Target point‐based path‐following controller for a car‐type vehicle using bounded controls

In this paper, we have studied the control problem of target point‐based path following for car‐type vehicles. This special path‐following task arises from the needs of vision‐based guidance systems, where a given target point located ahead of the vehicle, in the visual range of the camera, must follow a specified path. A solution to this problem is developed through a nonlinear transformation of the path‐following problem into a reference trajectory tracking problem, by modeling the target point as a virtual vehicle. The use of target point complicates the control problem, as the development produces a first‐order nonlinear nonglobally Lipschitz differential equation with finite escape time. This problem is solved by using small control signals. Bounded feedback laws are designed to control the real vehicle's angular acceleration and the virtual vehicle's velocity, to achieve stability. The resulting controller is globally asymptotically stable with respect to the origin, the proof of which is derived from Lyapunov‐based arguments and a bootstrap argument. It is also shown that the use of exponentially convergent observers/differentiators does not affect the stability of the closed‐loop system. The effectiveness of this controller has been illustrated through simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

A Smooth Path Tracking Algorithm for Wheeled Mobile Robots with Dynamic Constraints

In order to avoid wheel slippage or mechanical damage during the mobile robot navigation, it is necessary tosmoothly change driving velocity or direction of the mobile robot. This means that dynamic constraints of the mobile robotshould be considered in the design of path tracking algorithm. In the study, a path tracking problem is formulated asfollowing a virtual target vehicle which is assumed to move exactly along the path with specified velocity. The drivingvelocity control law is designed basing on bang-bang control considering the acceleration bounds of driving wheels. Thesteering control law is designed by combining the bang-bang control with an intermediate path called the landing curve whichguides the robot to smoothly land on the virtual target's tangential line. The curvature and convergence analyses providesufficient stability conditions for the proposed path tracking controller. A series of path tracking simulations and experimentsconducted for a two-wheel driven mobile robot show the validity of the proposed algorithm.     

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.     

离轴式拖车移动机器人的任意路径跟踪控制

离轴式拖车移动机器人属于非完整系统,当车头线速度随时间变化且过零变号时,难以用一个控制器实现系统对期望路径的跟踪.本文研究离轴式拖车移动机器人系统的任意路径跟踪问题.首先由系统和虚拟小车的运动学方程得到误差状态模型,线性化后用坐标变换将其化为标准型,然后基于Lyapunov方法构造出一种跟踪控制律.只要车头的运动线速度有界且不趋于零,其导数有界,则所设计的控制律就可以保证系统跟踪任意的期望路径,且跟踪误差最终一致有界,最终界的大小与期望路径的曲率变化率成比例.当期望路径的曲率变化率为零或趋于零时,所设计的控制律可以保证拖车移动机器人指数收敛到期望路径.仿真结果证实了控制律的有效性.     

Model predictive and adaptive neural sliding mode control for three-dimensional path following of autonomous underwater vehicle with input saturation

With model uncertainties and input saturation, a novel control method is developed to steer an underactuated autonomous underwater vehicle that realizes the following of the planned path in three-dimensional (3D) space. Firstly, Serret–Frenet frame is applied as virtual target, and the path following errors model in 3D is built. Secondly, the control method which includes kinematic controller and dynamic controller was presented based on cascade control strategy. The kinematic controller, which is responsible for generating a series of constrained velocity signals, is designed based on model predictive control. The adaptive radial basis function neural network is used to estimate the model uncertainty caused by hydrodynamic parameters. Moreover, sliding mode control technology is applied in the design of dynamic controller to improve its robustness. Then, the control effect is compared with that of LOS guidance law and PID controller by simulation experiment. The comparison results show that the proposed algorithm can improve path following effect and reduce input saturation.

     

Cooperative path following of constrained autonomous vehicles with model predictive control and event‐triggered communications

We present a solution to the problem of multiple vehicle cooperative path following (CPF) that takes explicitly into account vehicle input constraints, the topology of the intervehicle communication network, and time‐varying communication delays. The objective is to steer a group of vehicles along given spatial paths, at speeds that may be path dependent, while holding a feasible geometric formation. The solution involves decoupling the original CPF problem into two subproblems: (i) single path following of input‐constrained vehicles and (ii) coordination of an input‐constrained multiagent system. The first is solved by adopting a sampled‐data model predictive control scheme, whereas the latter is tackled using a novel distributed control law with an event‐triggered communication (ETC) mechanism. The proposed strategy yields a closed‐loop CPF system that is input‐to‐state‐stable with respect to the system's state (consisting of the path following error of all vehicles and their coordination errors) and the system's input, which includes triggering thresholds for ETC communications and communication delays. Furthermore, with the proposed ETC mechanism, the number of communications among the vehicles are significantly reduced. Simulation examples of multiple autonomous vehicles executing CPF maneuvers in 2D under different communication scenarios illustrate the efficacy of the CPF strategy proposed.     

Cooperative control of multiple surface vessels with discrete‐time periodic communications

This paper addresses the problem of cooperative path‐following of networked autonomous surface vessels with discrete‐time periodic communications. The objective is to steer a group of autonomous vehicles along given spatial paths, while holding a desired inter‐vehicle formation pattern. For a given class of marine vessels, we show how Lyapunov‐based techniques, graph theory, and results from networked control systems can be brought together to yield a decentralized control structure where the dynamics of the cooperating vessels and the constraints imposed by the topology of the inter‐vehicle communication network are explicitly taken into account. Cooperation is achieved by adjusting the speed of each vessel along its path according to information exchanged periodically on the positions of a subset of the other vessels, as determined by the communications topology adopted. The closed‐loop system that is obtained by putting together the path‐following and cooperation strategies takes an interconnected feedback form where both systems are input‐to‐state stable with respect to the outputs of each other. Using a small‐gain theorem, stability and convergence of the overall system are guaranteed for adequate choices of the controller gains. Copyright © 2011 John Wiley & Sons, Ltd.     

Pattern preserving path following of unicycle teams with communication delays

This paper examines the problem of pattern-preserving path following control for unicycle teams with time-varying communication delay. A key strategy used here introduces a virtual vehicle formation such that each real vehicle has a corresponding virtual vehicle as its pursuit target. Under an input-driven consensus protocol, the virtual vehicle formation is forced to stay close to the desired vehicle formation; and a novel controller design is proposed to achieve virtual leader tracking for each vehicle with constrained motion. It is shown that, by the proposed strategy, the pattern can be preserved if the formation speed is less than some computable value that decreases with increasing size of delay, and the exact desired formation pattern can be eventually achieved if this speed tends to zero.     

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.     

A control strategy for platoons of differential drive wheeled mobile robot

The strategy for the control of vehicle platooning is proposed and tested on different mobile robot platforms. The decentralized platooning is considered, i.e. a virtual train of vehicles where each vehicle is autonomous and decides on its motion based on its own perceptions. The following vehicle only has information about its distance and azimuth to the leading vehicle. Its position is determined using odometry. The reference position and the orientation of the following vehicle are determined by the estimated path of the leading vehicle in a parametric polynomial form. The parameters of the polynomials are determined using the least-squares method. This parametric reference path is also used to determine the feed-forward part and to suppress tracking errors by a feed-back part of the applied globally stable nonlinear control law. The results of the experiment and simulations demonstrate the applicability of the proposed algorithm for vehicle platoons.     

Immersion and invariance-based integrated guidance and control for unmanned aerial vehicle path following

An integrated guidance and control scheme is proposed on path following for the unmanned aerial vehicle. It is capable of handling the coupled non-linearities of the path's kinematics and the aircraft's dynamics independently. In the path coordinate, the guidance law is designed based on a nominal model, and the non-linearity of the path's kinematics is taken into full consideration. In the time coordinate, the flight control law is designed as a feed-forward controller, and it can guarantee the robustness of the guidance law with respect to the actual aircraft's dynamics. Instead of only employing Lyapunov method, the concept of immersion and invariance is also applied to explicitly analyse the stability in both time and path coordinates, and the asymptotic stability of the closed-loop system can be guaranteed. What is more, the regulation-based and immersion-based adaptive technologies are synthetically utilised to handle the unknown parameters. Finally, the numerical simulations demonstrate the effectiveness of the developed integrated guidance and control scheme.     

A linearizing feedback for stabilizing a car-like robot following a curvilinear path

The path following problem for a car-like robot is considered. The control goal is to bring the robot to a pre-assigned curvilinear path and to stabilize its motion along the path. A new canonical change of variables is suggested. It reduces the problem of stabilizing robot’s motion to that of stability of the zero solution of the transformed system in the form that admits feedback linearization. A new control law is synthesized that ensures linearity of the closed-loop system and stabilizes robot’s motion along a given target path if the initial conditions belong to a known region. Comparison of the new control law with two earlier obtained linearizing feedbacks known from the literature demonstrates its unquestionable advantages.     

基于迭代滑模增量反馈的欠驱动AUV地形跟踪控制

为实现欠驱动自治水下机器人(AUV)在未知海流干扰作用下的地形跟踪控制,提出一种基于非线性迭代滑模增量反馈的航迹跟踪控制器.基于虚拟向导的方法,建立AUV垂直面航迹跟踪误差方程.采用迭代方法,设计滑模增量反馈控制器,无需对AUV模型参数不确定部分和海流干扰进行估计,这样避免了AUV俯仰舵的抖振现象,并且减小了输出反馈控制的稳态误差与超调问题.仿真实验表明,所设计的控制器对AUV系统的模型参数摄动及海流干扰变化不敏感,所设计的参数易于调节.     

Curved Path Following Control for Fixed-wing Unmanned Aerial Vehicles with Control Constraint

The control inputs of a fixed-wing unmanned aerial vehicle (UAV) are affected by external environment, the largest mechanical limits and energy limits. It is essential to consider the control constraints for the curved path following problem when the curvature of the desired path is continuing-changed. This paper presents two approaches to address the curved path following problem of fixed-wing UAVs subject to wind and we explicitly account for the control constraints. First, a proper state feedback controller is developed that is based on the tracking error equation defined in the Frenet-Serret frame to confirm that there is a control Lyapunov function (CLF) for input constrained case. Second, a stabilizing guidance law with control damping based on the designed CLF, which satisfies the small control property, is implemented to ensure the global asymptotic stability of the fixed-wing UAV curved path following subject to wind. Meanwhile, a control scheme with the nested saturation (NS) theory for curved path following is also developed with proven stability. The simulation results are presented to illustrate the effectiveness and high tracking performances of the proposed control strategies.     

Current Estimation and Path Following for an Autonomous Underwater Vehicle (AUV) by Using a High-gain Observer Based on an AUV Dynamic Model

A path following problem for autonomous underwater vehicles (AUVs) under a nonuniform current is presented in this paper. A dynamic model of an AUV in a nonuniform flow was adopted to develop a high-gain observer (HGO) for estimation of the three-dimensional current velocities along AUV trajectories. The HGO was chosen as a nonlinear estimation algorithm, and the observer gain was computed by solving a Linear Matrix Inequality (LMI) which represented the estimation error dynamics. The current velocities were determined by calculating the differences between the measured absolute velocities of the vehicle and the estimated relative velocities of the vehicle estimated by the observer. The estimation error means of the HGO using the LMI have smaller values than the state observer with a gain matrix determined by the pole-placement approach. For the path following study, the desired curved path was represented by using a Serret-Frenet frame which propagated along the curve. The path-following system includes a guidance law, an update law and a proportional and integral controller. Two cases of numerical simulations were conducted to verify the performance of the path following system combined with HGO for current compensation, and the results of both cases have shown that the AUV reached and converged to the desired path.

     

基于滑模自抗扰的智能车路径跟踪控制

针对传统的基于精确数学模型的路径跟踪控制方法很难适应复杂多变驾驶环境的问题,提出一种基于终端滑模控制与自抗扰控制的路径跟踪控制方法.首先,通过构造一个期望偏航角函数能够满足当车辆的实际偏航角趋近于该期望偏航角时其侧向位移偏差趋近于零,从而简化路径跟踪控制;然后,采用扩张状态观测器实时估计系统的未建模动态,同时采用非奇异终端滑模来设计非线性误差反馈律,从而实现偏航角快速、准确地跟踪控制.仿真结果表明,所设计的控制器能够保证车辆稳定行驶的同时快速、精确地跟踪期望的路径.     

Ellipsoidal approximations of the attraction domain in the path following problem for a wheeled robot with constrained resource

The path following problem for a wheeled robot with constrained resource moving along a given curvilinear path is studied. With the help of an earlier introduced change of variables, the path following problem is reduced to that of stability of the zero solution, and a control law linearizing the system in the case of the unconstrained control resource is synthesized. For the closed-loop system, the problem of finding the best ellipsoidal approximation of the attraction domain of the target path is set. To take into account the control constraint, an approach based on absolute stability theory is used. In the framework of this approach, construction of an approximating ellipse reduces to solving a parameterized system of linear matrix inequalities. The LMI system in the considered case can be solved analytically. Owing to this, construction of the best ellipsoidal approximation is reduced to solving a standard constrained optimization problem for a function of two variables. The proposed method is further extended to finding the best ellipsoidal approximation with an additional constraint on the maximum deviation from the target path. The discussion is illustrated by numerical examples.     

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.     

Nested PID steering control for lane keeping in autonomous vehicles

In this paper a nested PID steering control in vision based autonomous vehicles is designed and experimentally tested to perform path following in the case of roads with an uncertain curvature. The control input is the steering wheel angle: it is designed on the basis of the yaw rate, measured by a gyroscope, and the lateral offset, measured by the vision system as the distance between the road centerline and a virtual point at a fixed distance from the vehicle. No lateral acceleration and no lateral speed measurements are required. A PI active front steering control based on the yaw rate tracking error is used to improve the vehicle steering dynamics. The yaw rate reference is computed by an external control loop which is designed using a PID control with a double integral action based on the lateral offset to reject the disturbances on the curvature which increase linearly with respect to time. The proposed control scheme leads to a nested architecture with two independent control loops that allows us to design standard PID controls in a multivariable context (two outputs, one input). The robustness of the controlled system is theoretically investigated with respect to speed variations and uncertain vehicle physical parameters. Several simulations are carried out on a standard big sedan CarSim vehicle model to explore the robustness with respect to unmodelled effects. The simulations show reduced lateral offset and new stable μ-split braking maneuvres in comparison with the model predictive steering controller implemented by CarSim. Finally the proposed control law is successfully tested by experiments using a Peugeot 307 prototype vehicle on the test track in Satory, 20 km west of Paris.     

Adaptive neural control for cooperative path following of marine surface vehicles: state and output feedback

This paper addresses the cooperative path-following problem of multiple marine surface vehicles subject to dynamical uncertainties and ocean disturbances induced by unknown wind, wave and ocean current. The control design falls neatly into two parts. One is to steer individual marine surface vehicle to track a predefined path and the other is to synchronise the along-path speed and path variables under the constraints of an underlying communication network. Within these two formulations, a robust adaptive path-following controller is first designed for individual vehicles based on backstepping and neural network techniques. Then, a decentralised synchronisation control law is derived by means of consensus on along-path speed and path variables based on graph theory. The distinct feature of this design lies in that synchronised path following can be reached for any undirected connected communication graphs without accurate knowledge of the model. This result is further extended to the output feedback case, where an observer-based cooperative path-following controller is developed without measuring the velocity of each vehicle. For both designs, rigorous theoretical analysis demonstrate that all signals in the closed-loop system are semi-global uniformly ultimately bounded. Simulation results validate the performance and robustness improvement of the proposed strategy.