academic example.     

A path following control for unicycle robots

In this work we present a new path following control for unicycle robots that is applicable for almost all the possible desired paths and whose analysis is very straightforward. First we select the path following method that consists of two steps: choosing a “projection” that relates the actual posture to the desired path and imposing a “motion exigency” to ensure that the robot advances. A “projection” that considers all the error coordinates is selected and closed equations are obtained for it. The uniqueness projection is carefully analyzed and a necessary and sufficient condition is also presented. This condition shows that a slight bound on the curvature derivative of desired paths must be imposed to preserve uniqueness. It is remarkable that the selected path following is applicable for paths containing zero‐radius turns, a problem that has never been resolved as far as we know. In addition, an asymptotically stable control law is found using the closed form equation of the proposed path following and the second Lyapunov method. Finally, we show the behavior of the path following and the control law through several simulated and experimental results, using a computerized wheelchair built at our research facility. © 2001 John Wiley & Sons, Inc.     

一种球形滚动机器人的路径跟踪控制器设计

对一种球形滚动机器人的路径跟踪问题进行研究,设计一种基于自适应滑模控制策略的路径跟踪控制器。所设计的路径跟踪控制器采用鲁棒滑模自适应增益控制律,能够有效实现带有扰动和不确定性的实际球形滚动机器人的路径跟踪。推导球壳纯滚动和无自转非完整约束下球形滚动机器人的运动方程,并在此基础上设计自适应滑模路径跟踪控制器。对于给定的参考几何路径,所设计的路径跟踪控制器能够确保路径跟踪误差在有限时间内收敛至很小的零邻域内。基于Lyapunov稳定性理论证明了闭环控制系统的稳定性,数值仿真与样机实验结果进一步验证了所设计的路径跟踪控制器的有效性。     

自适应模糊滑模软切换的PMSM无速度传感器鲁棒无源控制

针对永磁同步电机(PMSM)转速调节和估计问题,提出一种无速度传感器的PMSM调速系统.利用双曲正切函数代替符号函数,设计了自适应模糊滑模软切换控制器,实现了软切换连续控制,削弱了抖动现象.通过设计鲁棒无源控制器,得到了旋转坐标系下的u_d和u_q.建立了自适应滑模观测器,并给出了速度辨识律,观测器的增益通过求解线性矩阵不等式得到.仿真结果表明了该控制策略与观测器配合的有效性,且控制系统具有良好的动、稳态性能.     

采用非线性无源理论的MMC–MG并网电流控制

针对MMC半桥串联结构微电网(modular multilevel converter microgrids, MMC–MG)并网电流控制中, 采用 传统PI控制方法时其动态性能较差的问题, 提出一种利用无源控制理论的电流控制策略. 首先, 阐述了系统的拓扑 结构, 并建立了其欧拉–拉格朗日数学模型. 然后, 通过选取系统的状态变量, 设置误差能量函数及需注入的阻尼项, 以得到无源控制律; 并依据该控制律设计无源电流控制器. 此外, 通过观察采用不同阻尼值时控制器的稳定性、电 流谐波特性、幅频和相频特性曲线, 进而得到最佳的阻尼参数; 最后, 由系统的并网仿真模型验证所提无源电流控 制的有效性. 结果表明, 与传统PI控制相比, 阻尼注入无源控制方法能在不同运行工况下实现对电流和功率参考值 的快速跟踪. 同时, 具有良好的谐波特性和稳定性.     

Cooperative control of multiple surface vessels in the presence of ocean currents and parametric model uncertainty

This paper addresses the problem of cooperative path‐following of multiple autonomous vehicles. Stated briefly, the problem consists of steering a group of vehicles along specified paths while keeping a desired spatial formation. For a given class of autonomous surface vessels, it is shown how Lyapunov‐based techniques and graph theory can be brought together to design a decentralized control structure, where the vehicle dynamics and the constraints imposed by the topology of the inter‐vehicle communication network are explicitly taken into account. To achieve path‐following for each vehicle, a nonlinear adaptive controller is designed that yields convergence of the trajectories of the closed‐loop system to the path in the presence of constant unknown ocean currents and parametric model uncertainty. The controller derived implicitly compensates for the effect of the ocean current without the need for direct measurements of its velocity. Vehicle cooperation is achieved by adjusting the speed of each vehicle along its path according to information exchanged on the positions of a subset of the other vehicles, as determined by the communication topology adopted. Global stability and convergence of the closed‐loop system are guaranteed. Illustrative examples are presented and discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.