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A snake robot should be robust to actuator failures because it has more actuators than required for locomotion. However, controlling a snake robot is problematic if some of the joints become passive because of problems in power supply lines. In a recent study, we proposed a controller to achieve path-following in cases where one of the joints is passive. However, the controller applies only to cases with a single passive joint. With two or more passive joints, it cannot be applied even if sufficient active joints remain. This paper considers the path-following control of a snake robot with passive joints by extending our previous study (the single passive joint case). The validity of the method is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This article focuses on a double layer virtual ship guidance–based adaptive event–triggered path-following control for unmanned surface vehicle under the unknown actuator gain and deception attacks. In the guidance unit, the adaptive virtual ship is developed to derive the smooth reference paths for the controlled objective. That can effectively remove the abrupt phenomenon of actuators. Associated with the double layer virtual ship guidance strategy, a robust adaptive control algorithm is proposed for the unmanned surface vehicle by fusing the event-triggered rule and the adaptive compensated technique. In the algorithm, the deception attacks caused by the communication channel were compensated by constructing the attack adaptive parameters. That is critical to improve the accuracy and stabilize of the closed-loop control system. Besides, the transmission burden from the controller to the actuator was reduced for merits of the input-based event-triggered mechanism. Finally, the theoretical stability was proofed by the Lyapunov theorem, and the well performance was obtained through numerical simulation in presence of the time-varying disturbances. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator. Design/methodology/approach: When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method. Findings: Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits. Research limitations/implications: Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking. Originality/value: Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time. [ABSTRACT FROM AUTHOR]

The problem addressed in the present paper is the design of a controller based on an evolutionary neural network for autonomous flight in quadrotor systems. The controller's objective is to govern the quadcopter in such a way that it reaches a specific position, bearing on attitude limitations during flight and upon reaching a target. Given the complex nature of quadcopters, an appropriate neural network architecture and a training algorithm were designed to guide a quadcopter toward a target. The designed controller was implemented as a single multi-layer perceptron. On the basis of the quadcopter's current state, the developed neurocontroller produces the correct rotor speed values, optimized in terms of both attitude-limitation compliance and speed. The neural network training was completed using a custom evolutionary algorithm whose design put particular emphasis on the cost function's definition. The developed neurocontroller was tested in simulation to drive a quadcopter to autonomously follow a complex path. The obtained simulated results show that the neurocontroller manages to effortlessly follow several types of paths with adequate precision while maintaining low travel times. [ABSTRACT FROM AUTHOR]

In this research, we offer eigenvalue analysis and path following continuation to describe the impact, stick, and non-stick between the particle and boundaries to understand the nonlinear dynamics of an extended Fermi oscillator. The principles of discontinuous dynamical systems will be utilized to explain the moving process in such an extended Fermi oscillator. The motion complexity and stick mechanism of such an oscillator are demonstrated using periodic and chaotic motions. The major parameters are the frequency, amplitude in periodic excitation force, and the gap between the top and bottom boundary. We employ path-following analysis to illustrate the bifurcations that lead to solution destabilization. We present the evolution of the period solutions of the extended Fermi oscillator as the parameter varies. From the viewpoint of eigenvalue analysis, the essence of period-doubling, saddle-node, and Torus bifurcation is revealed. Numerical continuation methods are used to do a complete one- and two-parameter bifurcation analysis of the extended Fermi oscillator. The presence of codimension-one bifurcations of limit cycles, such as saddle-node, period-doubling, and Torus bifurcations, is shown in this work. Bifurcations cause all solutions to lose stability, according to our findings. The acquired results provide a better understanding of the extended Fermi oscillator mechanism and demonstrate that we may control the system dynamics by modifying the parameters. [ABSTRACT FROM AUTHOR]

Elastic instabilities have traditionally been considered a failure mechanism; however, recent years have seen numerous studies exploiting instabilities as a means to achieve structural functionality. By contrast, interacting instabilities and compound buckling are still largely viewed as a failure mechanism. In this paper, we show that interacting instabilities can also be exploited to achieve bespoke functionality. We focus on 'sequential instabilities', whose associated critical points cannot both lie on a fundamental equilibrium path. We obtain sequential instabilities by combining canonical bifurcations, (e.g. limit point, pitchfork) as building-blocks. Initially, this concept is explored through simple bar-and-spring models that are found to have several properties not exhibited by the building blocks from which they are constructed. Further, the utility of the building block approach, and that of sequential, interacting instabilities, is demonstrated through the development of a morphing structure which must rapidly deploy after a critical input displacement is attained, and meet specific post-deployment stiffness requirements. Two design concepts are proposed, each comprising building blocks to mirror the fundamental working principles identified through the bar-and-spring models. Finite-element models of the design solutions are presented, demonstrating how the designs positively use sequential, interacting instabilities in order to meet the challenging requirements of the application. This work extends the contextual framework of instabilities that can be used to create structures with novel functionality. [ABSTRACT FROM AUTHOR]

This paper uses a line-following approach to study the longitudinal and lateral problems in vehicle platooning. Under this setup, we assume that inter-vehicle distance sensing is unreliable and propose a cooperative control strategy to render the platoon less vulnerable to these sensing difficulties. The proposed control scheme uses the velocity of the predecessor vehicle, communicated through a Vehicle-to-Vehicle technology, to avoid significant oscillations in the local speed provoked by tracking using unreliable local distance measurements. We implement the proposed control algorithm in the RUPU platform, a low-cost experimental platform with wireless communication interfaces that enable the implementation of cooperative control schemes for mobile agent platooning. The experiments show the effectiveness of the proposed cooperative control scheme in maintaining a suitable performance even when subject to temporal distortions in local measurements, which, in the considered experimental setup, arise from losing the line-of-sight of the local sensors in paths with closed curves. [ABSTRACT FROM AUTHOR]

To ensure that a liquid tank semi-trailer has good yaw stability and path-following performance on low-adhesion roads under turning conditions, a multi-object PID differential braking-control method is proposed, which takes the tractor yaw rate, semi-trailer yaw rate, and articulation angle as the control parameters. According to the principle of equivalence, the trammel pendulum (TP) model is used to simulate the liquid sloshing effect in the liquid tank, and the Fluent software is used to identify the key parameters of the trammel pendulum model and verify the correctness of its simulation effect. Then, a co-simulation model is built based on TruckSim and MATLAB/Simulink. Based on the simplified six degrees of freedom model and the co-simulation model of a liquid tank semi-trailer, a multi-object PID differential braking-control method is designed, and the vehicle state responses with and without control are compared when it is turning on a low-adhesion road. The simulation results show that the proposed multi-object PID differential braking-control method can effectively improve the yaw stability and path-following performance of the liquid tank semi-trailer when turning on a low-adhesion road. [ABSTRACT FROM AUTHOR]

Conventional medical instruments are not capable of passing through tortuous anatomy as required for natural orifice transluminal endoscopic surgery due to their rigid shaft designs. Nevertheless, developments in minimally invasive surgery are pushing medical devices to become more dexterous. Amongst devices with controllable flexibility, so-called Follow-The-Leader (FTL) devices possess motion capabilities to pass through confined spaces without interacting with anatomical structures. The goal of this literature study is to provide a comprehensive overview of medical devices with FTL motion. A scientific and patent literature search was performed in five databases (Scopus, PubMed, Web of Science, IEEExplore, Espacenet). Keywords were used to isolate FTL behavior in devices with medical applications. Ultimately, 35 unique devices were reviewed and categorized. Devices were allocated according to their design strategies to obtain the three fundamental sub-functions of FTL motion: steering, (controlling the leader/end-effector orientation), propagation, (advancing the device along a specific path), and conservation (memorizing the shape of the path taken by the device). A comparative analysis of the devices was carried out, showing the commonly used design choices for each sub-function and the different combinations. The advantages and disadvantages of the design aspects and an overview of their performance were provided. Devices that were initially assessed as ineligible were considered in a possible medical context or presented with FTL potential, broadening the classification. This review could aid in the development of a new generation of FTL devices by providing a comprehensive overview of the current solutions and stimulating the search for new ones. [ABSTRACT FROM AUTHOR]

Path-following techniques of ships have received a lot of attention in recent years, to promote future autonomous ships and develop advanced autopilots. This paper deals with the path-following problem of underactuated ships without having prior knowledge regarding the hydrodynamic coefficients and ship parameters. A novel data-driven control strategy that combines Koopman operator theory and extended dynamic mode decomposition (EDMD) method and integrates with a model predictive control (MPC) framework is proposed. It makes use of data collected from experiments to learn the Koopman eigenfunctions of unknown ship dynamics via supervised learning, which are utilized as the lifting functions in the EDMD method to build a linear, lifted state-space model. The identified linear model acts as the predictor in the designed MPC controller, and a line-of-sight (LOS) algorithm is introduced as the guidance law for path-following. Simulation results show that the prediction model could provide sufficient prediction accuracy, and that it can be combined with MPC to achieve good path-following performance in a computationally efficient way. [ABSTRACT FROM AUTHOR]

Unmanned Aerial Vehicles (UAVs) are aircraft that can be manually operated or autonomously guided through an autopilot. In the last case, the system is responsible for stabilising the aircraft and executing guidance tasks such as path-following. In literature, several path-following algorithms were proposed for straight lines and loiter paths. Previous comparisons generally consider straight line algorithms in a 2D space using the kinematic model of an aircraft. In order to complement existing research, this paper compares four 3D path-following algorithms for loiter paths under different wind intensities. Tests are made through Software-in-the-Loop (SiL) simulations using the dynamic model of a fixed-wing UAV. Furthermore, a genetic algorithm is employed to tune the parameters and the analysis is carried out under varying wind conditions. The algorithms compared are four well-known geometric methods: Carrot-Chasing (CC), Non-Linear Guidance Law (NLGL), Pure Pursuit and Line-of-Sight (PLOS) and Vector Field (VF). Results show that Vector Field has the smallest errors, while PLOS is the most resistant to wind disturbance. [ABSTRACT FROM AUTHOR]

Inland waterway transportation is one of the most important means to transport cargo in rivers and canals. To facilitate autonomous navigation for ships in inland waterways, this paper proposes a data-driven approach for predictions and control of underactuated ships with unknown dynamics, which integrates model predictive control (MPC) with an iterative learning control (ILC) scheme. In each iteration, kernel-based linear regressors are used to identify the relations between the evolution of ship states and control inputs based on the stored data from previous iterations and the collected data during operation, so as to build the system prediction model. The data are dynamically used to fix the prediction model over iterations, as well as to improve the controller performance until it converges. The proposed approach does not require prior knowledge regarding the hydrodynamic coefficients and ship parameters, but learns from the data instead. In addition, it exploits the advantages of MPC in handling constraints with minimised overall cost. Simulation results show that the controller could start from a nominal, linear data-driven ship model and then learn to reduce the path-following errors based on the data obtained over iterations. [ABSTRACT FROM AUTHOR]

In this research, we offer a bifurcation analysis to describe impacting, stick, and grazing between a particle and the piston to better understand the nonlinear dynamics of a Fermi oscillator. The principles of hybrid dynamical systems will be utilized to explain the moving process in such a Fermi oscillator. The motion complexity and stick mechanism of such an oscillator are demonstrated using periodic and chaotic motions. We introduce the hybrid dynamical system and numerical continuation detection tool COCO. Physical and mathematical models are used to construct the obtained bounded mathematical model. The frequency, amplitude in oscillating base displacement, and the gap between the stationary boundary and the piston's equilibrium position are the major parameters. We employ path-following analysis to illustrate the bifurcation that leads to solution destabilization. From the viewpoint of eigenvalue analysis, the essence of period-doubling and Fold bifurcation is revealed. Numerical continuation methods are used to perform a complete one-parameter bifurcation analysis of the Fermi oscillator. The presence of codimension-1 bifurcations of limit cycles, like period-doubling, fold, and grazing bifurcations, is shown in this work. Then, the one-parameter continuation analysis is tracked in two-parameter bifurcation diagrams that include a second important factor of interest. Bifurcations cause all solutions to lose stability, according to our findings. The acquired results provide a better understanding of the Fermi oscillator mechanism and demonstrate that we may control the system dynamics by modifying the parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new approach for lane change and double-lane change planning and following for autonomous driving is proposed. Herein, we introduce a novel technique, based on exponential functions, to generate online and feasible lane change maneuvers; these maneuvers satisfy the constraints on the maximum allowable curvature a given vehicle can handle. In addition, a simultaneous local path planning and path-following control framework is adapted. The framework utilizes a multi-threading architecture to run the local planner module concurrently with the control module. The planning module generates parametric reference paths based on the proposed lane change and double-lane change maneuvers. The control module is based on a Model Predictive Path-following Control (MPFC) scheme, which achieves the path following objective while satisfying vehicle’s state and control limits. To validate the proposed framework, several real-time simulation scenarios are designed and tested on CARLA soft real-time vehicle simulator. The results show the effectiveness of the proposed framework in generating and smoothly following lane change maneuvers. [ABSTRACT FROM AUTHOR]

Due to the simultaneous existence of model uncertainties and external disturbances, designing automated ground vehicle path-following controllers is recognized as a challenging task. The $H_{\infty }$ robust control methodology, as one of the accomplished strategies for controller robustification, has been commonly adopted by researchers to address the vehicle path-tracking problems. Nevertheless, despite its advantages, the $H_{\infty }$ controller is only capable of limiting the total “energy” of the tracking errors. On the other hand, from a safety standpoint, constraining the “peak” of the tracking errors may carry an equal or more importance. To establish a guaranteed upper bound on the path-tracking errors, this paper proposes a novel methodology to synthesis the ground vehicle path-following controller in light of the energy-to-peak robust control theory. Additionally, to address the time-varying uncertainties presented in the tire dynamics, robust stabilization constraints based upon the small-gain theorem are also formulated into the overall controller design problem. Comparative study regarding the disturbance rejection performance between the proposed controller and the conventional $H_{\infty }$ approach is conducted via CarSim-Simulink joint simulations. Furthermore, the robustness and disturbance attenuation ability of the energy-to-peak path-tracking controller is experimentally verified on a scaled car. [ABSTRACT FROM AUTHOR]

Device-to-device (D2D) communication coexisted with a cell-free massive multiple-input multiple-output (MIMO) system will be one of the pieces of the B5G/6G jigsaw puzzle. In this article, a D2D underlaid cell-free massive MIMO system with low-resolution digital-to-analog converters is studied, where multiantenna D2D user equipments (DUEs) communicate pairwise with each other in the same time-frequency resources as cell-free with equipments (CFUEs). Assuming imperfect channel state information is available at access points (APs), the downlink closed-form achievable rates for both CFUEs and multiantenna DUEs are derived, which enable us to give insights into the impacts of the key design parameters (e.g., the AP number, the DUE density, and its antenna number) on achievable rate. After that, a power control scheme is developed to maximize the average sum rate of CFUEs and DUEs, and we show that the proposed power control problem can be effectively solved by using the path-following algorithm. Finally, numerical simulations are provided to highlight the system performance and verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel path-following and obstacle avoidance control method is given for nonholonomic wheeled mobile robots (NWMRs), based on deep reinforcement learning. The model for path-following is investigated first, and then applied to the proposed reinforcement learning control strategy. The proposed control method can achieve path-following control through interacting with the environment of the set path. The path-following control method is mainly based on the design of the state and reward function in the training of the reinforcement learning. For extra obstacle avoidance problems in following, the state and reward function is redesigned by utilizing both distance and directional perspective aspects, and a minimum representative value is proposed to deal with the occurrence of multiple obstacles in the path-following environment. Through the reinforcement learning algorithm deep deterministic policy gradient (DDPG), the NWMR can gradually achieve the path it is required to follow and avoid the obstacles in simulation experiments, and the effectiveness of the proposed algorithm is verified. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive neural fault-tolerant control algorithm for the path-following activity of the underactuated surface vehicle (USV) using the novel output-based triggering approach. In the algorithm, the event-triggered mechanism is designed utilizing the attitude states from the kinematics aspect of USV. Both the control inputs and the related calculation thread are implemented only at the trigger instants. Furthermore, neural networks (NNs) are employed to remodel the model uncertainties, and the adaptive observer is developed to estimate and compensate for the effect of the unknown actuator faults. With the direct Lyapunov theorem, the semi-global uniformly ultimately bounded (SGUUB) stability can be guaranteed for the closed-loop system in aspects of both the trigger instant and the continuous interval. The comparison experiment has been illustrated to verify the effectiveness of the proposed algorithm, which can effectively improve the information transmission performance and the fault-tolerant capability. [ABSTRACT FROM AUTHOR]

This paper proposes a novel control method for path-following of joints of a snake robot. The proposed method applies the port-controlled Hamiltonian based approach, which has originally been proposed for a full-actuated friction-less system. This paper extends the controller for an under-actuated system with friction. It is proven that, by the proposed controller, the path-following of the joints is achieved. The validity of the controller is checked through simulations. Furthermore, simulation results suggest that the controller is robust to modeling errors. [ABSTRACT FROM AUTHOR]

Aiming at the light rail train with rubber wheel bogies, a path-following control scheme based on road line recognition was proposed. The path-following performance and dynamics performance of the train were analyzed based on a dynamic model of a train with three car bodies. Acquiring the information of the road line, the "feedforward and feedback" method was used to ensure the train to path-following with better dynamics performance and riding quality by controlling the yaw angle of all the rubber wheelsets of the bogies. The simulation results show that under the effect of the path-following control scheme, the train can maintain good curve passing performance, dynamics performance and riding quality when passing through 15 m small curve radius and 50 m S-shaped curve section, respectively. [ABSTRACT FROM AUTHOR]

Autodriver algorithm aims to develop a path-following algorithm for autonomous vehicles using road geometry data and vehicle dynamics. In this study, a novel smart Autodriver algorithm is developed according to practical implications utilizing a more realistic vehicle model and consideration of real-time applicability. A ghost-car path-following approach is introduced to define the desired location of the vehicle at every instance during various maneuvers. Key steady-state characteristics of turning vehicles, namely the curvature, yaw rate, and side-slip responses are discussed and used to construct a path-following controller based on the Autodriver algorithm. A feedback control based on Sliding Mode Control (SMC) is also designed and applied to minimize transient errors between the road and the vehicle positions. Finally, simulations are performed to analyze the path-following performance of the proposed scheme compared to a Model Predictive Controller (MPC) as a widely accepted popular method for autonomous vehicles. Hardware-in-the-loop (HIL) tests are also performed to investigate real-time applicability of the controllers. The results show promising controller performance in terms of error minimization, passenger comfort, and low computational cost for the proposed method. [ABSTRACT FROM AUTHOR]

Maneuvering a truck-trailer system while docking is extremely challenging. This article aims to alleviate this problem by presenting an enhanced path-following control framework for autonomous semi-trailer docking. In the proposed system, adaptive controllers that utilize gain scheduling are introduced for forward and reverse path-following tasks in docking maneuvers to increase the robustness and path-following performance. The system includes an improved pure pursuit controller with adaptive look-ahead distance for forward path following; a cascade controller of reverse pure pursuit and a gain-scheduled LQ control for reverse path-following. In the evaluation of the path-following performance of forward and reverse controllers, the closed-loop system of path-following controllers with the truck-trailer kinematic model is simulated in MATLAB/Simulink for various test cases, and the results are compared with those of other studies. Furthermore, different docking scenarios are generated via the cascade path planning algorithm for autonomous semitrailer docking. These are tested with a high degree semi-trailer model within the IPG TruckMaker simulation environment, and with a full truck-trailer vehicle in the test field. The results of both simulations and physical testing clearly demonstrate improvements in terms of the control problem formulation, i.e., the stabilized path-following is obtained with acceptable path-following errors. [ABSTRACT FROM AUTHOR]

This article studies the design, modeling, and implementation of a path-following algorithm as a guidance, navigation, and control (GNC) architecture for an autonomous underwater vehicle (AUV). First, a mathematical model is developed based on nonlinear equations of motion and parameter estimation techniques, including the model validation based on field test data. Then, the guidance system incorporates a line-of-sight (LOS) algorithm with a combination of position PID controllers. The GNC architecture includes a modular and multi-layer approach with an LOS-based, path-following algorithm in the AUV platform. Furthermore, the navigation used in the path-following algorithm is developed based on a predefined coverage area. Finally, this study addresses simulation and field test control scenarios to verify the developed GNC architecture. [ABSTRACT FROM AUTHOR]

This paper analyzes the structure of the set of nodal solutions, i.e., solutions changing sign, of a class of one-dimensional superlinear indefinite boundary value problems with indefinite weight functions in front of the spectral parameter. Quite surprisingly, the associated high-order eigenvalues may not be concave as is the case for the lowest one. As a consequence, in many circumstances, the nodal solutions can bifurcate from three or even four bifurcation points from the trivial solution. This paper combines analytical and numerical tools. The analysis carried out is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously the numerical study confirms and illuminates the analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time three-dimensional path-following control problem for underactuated autonomous airship with error constraints and uncertainties. First, a five degrees-of-freedom path-following error model in the Serret-Frenet coordinate frame is established. By applying the finite-time stability theory, a virtual guidance-based finite-time adaptive neural backstepping path-following control approach is proposed. Barrier Lyapunov functions (BLFs) are introduced to deal with attitude error constraints. Neural networks (NNs) are presented to compensate for the uncertainties. To prevent the "explosion of complexity" in the design of the backstepping method, a finite-time convergent differentiator (FTCD) is introduced to estimate the time derivatives of virtual control signals. Stability analysis showed that all closed-loop signals are uniformly ultimately bounded, the constrained requirements on the airship attitude errors are never violated, and the path-following errors converge to a small neighborhood of the origin in a finite time. At last, simulation studies are provided to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper proposes a novel robust path-following strategy for autonomous road vehicles based on type-2 fuzzy PID neural network (PIDT2FNN) method coupled to an Extended Kalman Filter-based Fuzzy Neural Network (EKFNN) observer. Uncertain Gaussian membership functions (MFs) are employed to self-adjust the universe of discourse for MFs using the adaptation mechanism derived from Lyapunov stability theory and Barbalat’s lemma. External disturbances are significant in autonomous vehicles by changing the driving condition. Furthermore, parametric uncertainties related to the physical limits of tires and the change of the vehicle mass may significantly affect the desired performance of autonomous vehicles. The robustness of the proposed controller against the parametric uncertainties and external disturbances is compared with one active disturbance rejection control (ADRC) algorithm, and a linear-quadratic tracking (LQT) method. The obtained results in terms of the maximum error and root mean square error (RMSE), demonstrate the effectiveness of the proposed control algorithm to reach the minimized path-tracking error. [ABSTRACT FROM AUTHOR]

A solution to the problem of path-following by a team of terrestrial mobile robots is proposed in this paper. The proposal, in this case, is a formation controller dealing with three robots navigating in a coordinate way (as a formation). Based on the controller proposed to guide the formation to follow a prescribed path, an extension to the case of path-following with a single terrestrial mobile robot is also proposed. When regarding a formation of mobile robots, the proposed solution consists in applying a path-following controller to the center of mass of the formation, dealt with as a single virtual robot, and trajectory-tracking controllers to the individual robots in the formation. The advantage of such approach is that it allows planning the motion of the desired formation without specifying how each robot should move. The movement is specified for the formation as a whole, using a representation called cluster-space, and the movement of the individual robots is derived from the specification of the formation movement directly, using transformations from the cluster-space to the space of the robots and vice versa. In the sequel, the path-following controller designed for the virtual robot is analyzed in detail, now dealing with the possibility of being also used as a path-following controller applied to a single real robot. Theoretical stability analysis is presented, as well as some experimental results, whose analysis allows claiming that the proposed controller is suitable to guide either a single robot or a multi-robot formation when following a path. [ABSTRACT FROM AUTHOR]

In this note, we consider the iteration complexity of solving strongly convex multi-objective optimization problems. We discuss the precise meaning of this problem, noting that its definition is ambiguous, and focus on the most natural notion of finding a set of Pareto optimal points across a grid of scalarized problems. We prove that, in most cases, performing sensitivity based path-following after obtaining one solution is the optimal strategy for this task in terms of iteration complexity. [ABSTRACT FROM AUTHOR]

The paper addresses path planning and path-following problems in an unknown complex environment for an underactuated autonomous underwater vehicle (AUV). The AUV is required to follow a given reference path represented as a sequence of smoothly joined lines and arcs, bypassing obstacles encountered on the path. A two-level control system is proposed with an upper level for event-driven path planning and a lower level for path-following. A discrete event system is designed to identify situations that require planning a new path. An improved waypoint guidance algorithm and a Dubins curves based algorithm are proposed to build paths that allow the AUV to avoid collision with obstacles and to return to the reference path respectively. Both algorithms generate paths that meet the minimum turning radius constraint. A robust parameter-varying controller is designed using sublinear vector Lyapunov functions to solve the path-following problem. The performance of the developed event-based control system is demonstrated in three different simulation scenarios: with a sharp-edged obstacle, with a U-shaped obstacle, and with densely scattered obstacles. The proposed scheme does not require significant computing resources and allows for easy implementation on board. [ABSTRACT FROM AUTHOR]

We present an electrothermal drift–diffusion model for organic semiconductor devices with Gauss–Fermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature-dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized Scharfetter–Gummel scheme. Using path-following techniques, we demonstrate that the model exhibits S-shaped current–voltage curves with regions of negative differential resistance, which were only recently observed experimentally. [ABSTRACT FROM AUTHOR]

In this paper, a full-Newton step Interior-Point Method for solving monotone Weighted Linear Complementarity Problem is designed and analyzed. This problem has been introduced recently as a generalization of the Linear Complementarity Problem with modified complementarity equation, where zero on the right-hand side is replaced with the nonnegative weight vector. With a zero weight vector, the problem reduces to a linear complementarity problem. The importance of Weighted Linear Complementarity Problem lies in the fact that it can be used for modelling a large class of problems from science, engineering and economics. Because the algorithm takes only full-Newton steps, the calculation of the step size is avoided. Under a suitable condition, the algorithm has a quadratic rate of convergence to the target point on the central path. The iteration bound for the algorithm coincides with the best iteration bound obtained for these types of problems. [ABSTRACT FROM AUTHOR]

This article studies the design, modeling, and implementation challenges of a path-following with obstacle avoidance algorithms as guidance, navigation, and control (GNC) architecture of an unmanned surface vehicle (USV) in harbor conditions. First, an effective mathematical model is developed based on system identification, validating the USV model with field-test data. Then, a guidance system is addressed based on a line-of-sight algorithm, which uses a LiDAR as the main perception sensor for the obstacle avoidance algorithm. The GNC architecture uses a modular approach, including obstacle detection, path-following, and control in the USV platform. Finally, an implementation challenge in two control scenarios, simulation and field test, is addressed to validate the designed GNC architecture. [ABSTRACT FROM AUTHOR]

The actual performance of model-based path-following methods for unmanned aerial vehicles (UAVs) shows considerable dependence on the wind knowledge and on the fidelity of the dynamic model used for design. This study analyzes and demonstrates the performance of an adaptive vector field (VF) control law which can compensate for the lack of knowledge of the wind vector and for the presence of unmodeled course angle dynamics. Extensive simulation experiments, calibrated on a commercial fixed-wing UAV and proven to be realistic, show that the new VF method can better cope with uncertainties than its standard version. In fact, while the standard VF approach works perfectly for ideal first-order course angle dynamics (and perfect knowledge of the wind vector), its performance degrades in the presence of unknown wind or unmodeled course angle dynamics. On the other hand, the estimation mechanism of the proposed adaptive VF effectively compensates for wind uncertainty and unmodeled dynamics, sensibly reducing the path-following error as compared to the standard VF. [ABSTRACT FROM AUTHOR]

This paper introduces a scheme for waypoint-based path-following control for an Unmanned Robot Sailboat (URS) in the presence of actuator gain uncertainty and unknown environment disturbances. The proposed scheme has two components: intelligent guidance and an adaptive neural controller. Considering upwind and downwind navigation, an improved version of the integral Line-Of-Sight (LOS) guidance principle is developed to generate the appropriate heading reference for a URS. Associated with the integral LOS guidance law, a robust adaptive algorithm is proposed for a URS using Radial Basic Function Neural Networks (RBF-NNs) and a robust neural damping technique. In order to achieve a robust neural damping technique, one single adaptive parameter must be updated online to stabilise the effect of the gain uncertainty and the external disturbance. To ensure Semi-Global Uniform Ultimate Bounded (SGUUB) stability, the Lyapunov theory has been employed. Two simulated experiments have been conducted to illustrate that the control effects can achieve a satisfactory performance. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to the visual path following problem based on Nonlinear Model Predictive Control. Simplified visual features are extracted from the path to be followed. Then, aiming to calculate the control actions directly from the image plane, a regulatory model is obtained in the optimal control problem scope. For this purpose a Serret-Frenet system is placed in the center of camera's field of view and the optimal control actions generate velocity references to an inner loop embedded in the robot. Stability issues are handled through a classical method and a new approach based on constraints relaxation is proposed in order to guarantee feasibility. Experimental results with a nonholonomic platform illustrate the performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

An efficient, function-space-based second-order method for the |$H^1$| -projection onto the Gibbs simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau–Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first- and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior. [ABSTRACT FROM AUTHOR]

This paper focuses on the controller design for path-tracking problem of autonomous ground vehicles (AGVs) by employing a multi-constraint nonlinear predictive control (NMPC) schema. It is aimed to improve the transient performance of the vehicle and to consider a rollover prevention criterion in the proposed method. The path-tracking problem is transformed into the yaw stabilization issue, and a feedback control law with input saturation is developed to decrease the steady-state errors. Furthermore, the yaw-rate signal is generated for the desired path-tracking performance. The major contributions of the present paper are, first, developing a neural network autoregressive with exogenous input system to assist in obtaining an accurate and explicit model in order to contribute to the control of the system over the prediction horizon; second, describing a Frenet–Serret differential geometry based path-following agenda and developing AGV dynamic model by incorporating the vehicle vertical mode of motion to prevent vehicle rollover during critical maneuvers, and finally, achieving an enhanced yaw stabilization and transient tracking performance considering saturated input signal by employing the proposed system identification algorithm. The effectiveness of the proposed control system is verified by comparing with the traditional NMPC method by employing a high fidelity CarSim/MATLAB framework. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional (3-D) path-following control design for an underactuated stratospheric airship is proposed based on the parameterized path description. The desired attitude, velocity, and the path parameter updating law are obtained by employing the guidance-based path-following principle. The resultant system possesses a cascaded structure, which consists of a guidance loop, an attitude stabilization loop, and a velocity tracking loop. The stability analysis shows that the path-following error and all states of the closed-loop system are ultimately uniformly bounded. Simulation results demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

We investigate uniform versions of (metric) regularity and strong (metric) regularity on compact subsets of Banach spaces, in particular, along continuous paths. These two properties turn out to play a key role in analyzing path-following schemes for tracking a solution trajectory of a parametric generalized equation or, more generally, of a differential generalized equation (DGE). The latter model allows us to describe in a unified way several problems in control and optimization such as differential variational inequalities and control systems with state constraints. We study two inexact path-following methods for DGEs having the order of the grid error and , respectively. We provide numerical experiments, comparing the schemes derived, for simple problems arising in physics. Finally, we study metric regularity of mappings associated with a particular case of the DGE arising in control theory. We establish the relationship between the pointwise version of this property and its counterpart in function spaces. [ABSTRACT FROM AUTHOR]

In this paper, a new robust adaptive controller is investigated to force an underactuated surface marine vessel to follow a predefined parameterised path at a desired speed, despite actuator saturation and the presence of model uncertainties as well as environmental disturbances induced by waves, wind and sea-currents. To ensure robustness of the path-following controller, time-varying constraint on the off-track error (i.e. the maximal distance from the ship to the reference path) is considered. To address the off-track error constraint the tan-barrier Lyapunov function is incorporated with the control scheme, where the idea of auxiliary design system introduced in Chen, Sam, and Ren (2011) is adopted and its states are used in combination with backstepping and Lyapunov synthesis to adaptive tracking control design with guaranteed stability. Furthermore, the command filters are adopted to implement physical constraints on the virtual control laws so that analytic differentiation of the virtual control laws is avoided. We show that the proposed robust adaptive control law is able to guarantee semi-global uniform ultimate bounded stability of the closed-loop system. Numerical simulations and experimental results are carried out to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a design method for output-feedback path-following control of under-actuated autonomous underwater vehicles moving in a vertical plane without using surge, heave, and pitch velocities. Specifically, an extended state observer (ESO) is developed to recover the unmeasured velocities as well as to estimate total uncertainty induced by internal model uncertainty and external disturbance. At the kinematic level, a commanded guidance law is developed based on a vertical line-of-sight guidance scheme and the observed velocities. To optimize guidance signals, optimization-based reference governors are formulated as bound-constrained quadratic programming problems for computing optimal reference signals. Two globally convergent recurrent neural networks called projection neural networks are used to solve the optimization problems in real-time. Based on the optimal reference signals and ESO, a kinetic control law with disturbance rejection capability is constructed at the kinetic level. It is proved that all error signals in the closed-loop system are uniformly and ultimately bounded. Simulation results substantiate the efficacy of the proposed method for output-feedback path-following of under-actuated autonomous underwater vehicles. [ABSTRACT FROM PUBLISHER]

In this paper we consider a control system coupled with a generalized equation, which we call a differential generalized equation (DGE). This model covers a large territory in control and optimization, such as differential variational inequalities, control systems with constraints, as well as necessary optimality conditions in optimal control. We study metric regularity and strong metric regularity of mappings associated with DGE by focusing in particular on the interplay between the pointwise versions of these properties and their infinite-dimensional counterparts. Metric regularity of a control system subject to inequality state-control constraints is characterized. A sufficient condition for local controllability of a nonlinear system is obtained via metric regularity. Sufficient conditions for strong metric regularity in function spaces are presented in terms of uniform pointwise strong metric regularity. A characterization of the Lipschitz continuity of the control part of the solution mapping as a function of time is established. Finally, a path-following procedure for a discretized DGE is proposed for which an error estimate is derived. [ABSTRACT FROM AUTHOR]

We propose a modified path-following algorithm in a wide neighborhood for monotone linear complementarity problems. The algorithm takes two steps in one iteration, called a fast step and a safe step, respectively. In the algorithm, if a fast step fails, a safe step will be taken. However, when iterations are sufficiently large, fast steps are taken all through. We prove that the algorithm has not only the complexity bound but also local superlinear convergence. Furthermore, assuming a strictly complementary solution exists, the sequence , generated by the algorithm, is convergent. Finally, the numerical results show the algorithm effective. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to path following control design for an autonomous underwater vehicle (AUV). A NARMAX model of the AUV is derived first and then its parameters are adapted online using the recursive extended least square algorithm. An adaptive Propotional-Integral-Derivative (PID) controller is developed using the derived parameters to accomplish the path following task of an AUV. The gain parameters of the PID controller are tuned using an inverse optimal control technique, which alleviates the problem of solving Hamilton–Jacobian equation and also satisfies an error cost function. Simulation studies were pursued to verify the efficacy of the proposed control algorithm. From the obtained results, it is envisaged that the proposed NARMAX model-based self-tuning adaptive PID control provides good path following performance even in the presence of uncertainty arising due to ocean current or hydrodynamic parameter. [ABSTRACT FROM AUTHOR]

This paper investigates the minimum-energy joint path-following problem for space manipulators whose base attitude is stabilized by reaction wheels. In the problem, manipulator joint path is specified for rest-to-rest motion and constraints are imposed as the upper bound on both motion completion time and the voltage/current limits of DC motors in manipulator joints and reaction wheels. We suggest a simple two-stage algorithm to address this problem. The algorithm first tries to find a global optimal solution by solving a relaxed convex problem. If the convex relaxation is not successful, then the algorithm solves subproblems iteratively to find a suboptimal solution. Since both problems are formulated as second-order cone programming (SOCP) form, they can be solved efficiently using dedicated SOCP solvers. The effectiveness of the proposed method is verified by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper vehicle path-following in the presence of rollover risk is investigated. Vehicles with high centre of mass are prone to roll instability. Untripped rollover risk is increased in high centre of gravity vehicles and high-friction road condition. Researches introduce strategies to handle the short-duration rollover condition. In these researches, however, trajectory tracking is affected and not thoroughly investigated. This paper puts stress on tracking error from rollover prevention. A lower level model predictive front steering controller is adopted to deal with rollover and tracking error as a priority sequence. A brake control is included in lower level controller which directly obeys an upper level controller (ULC) command. The ULC manages vehicle speed regarding primarily tracking error. Simulation results show that the proposed control framework maintains roll stability while tracking error is confined to predefined error limit. [ABSTRACT FROM PUBLISHER]

Researchers in the domain of haptic training are now entering the long-standing debate regarding whether or not it is best to learn a skill by experiencing errors. Haptic training paradigms provide fertile ground for exploring how various theories about feedback, errors and physical guidance intersect during motor learning. Our objective was to determine how error minimizing, error augmenting and no haptic feedback while learning a self-paced curve-tracing task impact performance on delayed (1 day) retention and transfer tests, which indicate learning. We assessed performance using movement time and tracing error to calculate a measure of overall performance -- the speed accuracy cost function. Our results showed that despite exhibiting the worst performance during skill acquisition, the error augmentation group had significantly better accuracy (but not overall performance) than the error minimization group on delayed retention and transfer tests. The control group's performance fell between that of the two experimental groups but was not significantly different from either on the delayed retention test. We propose that the nature of the task (requiring online feedback to guide performance) coupled with the error augmentation group's frequent off-target experience and rich experience of error-correction promoted information processing related to error-detection and error-correction that are essential for motor learning. [ABSTRACT FROM AUTHOR]

This paper presents a new method to design global path-following controllers for underactuated ships under both deterministic and stochastic sea loads. The path-following errors are first interpreted in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov's direct methods. Weak and strong nonlinear Lyapunov functions are introduced to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule, and to guarantee boundedness of the sway velocity. Potential projection functions are introduced to design update laws that provide bounded estimates of the mean values and covariances of the disturbances. Simulations are included to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]