Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles:A path-following framework

This article investigates a multi-circular path-following formation control with reinforced transient profiles for nonholonomic vehicles connected by a digraph.A multi-circular formation controller endowed with the feature of spatial-temporal decoupling is devised for a group of vehicles guided by a virtual leader evolving along an implicit path,which allows for a circumnavigation on multiple circles with an anticipant angular spacing.In addition,notice that it typically imposes a stringent time constraint on time-sensitive enclosing scenarios,hence an improved prescribed performance control(IPPC)using novel tighter behavior boundaries is presented to enhance transient capabilities with an ensured appointed-time convergence free from any overshoots.The significant merits are that coordinated circumnavigation along different circles can be realized via executing geometric and dynamic assignments independently with modified transient profiles.Furthermore,all variables existing in the entire system are analyzed to be convergent.Simulation and experimental results are provided to validate the utility of suggested solution.

A Novel Prescribed-Performance Path-Following Problem for Non-Holonomic Vehicles

The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlled vehicle.In this context,a novel form of the prescribed performance guiding vector field is introduced,accompanied by a prescribed-time sliding mode con-trol approach.Furthermore,the interdependence among the pre-scribed parameters is discussed.To validate the effectiveness of the proposed method,numerical simulations are presented to demonstrate the efficacy of the approach.

Finite-Time Sideslip Differentiator-Based LOS Guidance for Robust Path Following of Snake Robots

This paper presents a finite-time sideslip differentiator-based line-of-sight(LOS)guidance method for robust path following of snake robots.Firstly,finite-time stable sideslip differentiator and adaptive LOS guidance method are proposed to counteract sideslip drift caused by cross-track velocity.The proposed differentiator can accurately observe the cross-track error and sideslip angle for snake robots to avoid errors caused by calculating sideslip angle approximately.In our method,the designed piecewise auxiliary function guarantees the finite-time stability of position errors.Secondly,for the case of external disturbances and state constraints,a Barrier Lyapunov functionbased backstepping adaptive path following controller is presented to improve the robot’s robustness.The uniform ultimate boundedness of the closed-loop system is proved by analyzing stability.Additionally,a gait frequency adjustment-based virtual velocity control input is derived to achieve the exponential convergence of the tangential velocity.At last,the availability and superiority of this work are shown through simulation and experiment results.

LSTM-DPPO based deep reinforcement learning controller for path following optimization of unmanned surface vehicle

To solve the path following control problem for unmanned surface vehicles(USVs),a control method based on deep reinforcement learning(DRL)with long short-term memory(LSTM)networks is proposed.A distributed proximal policy opti-mization(DPPO)algorithm,which is a modified actor-critic-based type of reinforcement learning algorithm,is adapted to improve the controller performance in repeated trials.The LSTM network structure is introduced to solve the strong temporal cor-relation USV control problem.In addition,a specially designed path dataset,including straight and curved paths,is established to simulate various sailing scenarios so that the reinforcement learning controller can obtain as much handling experience as possible.Extensive numerical simulation results demonstrate that the proposed method has better control performance under missions involving complex maneuvers than trained with limited scenarios and can potentially be applied in practice.

Constrained Moving Path Following Control for UAV With Robust Control Barrier Function

This paper studies the moving path following(MPF)problem for fixed-wing unmanned aerial vehicle(UAV)under output constraints and wind disturbances.The vehicle is required to converge to a reference path moving with respect to the inertial frame,while the path following error is not expected to violate the predefined boundaries.Differently from existing moving path following guidance laws,the proposed method removes complex geometric transformation by formulating the moving path following problem into a second-order time-varying control problem.A nominal moving path following guidance law is designed with disturbances and their derivatives estimated by high-order disturbance observers.To guarantee that the path following error will not exceed the prescribed bounds,a robust control barrier function is developed and incorporated into controller design with quadratic program based framework.The proposed method does not require the initial position of the UAV to be within predefined boundaries.And the safety margin concept makes error-constraint be respected even if in a noisy environment.The proposed guidance law is validated through numerical simulations of shipboard landing and hardware-in-theloop(HIL)experiments.

Kinematics and Path Following Control of an Articulated Drum Roller

Automatic navigation of an articulated drum roller, which is an articulated steering type vehicle widely used in the construction industry, is highly expected for operation cost reduction and improvement of work effi- ciency. In order to achieve the path following control, considering that its steering system is articulated steering and two frames are articulated by an active revolute joint, a kinematic model and an error dynamic state-space equation of an articulated drum roller are proposed. Besides, a state- feedback control law based on Lyapunov stability theory is also designed, which can be proved to achieve the purpose of control by the analysis of stability. What＇s more, to evaluate the performance of the proposed method, simu- lation under the MATLAB/Simulink and experiments using positioning algorithm and errors correction at the uneven construction site are performed, with initial dis- placement error （-1.5 m）, heading error （-0.11 tad） and steering angle （-0.19 rad）. Finally, simulation and exper- imental results show that the errors and steering angle can decrease gradually, and converge to zero with time. Meanwhile, the control input is not saturated. An articu- lated drum roller can lock into a desired path with the proposed method in uneven fields.

Path Following Control of A Deep-Sea Manned Submersible Based upon NTSM

In this paper, a robust path following control law is proposed for a deep-sea manned submersible maneuvering along a predeterminated path. Developed in China, the submersible is underactuated in the horizontal plane in that it is actuated by two perpendicular thrusts in this plane. The advanced non-singular terminal sliding mode （NTSM） is implemented for the design of the path following controller, which can ensure the convergence of the motion system in finite time and improve its robustness against parametric uncertainties and environmental disturbances. In the process of controller design, the close-loop stability is considered and proved by Lyapunov＇ s stability theory. With the experimental data, numerical simulations are provided to verify the control law for path following of the deep-sea manned submersible.

Adaptive sliding-mode path following control system of the underactuated USV under the influence of ocean currents

The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller.

Inverse Optimal Control for Speed-varying Path Following of Marine Vessels with Actuator Dynamics

A controller which is locally optimal near the origin and globally inverse optimal for the nonlinear system is proposed for path following of over actuated marine crafts with actuator dynamics. The motivation is the existence of undesired signals sent to the actuators, which can result in bad behavior in path following. To attenuate the oscillation of the control signal and obtain smooth thrust outputs, the actuator dynamics are added into the ship maneuvering model. Instead of modifying the Line-of-Sight (LOS) guidance law, this proposed controller can easily adjust the vessel speed to minimize the large cross-track error caused by the high vessel speed when it is turning. Numerical simulations demonstrate the validity of this proposed controller.

Path following control of underactuated ships based on nonswitch analytic model predictive control

A path following controller is developed for underactuated ships with only surge force and yaw moment available to follow a predefined path.The proposed controller is based on nonswitch analytic model predictive control.It is shown that the optimal control law for a nonlinear path following system with ill-defined relative degree is continuous and nonsingular.The problem of ill-defined relative degree is solved.The path-following ability of the nonlinear system is guaranteed.Numerical simulations are provided to demonstrate the effectiveness of the proposed control law.

Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties

The path following problem for an underactuated unmanned surface vehicle(USV) in the Serret-Frenet frame is addressed. The control system takes account of the uncertain influence induced by model perturbation, external disturbance, etc. By introducing the Serret-Frenet frame and global coordinate transformation, the control problem of underactuated system(a nonlinear system with single-input and ternate-output) is transformed into the control problem of actuated system(a single-input and single-output nonlinear system), which simplifies the controller design. A backstepping adaptive sliding mode controller(BADSMC)is proposed based on backstepping design technique, adaptive method and theory of dynamic slide model control(DSMC). Then, it is proven that the state of closed loop system is globally stabilized to the desired configuration with the proposed controller. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Adaptive back-stepping control on container ships for path following

A feedback-dominance based adaptive back-stepping(FDBAB) controller is designed to drive a container ship to follow a predefined path. In reality, current, wave and wind act on the ship and produce unwanted disturbances to the ship control system.The FDBAB controller has to compensate for such disturbances and steer the ship to track the predefined(or desired) path. The difference between the actual and the desired path along which the ship is to sail is defined as the tracking error. The FDBAB controller is built on the tracking error model which is developed based on Serret-Frenet frame transformation(SFFT). In additional to being affected by external disturbances, the ship has more outputs than inputs(under-actuated), and is inherently nonlinear.The back-stepping controller in FDBAB is used to compensate the nonlinearity. The adaptive algorithms in FDBAB is employed to approximate disturbances. Lyapunov's direct method is used to prove the stability of the control system. The FDBAB controlled system is implemented in Matlab/Simulink. The simulation results verify the effectiveness of the controller in terms of successful path tracking and disturbance rejection.

Robust Adaptive Path Following for Underactuated Surface Vessels with Uncertain Dynamics

柔韧的适应控制策略被开发强迫一个 underactuated 表面容器跟随一条引用路径，尽管有包括外长的骚乱和测量噪音的不明确的参数和未组织的无常的存在。参考路径能是一条曲线或一根直线。建议控制器被使用 Lyapunovs 直接方法和滑动模式控制和 backstepping 技术设计。因为容器的摇摆轴直接没被激活，二滑动表面被介绍，第一以追踪的巨浪运动，为 yaw 的错误和第二个错误打手势追踪错误。适应控制法律保证制服得到了追踪的错误的最终的固定。数字模拟结果被提供为路径列在后面 underactuated 表面容器验证建议控制器的有效性。

PREDICTIVE CONTROL FOR OPTIMAL PATH TERRAIN FOLLOWING SYSTEM

In this paper output predictive algorithm is applied to the design of predictive controller for an optimal path terrain following system. In this way, the error of path tracking is decreased to a minimum degree simply and efficiently and the computation time for the optimal path is shortened greatly. Therefore, the real-time processing of the optimal path terrain following system is made to be very helpful.

Following Control for a UUV using Temporary Path Generation Guidance

一个路径追随者控制算法为一无人在水下用暂时的路径产生指导的车辆(UUV ) 在这份报纸被建议。由于车辆的不同起始的状态，例如位置和取向，在水平飞机的路径追随者控制可以产出差的表演。为了处理否定效果，由起始的状态导致了，暂时的路径代基于在原来的参考书路径和车辆之间的关系被介绍起始的状态。与在车辆和参考书路径之间的不同相对位置，从直线，以及里面并且在一个圆外面包括，指导车辆到参考书路径的相关暂时的路径能在实时被产生。车辆被指导驾驶暂时的路径直到它在参考书路径到达了正切点，在控制器用输入产量反馈 linearization 方法被设计的地方。模拟结果证明建议算法在上面提及的三种不同状况下面是有效的。

Virtual Simulation System with Path-following Control for Lunar Rovers Moving on Rough Terrain

Virtual simulation technology is of great importance for the teleoperation of lunar rovers during the exploration phase, as well as the design of locomotion systems, performance evaluation, and control strategy verification during the R&D phase. The currently used simulation methods for lunar rovers have several disadvantages such as poor fidelity for wheel-soil interaction mechanics, difficulty in simulating rough terrains, and high complexity making it difficult to realize mobility control in simulation systems. This paper presents an approach for the construction of a virtual simulation system that integrates the features of 3D modeling, wheel-soil interaction mechanics, dynamics analysis, mobility control, and visualization for lunar rovers. Wheel-soil interaction experiments are carried out to test the forces and moments acted on a lunar rover’s wheel by the soil with a vertical load of 80 N and slip ratios of 0, 0.03, 0.05, 0.1, 0.2, 0.3, 0.4, and 0.6. The experimental results are referenced in order to set the parameters’ values for the PAC2002 tire model of the ADAMS/Tire module. In addition, the rough lunar terrain is simulated with 3DS Max software after analyzing its characteristics, and a data-transfer program is developed with Matlab to simulate the 3D reappearance of a lunar environment in ADAMS. The 3D model of a lunar rover is developed by using Pro/E software and is then imported into ADAMS. Finally, a virtual simulation system for lunar rovers is developed. A path-following control strategy based on slip compensation for a six-wheeled lunar rover prototype is researched. The controller is implemented by using Matlab/Simulink to carry out joint simulations with ADAMS. The designed virtual lunar rover could follow the planned path on a rough terrain. This paper can also provide a reference scheme for virtual simulation and performance analysis of rovers moving on rough lunar terrains.

Sliding-mode control of path following for underactuated ships based on high gain observer

A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.

Dynamic Path Following Control of a Ground Ackerman Steering Robot to Avoid a Collision

A novel method is proposed to dynamically control the path following of a ground Ackerman steering robot to avoid a collision.The method consists of collision prediction module,collision avoidance module and global path following module.The elliptic repulsive potential field method（ER-PFM）and the enhanced vector polar histogram method（VPH＋）based on the Ackerman steering model are proposed to predict the collision in a dynamic environment.The collision avoidance is realized by the proposed cost function and speed control law.The global path following process is achieved by pure pursuit.Experiments show that the robot can fulfill the dynamic path following task safely and efficiently using the proposed method.

Mouse-Sensitive Following Path Suggestion for Drawing Travel Routes in Web Map Systems

This paper proposes a web map system for drawing an arbitrary travel route using a mouse-sensitive following path suggestion. The interaction model of the system allows users to intuitively understand the sequence of user actions needed to draw a conceived route and reduces the number of user actions required. Moreover, the system allows users to understand at a glance several drawing alternatives (static suggestion) and also consider a particular drawing alternative (dynamic suggestion) without making any commitment. The proposed architecture of the system reduces the influence caused by communication delay between a map server and a web client by delivering in advance road network data from a map server to a web client. Experimental evaluations on a prototype we developed demonstrated that the proposed system enables users to draw arbitrary routes within noticeably less clicks, in less time, and with less stress than previous systems.

Russian-Chinese economic cooperation: flat roads following a path overgrown with brambles

Russian-Chinese trade began to achieve fairly rapid development in the late 1980s. In recent years, however, bilateral trade has shown a declining trend. In 1997, the amount dropped by 10.6 percent from 1996 to US$6.12 billion. Whether in Moscow or Beijing, people distinctly realize that both sides earnestly hope to enhance cooperation on a brand-new basis. For this purpose, both governments are putting into practice longterm mutually beneficial large cooperation projects in areas of technological investment. In December 1997, the two sides signed the contract on