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This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime. • A global LPV model of the BSD is built by interpolation modeling. • A modal-based LPV pole placement control is proposed to achieve modal control. • The proposed modeling and control achieve precise tracking and excellent robustness. [ABSTRACT FROM AUTHOR]

This paper proposes a novel adaptive variable power sliding mode observer-based model predictive control (AVPSMO-MPC) method for the trajectory tracking of a Mecanum-wheeled mobile robot (MWMR) with external disturbances and model uncertainties. First, in the absence of disturbances and uncertainties, a model predictive controller that considers various physical constraints is designed based on the nominal dynamics model of the MWMR, which can transform the tracking problem into a constrained quadratic programming (QP) problem to solve the optimal control inputs online. Subsequently, to improve the anti-jamming ability of the MWMR, an AVPSMO is designed as a feedforward compensation controller to suppress the effects of external disturbances and model uncertainties during the actual motion of the MWMR, and the stability of the AVPSMO is proved via Lyapunov theory. The proposed AVPSMO-MPC method can achieve precise tracking control while ensuring that the constraints of MWMR are not violated in the presence of disturbances and uncertainties. Finally, comparative simulation cases are presented to demonstrate the effectiveness and robustness of the proposed method. • kinematic and dynamic constraints are handled efficiently. • The improved observer has a fast convergence rate without chattering. • The method can improve tracking performance. [ABSTRACT FROM AUTHOR]

Wheeled Mobile Robots (WMRs) are systems with applications in diverse fields such as transportation, civilian services, military use, and space exploration. Then, their use will continue increasing, making WMRs an essential research topic that deserves further study. To this end, this work presents a novel observer-based finite-time controller for trajectory tracking control of WMRs disturbed by kinematic disturbances. In the proposed approach, the kinematic model of the WMR is transformed into a set of two decoupled second-order systems. Then, the proposed controller is divided into two parts. The first one employs an observer to estimate the effect of the kinematic disturbances. The second part consists of a finite-time controller designed to achieve finite-time convergence of the tracking error. A detailed synthesis procedure theoretically demonstrates the feasibility of the proposed controller. Subsequently, the proposed scheme is compared against finite-time, feedback, and H ∞ controllers. Exhaustive numerical simulations show that the proposed new control methodology achieves the trajectory tracking objective despite kinematic disturbances and outperforms the other control procedures. Finally, some comments and numerical results are given to clarify how the proposed control methodology can be used to design new controllers for trajectory tracking in WMRs and demonstrate that the new proposal remains to have a good performance when the system's coordinates are corrupted by measurement noise. [Display omitted] • A new observer-based finite-time control for wheeled mobile robots is proposed. • The new control scheme permits achieving the trajectory-tracking task efficiently. • The novel methodology outperforms existing finite-time, feedback, and H ∞ methodologies. • Excellent performance is obtained even in the presence of kinematic disturbances and measurement noise. • The proposed scheme permits the design of new controllers for WMRs easily. [ABSTRACT FROM AUTHOR]

To improve the transient response, accuracy and robustness of trajectory tracking control for cable-driven continuum robots (CDCRs), a recursive integral terminal sliding mode control combined with an adaptive disturbance observer (ADO-RITSMC) is proposed. The recursive integral terminal sliding mode control (RITSMC) guarantees fast transient response and high tracking accuracy with a fast zero convergence of the tracking error without chattering. To attenuate the effect of uncertain dynamics, an adaptive disturbance observer (ADO) is constructed to derive uncertain dynamics. Particularly, an improved grey wolf optimizer (IGWO) is merged into the ADO to enhance the estimating accuracy of uncertain dynamic factors. Simulation and experiment results demonstrate the superiority of the ADO-RITSMC in enabling fast transient response, high accuracy and strong robustness of trajectory tracking control. • The RITSMC achieves a fast zero convergence and high-precision trajectory tracking control without chattering. • Assigning a starting value for the integral term of the RISMC function to improve the transient response of the controller. • An ADO is designed to estimate uncertain dynamic factors and compensate for the control input. • An improved grey wolf optimizer (IGWO) is introduced into ADO for more accurate estimation of uncertain dynamic factors. [ABSTRACT FROM AUTHOR]

For robot manipulators composed of Lagrange subsystems driven by direct current (DC) motors under stochastic environments, multi-stage trajectory tracking is investigated in this paper. The main challenge is how to achieve the end-effector drive of manipulators from a given initial state to a final state. First, the inverse kinematics method and the partition of the task space are adopted to tackle multi-stage trajectory planning. Second, the adaptive backstepping technique is used to design tracking controller for stochastic Lagrangian subsystems. Then, based on the state-dependent switching signal, a multi-stage switched controller is designed for trajectory tracking of robot manipulators. All signals in the close-loop error switched system are bounded in probability, and the tracking error in mean square can be made arbitrarily small enough by parameters-tuning The effectiveness of the proposed control method is illustrated by simulation results. • The multi-stage trajectory planning is proposed by the partition of the task space. • The adaptive backstepping controller is designed to track the pre-planned trajectory. • The multi-stage switched controller is proposed for performing a grab task. [ABSTRACT FROM AUTHOR]

We propose a self-organising kernel extreme learning machine (KELM) adaptive controller for nonaffine nonlinear systems. Literature survey reveals that neural network (NN) is extensively used to design adaptive controllers for nonlinear systems. When conventional NN, like multilayer feedforward NN and radial basis function NN (RBFNN), is used for controller design, the parameters of these networks converge slowly. Researchers have overcome this shortcoming by using extreme learning machine (ELM). The motivation to use KELM for controller design in our research is to utilise the advantages of ELM and radial basis function kernels. The structure of neural networks is seldom altered during training, resulting in unnecessarily small or large networks. The self-organising nature of our proposed controller caters to solving this problem. The structure of the self-organising KELM updates itself based on a threshold value set for the normalised change in the output weight. In our work, the control input meets three objectives : feedback linearisation, stabilisation of the linearised system and providing immunity to process and measurement noises. The update law for the hidden layer parameters of the KELM is obtained using the Lyapunov technique to ensure the overall stability of the system. A comparative analysis of different performance criteria is performed for trajectory tracking control, in the presence of process and measurement noises, for a numerical example and the Duffing–Holmes chaotic nonlinear system. The simulation results of these analyses demonstrate the superiority of the self-organising KELM compared to ELM and RBFNN based adaptive controllers. The experimental results with a rotary servo system validate the efficacy of the proposed controller in real-time systems. Furthermore, the robustness of the self-organising adaptive controller is verified with the results obtained for the servo system on varying the system parameter and operating condition. • Nonaffine nonlinear system controller design performed with extreme learning machine. • Controller structure varies with the amount of nonlinearity present in system model. • Tight tracking of reference trajectory. • Drastic reduction in training time. • Real-time implementation of proposed controller. [ABSTRACT FROM AUTHOR]

In this study, a three degrees of freedom (3 DOF) rigid-link robotic manipulator (RLM) has been simulated by using the Simscape model and the mathematical model derived by Lagrange method. The robot arm has been regulated by an Optimized PID Controller to achieve better tracking performance and reasonable robustness against disturbances and payload uncertainty. To optimize the controller, a novel nature-inspired Golden Jackal Optimization (GJO) algorithm has been used due to its efficient exploration that increases the diversity of the released solutions and its exploitation schemes which enhance the best-explored solutions. The tuning process has utilized a Lyapunov stability function as the objective function (OF) and the efficacy of the proposed algorithm is evaluated through a comprehensive comparison with various state-of-the-art metaheuristic techniques such as Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Jellyfish Search Optimizer (JSO), Whale Optimization Algorithm (WOA), Arithmetic Optimization Algorithm (AOA) and Sine Cosine Algorithm (SCA). The assessment has been conducted on benchmark error-based functions, providing rigorous testing and validation of the algorithm's performance. Furthermore, the performance evaluation has focused on the system's robustness against disturbances, noise, and variations in the payload mass, particularly in the context of Pick and Place (PNP) industrial tasks. The results of simulation have demonstrated that the optimized system, employing the Lyapunov function, demonstrated superior performance in minimizing the objective function value compared to other benchmark functions. [Display omitted] • Efficient 3-DOF robotic model using MATLAB Simscape, enabling precise representation and efficient simulation. • Utilizing the new approach of Lyapunov function as the objective function in the optimization process. • Comparing the performance of the GJO algorithm with other recent optimization algorithms commonly used in the literature. • Comprehensive performance analysis to offer valuable insights into the controller's adaptability in real-world scenarios. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study. • A novel adaptive finite-time global integral terminal sliding mode control scheme is designed. • A novel global integral terminal sliding mode surface is proposed to ensure faster convergence and better global robustness. • A novel adaptive law is designed to adjust the estimation parameters according to the change of system state to avoid overestimation. • The actuator fault is considered to make the proposed control logic more suitable for practical applications. [ABSTRACT FROM AUTHOR]

This paper aims to tackle the three-dimensional trajectory tracking problems of small fixed-wing unmanned aerial vehicles subject to nonlinearities, uncertainties and wind disturbances via adaptive techniques. The control objective is to efficiently control the thrust and the deflections of control surfaces to ensure the unmanned aerial vehicle arrives at a specified location within a given time frame. However, achieving this goal for small fixed-wing unmanned aerial vehicles can be challenging because the precise dynamic model and several parameters are not accessible, making most existing control strategies unworkable. Motivated by these facts, based on feedback linearization techniques, we derive linear models with equivalent disturbances to describe the translational dynamics without requiring precise aerodynamic force model information. To deal with the dilemmas where the norm bounds of equivalent disturbances depend on control inputs, system states, and unknown disturbances, a novel robust adaptive control strategy is designed for position control. Based on the assumption of two-time separation, the control scheme incorporates two parts, namely, a position controller containing the horizontal-plane and altitude parts and a robust filter-based attitude regulator. Also, to prevent chattering issues, we design a practical and robust adaptive position controller under which the tracking error is ultimately bounded The overall closed-loop stability is theoretically investigated based on the Lyapunov arguments. Hardware-in-loop simulation experiments are performed to testify our developed control scheme. • A novel robust adaptive control strategy is proposed to deal with the uncertainties related to not only system states but also to control inputs. • A cascade control strategy is employed to solve the trajectory tracking problems of fixed-wing UAVs. • A robust adaptive three-dimensional trajectory tracking controller is designed. • Hardware-in-Loop simulations are conducted. [ABSTRACT FROM AUTHOR]

In order to solve the trajectory tracking problem for robotic manipulators with dynamic uncertainty, external disturbance and input saturation, a novel second-order sliding mode control scheme based on neural network is proposed in this paper. First of all, a model-based second-order non-singular fast terminal sliding mode controller (SONFTSMC) is designed to overcome the chattering problem under the consideration of uncertain parameters. Then attention is focused on the scenario that all those nonlinear uncertainties are unknown, and a new fuzzy wavelet neural network (FWNN) is designed to estimate those unknown uncertainties via lumping them into one compounded uncertainty. In addition, all parameters in FWNN are adjusted autonomously by using an adaptive method. The proposed second-order non-singular fast terminal sliding mode (SONFTSM) control method not only improves the convergence speed and tracking accuracy of the robotic manipulator, but also enhances its robustness. Finally, the advantages of SONFTSM control strategy over existing sliding mode control methods are verified with comparative simulations. • A new second-order non-singular fast terminal sliding mode controller (SONFTSMC) based on neural network is designed. • The lumped uncertainty is estimated by using an improved fuzzy wavelet neural network (FWNN). • The input saturation problem is considered, which makes the proposed control logic more suitable for practical applications. • By modifying the second-order NFTSM surface, the fixed-time convergence of the sliding mode variable r is guaranteed. [ABSTRACT FROM AUTHOR]

This paper presents a new Global Fast Non-singular Terminal Sliding Mode Controller (GFNTSMC) that delivers high-precision tracking of high-frequency trajectories when applied to a piezo-driven nanopositioner. The control scheme is realized by combing inverse hysteresis model and global fast non-singular terminal sliding mode compensation. The inverse Bouc–Wen hysteresis model is used to calculate the required hysteresis-compensating feedforward control voltage according to the reference signal. The key uniqueness of the proposed control strategy is it's red global fast convergence, achieved with high accuracy and high bandwidth. The stability of the reported GFNTSMC controller is proved with the Lyapunov theory. Its performance is verified through experimentally recorded tracking results, and its superiority over three benchmark control approaches, namely the Proportional–Integral–Derivative (PID), the Positive Position Feedback with integral action (PPF+I) and the conventional linear high-order sliding mode controller (LHOSMC) is demonstrated through comparative tracking error analysis. Its wide-band stability as well as its significant robustness to parameter uncertainty is also showcased. • A high-order global fast nonsingular terminal sliding mode controller is proposed. • The stability and robustness of the controller are proved with the Lyapunov theory. • The system state can quickly reach the equilibrium point from any initial state. • Experimental results demonstrate significant accuracy improvement and superior robustness. [ABSTRACT FROM AUTHOR]

This paper proposes a disturbance observer-based prescribed performance super-twisting sliding mode control (DOB PPSTSMC) for trajectory tracking of the autonomous surface vessels (ASVs) subject to unknown external disturbances and modeling errors. Both unknown external disturbances and system modeling errors are approximated by the disturbance observer, thus eliminating most of the effect caused by lumped disturbances in the control performance. Based on this, a prescribed performance super-twisting sliding mode controller is explored to further suppress the residual error of disturbance compensation. Prescribed performance constraints are considered in the coming up with the super-twisting sliding mode controller, so that ASVs not only achieve effective tracking of time-varying desired trajectories, but also improve the transient performance of the control system. In addition, the controller is continuous and chatter-free, which has greater practical value. The excellence of the control project design is highlighted through the simulation and comparison results. • Based on the ASVs model, the DOB PPSTSMC is proposed. • The derivatives of the considered lumped disturbances are square-integrable. • The disturbance observer effectively compensates for the lumped disturbance. • The transient response of the system is improved. • The control signal is smooth and continuous without chatter. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered model predictive control (EMPC) with adaptive artificial potential field (APF) is designed to realize obstacle avoidance and trajectory tracking for autonomous electric vehicles. An adaptive APF cost function is added to achieve obstacle avoidance and guarantee stability. The optimization problem for MPC is feasible by considering a special obstacle avoidance constraint. An event-triggered mechanism is proposed to reduce computational burden and ensure effectiveness of obstacle avoidance. Input and state constraints of autonomous electric vehicles are considered in both feasibility and stability by a robust terminal set. Effectiveness of both obstacle avoidance and trajectory tracking is shown by experimental results on autonomous electric vehicles. • A terminal set is designed to ensure stability under constraints and disturbance. • An adaptive force coefficient is designed to achieve stable tracking and avoiding. • An event-triggered mechanism considering obstacles is used to reduce computation. • A special constraint is developed to ensure the optimization feasibility. • Experimental results are given to show effectiveness of the EMPC strategy. [ABSTRACT FROM AUTHOR]

This paper studies the trajectory tracking problem of unmanned surface vehicle subject to unmeasurable velocities and unknown disturbances. By combining a fixed-time extended state observer (FESO) and a fixed-time differentiator, a fixed-time sliding mode control (FTSMC) law is proposed, in which a saturation function is adopted to make the terminal sliding mode surface leave the singularity area. The value of this paper can be described: first, this paper designs a novel guidance law that can converge in a fixed time to reduce the convergence time of the error. Then, unmeasurable velocities and lumped disturbances are estimated by applying a FESO. Meanwhile, a fixed-time differentiator is used to obtain real-time differential signals, thus reducing the difficulty of controller design. Subsequently, a novel auxiliary dynamic system is designed to address actuator saturation. According to Lyapunov's theory, the entire closed-loop control system has uniformly global fixed-time stability (UGFTS). The superiority of the designed controller is demonstrated through numerical simulations. • A novel fixed time guidance law is developed, which makes position errors reach zero within a fixed time. • A FESO is designed to estimate unknown dynamics within a fixed time, which does not require precise model parameters. • A novel auxiliary dynamic system is designed to handle input saturation, which can ensure that the state converges in finite time. • The fixed-time differentiator is introduced to achieve satisfactory filter and differential performance. • A novel FTSMC strategy is proposed for underactuated USV. Finally, the system proved to be uniformly global finite-time stable. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of practical fixed-time trajectory tracking for wheeled mobile robots (WMRs) subject to kinematic disturbances and input saturation. Firstly, considering the under-actuated characteristics of the WMR systems, the WMR model under kinematic disturbances is transformed into a two-input two-output interference system by using a set of output equations. Then, the tracking error state equation with lumped disturbances in the acceleration-level pseudo-dynamic control (ALPDC) structure is established. The lumped disturbances are estimated by a designed fixed-time extended state observer (FESO) without requiring the differentiability of the first-time derivatives of the kinematic disturbances. Meanwhile, a practical fixed-time output feedback control law is developed for trajectory tracking. By resorting to the Lyapunov stability theorem, the fixed-time stability analysis of the closed-loop WMR system in the presence of input saturation is conducted. Finally, simulation results are presented to show the effectiveness of the proposed approach. • The ESO technique is utilized to deal with the fixed-time trajectory tracking problem of WMRs with unknown kinematic disturbance. • The proposed practical fixed-time trajectory tracking control approaches are proposed without the requirement of the PE conditions. • The input compensation technique is utilized to achieve the bounded output feedback control. [ABSTRACT FROM AUTHOR]

This correspondence deals with the trajectory tracking control of an un-crewed helicopter during hover/low-speed flights. A multi-loop architecture is used in which the inner-loop holds the fast changing dynamics and the outer-loop establishes the trajectory tracking. The inner-loop is closed with a constrained H ∞ based controller which is cautiously designed to address actuator saturation, atmospheric wind disturbance, and parametric uncertainty. The outer-loop adaptive composite nonlinear control comprises of a linear part and a nonlinear part. A novel adaptive controller is proposed as the nonlinear part which improves the tracking performance by adaptively adjusting the damping ratio. The linear control element of the outer-loop is framed similar to inner-loop. Utilization of output feedback instead of full state feedback makes the flight control design simple and practically feasible. The closed loop stability and robustness property of the proposed scheme are analyzed. Simulation studies are performed to establish the hovering, station keeping, and trajectory tracking performance of the suggested control structure. Further, the performance of the proposed scheme is compared with a constrained static output feedback controller and a model reference adaptive proportional integral controller to confirm its superiority. • Trajectory tacking of a small scale unmanned helicopter in hover/low speed flights. • Design of a constrained H ∞ controller for inner-loop dynamics. • Formulation of inner-loop controller as a convex optimization problem. • Design of an adaptive composite nonlinear output feedback controller for outer-loop. • Simulation of different flight tasks with the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a robust cooperative trajectory tracking control scheme for an unactuated floating object with multiple vessels under environmental disturbances. The object and multiple vessels are connected by using towlines. The proposed control scheme consists of three parts: a virtual controller for the object, a control allocation algorithm and a distributed robust time-varying formation controller for vessels. The virtual controller is first designed to obtain the control forces of the object to track the reference trajectory. To compute the optimal tension of each towline, the control allocation algorithm is introduced. Then, the time-varying relative positions from the object to vessels are gained by using a nonlinear towline model and the towline attachment geometry. Furthermore, the distributed robust time-varying formation controller is devised for vessels based on dynamic surface control technique, an adaptive law and graph theory. It is proved that the tracking errors of the object and vessels are bounded. Simulations substantiate that the proposed method can achieve good cooperative control performance and robustness, and the unactuated object can track the reference trajectory with high accuracy. • Cooperative tracking control for an unactuated object and multi-vessel is studied. • Time-varying formation is gained via a towline model and towline attachment geometry. • The proposed control scheme is robust against environmental disturbances. [ABSTRACT FROM AUTHOR]

This paper considers the trajectory tracking problem of an underactuated underwater vehicle actuated by control moment gyros (CMGs) in three-dimensional (3D) space, with the constraints from input saturation, partial parameter uncertainty and unknown external disturbance. First, utilizing a physical translation of the motion equations, the overall system can be decomposed to an input decoupling system. Then a modified virtual velocity guidance law is derived to transform the tracking error signals into the controllable velocity signals. Subsequently, the Gaussian error function is employed to update the common saturation model. To avoid complex derivations of the virtual control signals, first-order sliding mode differentiator is explored in the dynamic control layer. Then, the adaptive neural network (NN) control method is introduced into the backstepping procedure to account for nonlinear uncertainties and bounded disturbances. Among this, the constrained steering law is used to steer the CMG system to avoid its inherent singularity and fulfill the global tracking control. It is proved that the proposed controller can guarantee all closed-loop signals converge to a small neighborhood of the origin. Finally, two case studies are presented to illustrate the tracking performance of the proposed design. • This paper investigates the 3D trajectory tracking control for a CMG-actuated AUV.. • A physical translation and an improved velocity guidance law are introduced. • Adaptive NN control method is introduced to evaluate the compound error. • Two case studies are provided to demonstrate the effective of the proposed method. [ABSTRACT FROM AUTHOR]

Obtaining a control algorithm capable of navigating the system both in forward and backward motions is one of the control objectives for tractor-trailer wheeled robots (TTWRs). In this paper, a relatively general structure is presented for both forward and backward control of an n-trailer wheeled mobile robot (NTWMR) in the presence of wheel slip effects. To keep better overall performance and track the reference trajectories in forward and backward motions, the NTWMR is intended to be controlled in the presence of slip effects. A control algorithm accompanied by a slip compensation procedure is proposed for the system simultaneously. First, the mathematical model of the system in the presence of slip effects is obtained. A novel physically motivated algorithm is proposed for the tracking control in the presence of unknown uncertainties (longitudinal and lateral slips) for both forward and backward motions. By estimating the slip effects at any instant, the control inputs are produced to compensate for their destructive effects on tracking control of the NTWMR. Then the stability of the closed-loop system is evaluated using the Lyapunov theory. The potential of the proposed controller was verified through several case studies, including comparative results and experimental validation in various motion control manoeuvers for a vehicle with trailers. The proposed method is the first algorithm that can cover a broad range of TTWR motion tasks (forward and backward trajectory tracking, slip attenuation, and global stability), which are required to be developed in NTWMRs. • Proposing a control algorithm for forward and backward trajectory tracking. • Designing the controller in the configuration space without using transformations. • Investigating a slip estimator to attenuate the effects of unknown uncertainties. • Analyzing the stability of the control algorithm using the Lyapunov method. • Presenting various case studies and comparative results to show the effectiveness. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive and robust adaptive control strategy based on type-2 fuzzy neural network (T2FNN) for tracking the desired trajectories of a quadrotor. The designed methods can control both the position and the orientation of a quadrotor. Contrary to common sliding mode controllers (SMCs), the robust adaptive trajectory tracking scheme presented here is based on SMC with exponential reaching law; which helps reduce the phenomenon of chattering. Moreover, parameters including the gains of sliding surfaces, are optimized by cuckoo optimization algorithm (COA), and the results are compared with those obtained by genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO). The designed methods in this study are called adaptive T2FNN controller and the exponential SMC (ESMC)-T2FNN. The law for updating the T2FNN is obtained online by using the Lyapunov stability theory. Considering undesired factors such as uncertainties, external disturbances and control signal saturation, the results of our controllers are compared with those of the adaptive type-1 fuzzy neural network controller (T1FNN) and ESMC-T1FNN. The extensive simulations demonstrate the effectiveness of the proposed COA-based ESMC-AT2FNN approach compared to the other tested techniques (i.e. GA, PSO and ACO) in terms of the improved transient and steady-state trajectory-tracking performance. The mean and standard deviation values concerning the COA are obtained through statistical analyses at 0.00006173 and 0.000092, respectively. This paper also examines the complexity of COA in optimizing the trajectory tracking control of quadrotor and investigates the effects of COA parameters on optimization results. The stable performance of the cuckoo algorithm is demonstrated by varying its parameters and analyzing the obtained results. These results also show the convergence of COA for the considered problem. • Trajectory tracking of a quadrotor is proposed using a type-2 fuzzy neural controller. • Strong robustness is provided against the structured and unstructured uncertainties. • Exponential sliding mode reaching law is introduced for a smooth asymptotic stability. • Controller design parameters are obtained optimally through Cuckoo optimization algorithm. [ABSTRACT FROM AUTHOR]

This paper develops a trajectory tracking control design algorithm to be applied in unmanned aerial vehicles (UAVs). The strategy is simple but effective and it is based on linear algebra theory. The proposed approach reforms the column space of a system of linear equations at each sampling time to ensure the tracking objective when environmental disturbances appear. This new formulation ensures a uniform signal without affecting the error convergence to zero (demonstration available), which is one of the main contributions of this work. A statistical method is used to tune the system control minimizing a pre-defined cost function. In addition, the convergence to zero of the tracking errors is demonstrated in this work. Finally, the controller's effectiveness is tested through several simulations in realistic test scenarios in the presence of disturbances. • The trajectory tracking control in UAV under uncertainties is addressed. • The controller design for trajectory tracking is based on linear algebra. • The approach is applied in a nonlinear system with additive uncertainty. • The zero convergence of tracking error under polynomial uncertainties is demonstrated. • Several simulations in realistic scenarios were performed. [ABSTRACT FROM AUTHOR]

The Active Disturbance Rejection Control (ADRC) is an object of the ever growing interest in the latest years due to its limited requirements concerning knowledge of a plant's mathematical model. In this paper, a problem of system stability in presence of modelling uncertainties is investigated. Precisely, imperfect knowledge of the manipulator dynamics and an inertia matrix is considered by the means of the Lyapunov analysis and conditions are formulated which guarantees convergence of the errors in the system to some finite boundary. Influence of the unknown inertia matrix is thoroughly investigated. It is shown, that if the third derivative of the desired trajectory is small enough then an intentional increase of the input matrix estimation error may lead to a reduction of the tracking error boundary. Obtained results are supported by presented simulations and experiments. • The ADRC is practically stable at least for some range of modelling inaccuracy. • Asymptotical stability can be guaranteed for constant input gain and disturbance. • Overestimation of model's inertia matrix can lead to increase of tracking quality. • High-precision practical experiments confirm previous remarks. [ABSTRACT FROM AUTHOR]

The main goal of this study is developing an adaptive controller which can solve the trajectory tracking for a class of quadcopter unmanned aerial system (UAS), namely a quadrotor. The control design introduces a new paradigm for adaptive controllers based on the implementation of a set of differential neural networks (DNNs) in the consequence section of a Takagi–Sugeno (T–S) fuzzy inference system. This dynamic fuzzy inference structure was used to approximate the UAS description. The particular form of interaction between neural networks and fuzzy inference systems proposed in the present work received the name of dynamic neural fuzzy system (DNFS). An adaptive controller based on this DNFS form was the main solution attained in this study. This DNFS controller was focused on the estimation and compensation of the uncertain section of the Quadrotor dynamics and then, forced the UAS to perform a hover flight while the tracking of desired angular positions succeeded, which results in tracking a desired trajectory in the X-Y plane. The control design methodology supported on the Lyapunov stability theory guaranteed ultimate boundedness of the estimation and tracking errors simultaneously. Several experimental tests in an outdoor environment by using a real Quadrotor platform was performed by using an RTK-GPS (Real Time Kinematic) system to determine the position of the vehicle in the X-Y plane. The experimental results confirmed the superior performance of the proposed algorithm based on the combination of DNNs and T–S techniques with respect to classical robust controllers. • A neuro fuzzy adaptive controller is designed to solve trajectory tracking problem for a Quadrotor unmanned aerial system. • The control algorithm uses a neuro-fuzzy structure by aggregating differential neural networks (DNNs) with a T–S inference system. • An adaptive compensation was applied by using the estimation of the uncertain section of the Quadrotor dynamics. • This adaptive neuro-fuzzy controller enforces the Quadrotor UAS to perform a hover flight. • Experiments confirmed the superior performance of the proposed neuro-fuzzy controller with respect to classical controllers. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of adaptive trajectory tracking control for remotely operated vehicles (ROVs). Considering thruster dynamics, a third-order state space equation is used to describe the dynamic model of ROVs. For the problem of unknown dynamics and partially known input gain, an adaptive sliding mode control design scheme based on RBF neural networks is developed using a backstepping design technique. Because of the saturation constraints of the thrusters, a first-order auxiliary state system is applied, and subsequently, a saturation factor is constructed for designing adaptive laws to ensure the stability of the adaptive trajectory tracking system when the thrusters are saturated. The proposed controller guaranteed that trajectory tracking errors are uniformly ultimately bounded (UUD). Finally, the effectiveness of the proposed controller is verified by simulations. • The thruster dynamics and saturation constraints were considered in controller design. • A third-order state space equation was constructed to describe the dynamic of ROVs. • The unknown dynamics and partially known gain were considered in controller design. • A saturation factor was constructed for the design of the adaptive laws. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of trajectory tracking control of underactuated surface vessels in a quantitative method with only position and attitude available. Combined with high-gain observer, parameter compression algorithm and performance function, an adaptive control scheme with prescribed performance is proposed. The high-gain observer is constructed to estimate the velocities, and the parameter compression algorithm is adopted to address persistent perturbations and model uncertainties in a more concise way. By prescribed performance function, the controller can be designed with prescribed performance. The results about system stability is given and proved by using the Lyapunov direct method. The signals concerning with all the errors converge to a bounded set. Compared with the existing methods, the developed scheme can reduce the number of tuning parameters, and guarantee the tracking errors bounded within the prescribed performance constraints in the transformed coordinate, which means the steady errors, convergence rates and maximum overshoots can be guaranteed by the performance function. Comparison and numerical simulations are given to demonstrate the effectiveness of the proposed scheme. • An adaptive control scheme is proposed with only position and yaw angle available. • Parameter compression algorithm is adopted to reduce the number of tuning parameters. • The proposed scheme can guarantee the tracking errors with prescribed performance. [ABSTRACT FROM AUTHOR]

This paper proposes a novel fixed-time output feedback control scheme for trajectory tracking of marine surface vessels (MSVs) subject to unknown external disturbances and uncertainties. A fixed-time extended state observer (FESO) is proposed to estimate unknown lumped disturbances and unmeasured velocities, and the observation errors will converge to zero in fixed time. Based on the estimated values, a novel fixed-time trajectory tracking controller is designed for an MSV to track a time-varying reference trajectory by the extension of an adding a power integrator (API), and the tracking errors can converge to zero in fixed time as well. Additionally, the convergence time of the controller and the FESO is independent of initial state values. Finally, simulation results and comparisons illustrate the superiority of the proposed control scheme. • A fixed-time extended state observer (FESO) is proposed. • A novel fixed-time output feedback control scheme is proposed. • The observation errors and tracking errors converge to zero in fixed time. • The convergence time is independent of initial states of a vessel. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear partial-state feedback control is designed for a 3-DOF pantograph–catenary system by using backstepping approach, such that the contacting force of the closed-loop system is capable of tracking its reference profile. In the control design, the pantograph–catenary model is transformed into a triangular form, facilitating the utilization of backstepping. Derivatives of virtual controls in backstepping are calculated explicitly. A high-order differentiator is designed to estimate the unknown time derivatives of elasticity coefficient; and an observer is proposed to reconstruct the unmeasurable states. It can be proved theoretically that, with the proposed nonlinear partial-state feedback control, the tracking error of the contacting force is ultimately bounded with tunable ultimate bounds. Theoretical results are demonstrated by numerical simulations. • The backstepping approach is firstly applied to control design for pantograph–catenary system. • The closed-loop system is capable of tracking not only constant reference contacting force but also time-varying periodic reference forces. • A high-order differentiator is designed to approximate the unknown derivatives of time-varying elasticity coefficient. • A simple observer is designed to reconstruct the un-measurable system states. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive chattering-free sliding mode controller for trajectory tracking of robotic manipulators in the presence of external disturbances and inertia uncertainties. To achieve fast convergence and desirable tracking precision, a second-order fast nonsingular terminal sliding mode (SOFNTSM) controller is designed to guarantee system performance and robust stability. Chattering is eliminated using continuous control law due to high-frequency switching terms contained in the first derivative of actual control signals. Meanwhile, uncertainties are compensated by introducing the adaptive technique, whose prior knowledge about upper bound is not required. Finally, simulation results validate the effectiveness of the proposed control scheme. • A SOFNTSM controller is designed to ensure fast convergence and trajectory tracking. • Actual control law after integral is continuous and thus system is chattering-free. • Without prior knowledge of uncertainties, adaptive laws are designed to estimate them. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a dynamic path planning and trajectory tracking algorithm for an autonomous satellite, released from the space station, to get to the desired position for performing space tasks. The complex construction of the space station results in the presence of a geometric channel constraint for the obstacles avoidance. In addition, a three dimension B-spline template with minimizing the curvature of the path is designed, which could guarantee the continuity of the curvature to make the trajectory smooth and avoid the satellite from stopping at discontinuities waypoints. Then, the reference states and inputs are solved by a new projection method, which provides a foundation for the subsequent trajectory tracking. Subsequently, a finite horizon model predictive control method is constructed for the path tracking. The benefits of this approach are to take constraints into consideration, and to get optimal performance by minimizing the fuel consumption compared with other tracking controllers. The closed-loop stability is guaranteed by the feedback controller, terminal penalty, and a newly terminal constraint set. In simulation experiments, results illustrate the effectiveness and practicality of the algorithm. Highlights • A novel three dimension B-spline template is developed with minimizing the curvature of the path. • A novel finite horizon model predictive control method is constructed for the trajectory tracking. • Simulation results validate the effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

This paper addresses the fixed-time trajectory tracking control problem of a stratospheric airship. By extending the method of adding a power integrator to a novel adaptive fixed-time control method, the convergence of a stratospheric airship to its reference trajectory is guaranteed to be achieved within a fixed time. The control algorithm is firstly formulated without the consideration of external disturbances to establish the stability of the closed-loop system in fixed-time and demonstrate that the convergence time of the airship is essentially independent of its initial conditions. Subsequently, a smooth adaptive law is incorporated into the proposed fixed-time control framework to provide the system with robustness to external disturbances. Theoretical analyses demonstrate that under the adaptive fixed-time controller, the tracking errors will converge towards a residual set in fixed-time. The results of a comparative simulation study with other recent methods illustrate the remarkable performance and superiority of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper develops a backstepping controller for model helicopters to achieve trajectory tracking without singularity, which occurs in the attitude representation when the roll or pitch reaches ± π 2 . Based on a simplified model with unmodeled dynamics, backstepping technique is introduced to exploit the controller and hyperbolic tangent functions are utilized to compensate the unmodeled dynamics. Firstly, a position loop controller is designed for the position tracking, where an auxiliary dynamic system with suitable parameters is introduced to warrant the singularity-free requirement for the extracted command attitude. Then, a novel attitude loop controller is proposed to obviate singularity. It is demonstrated that, based on the established criteria for selecting controller parameters and desired trajectories, the proposed controller realizes the singularity-free trajectory tracking of the model helicopter. Simulations confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers. [ABSTRACT FROM AUTHOR]

In this paper, a new composite scheme is proposed, where the total control action is composed of the sum of a feedback-linearization-based controller and an energy-based compensation. This new proposition is applied to the rotary inverted pendulum or Furuta pendulum. The Furuta pendulum is a well-known underactuated mechanical system with two degrees of freedom. The control objective in this case is the tracking of a desired periodic trajectory in the actuated joint, while the unactuated link is regulated at the upward position. The closed-loop system is analyzed showing uniformly ultimately boundedness of the error trajectories. The design procedure is shown in a constructive form, such that it may be applied to other underactuated mechanical systems, with the proper definitions of the output function and the energy function. Numerical simulations and real-time experiments show the practical viability of the controller. Finally, the proposed algorithm is compared with a tracking controller previously reported in the literature. The new algorithm shows better performance in both arm trajectory tracking and pendulum regulation. [ABSTRACT FROM AUTHOR]