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In this study, we applied deep learning to improve the control of a KUKA LBR4 7 Degrees of Freedom (DOF) robotic arm. We developed a dynamic model using a comprehensive dataset of joint angles and actuator torques obtained from pick-and-place operations. This model was incorporated into a Model Predictive Control (MPC) framework, enabling precise trajectory tracking without the need for traditional analytical dynamic models. By integrating specific constraints within the MPC, we ensured adherence to operational and safety standards. Experimental results demonstrate that deep learning models significantly enhance robotic control, achieving precise trajectory tracking. This approach not only surpasses traditional control methods in terms of accuracy and efficiency but also opens new avenues for research in robotics, showcasing the potential of deep learning models in predictive control techniques.

Most of the previous research about unmanned surface vehicle (USV) control system just focuses on reaching the target but not considers berthing. Moreover, computation cost is rarely concerned. For automatic target arriving and berthing of USV in presence of multi-shape convex obstacles and disturbances, this paper designs a composite control system including trajectory optimization and trajectory tracking. In order to generate a smooth and optimal trajectory, two objectives including minimum running time and energy consumption are proposed, and their priority requirement is presented. Fuzzy satisfactory optimization is introduced to reformulate the objective functions, and the membership degree difference is used to model priority between two objectives. The obstacle avoidance constraint is developed based on the improved P-criterion. The comprehensive optimization model is established to obtain the maximum membership degree. Further, the priority optimization model is proposed to expand the feasible domain by relaxing the comprehensive optimization result. Two models are discretized by Gaussian pseudospectral method to find the optimal solution. To achieve good trajectory tracking under disturbances, two first-order active disturbance rejection control (ADRC) controllers are designed to follow the desired longitudinal velocity and course angular velocity. All the velocities of USV can converge. The simulation proves the effectiveness of the proposed co-designed system by comparing with other methods.

This paper deals with the nonlinear robust PWM control of a DC/AC differential boost inverter based on dynamic feedback linearization, active disturbance rejection, and sliding mode control techniques. The inverter topology consists of two synchronous boost converters linked through a load resistance. The model of each boost converter is put in Brunovski’s canonical form through dynamic feedback linearization, defining an auxiliary input depending on the control variable in an affine mode and a nonlinear disturbance containing endogenous and exogenous variables. Each disturbance is estimated by an extended state observer and compensated through a control law designed for tracking the desired trajectory, according to the active disturbance rejection control technique. Finally, a sliding mode component is designed and added to the previous control law to assure the robustness of the closed loop system against uncertainties due to electric parameters, supply voltage and load resistance deviations, and disturbance estimation errors. Experimental results validate the proposed control methodology.

Chemotherapy, a vital cancer treatment, operates by delivering drugs to target and eliminate cancer cells in the patient body. Mathematical models like the log-kill, Norton-Simon, and $E_{\max }$ hypotheses describe the growth/shrinking of the cancerous tumor due to the interaction and administration of the drugs with the tumor. This paper proposes a robust control approach based on artificial time-delayed theory to track the desired rate of change in tumor volume under model uncertainties and disturbances. The proposed algorithm relaxes the assumption on a priori knowledge of disturbance bound and its derivative. Unlike traditional methods, the control structure is simple, and the total disturbance is estimated by analyzing the previous input and output of the feedback state and control variables. Thus, robustness is ensured without relying on high-frequency switching or high gain. The stability analysis of the proposed scheme is investigated based on the Lyapunov theory. Moreover, extensive simulation results with comparative analysis affirm the efficacy of the proposed approach.

A predefined-time $H_{\mathrm {\infty }}$ trajectory tracking control scheme based on self-adjusting prescribed performance functions and dynamic relative threshold event-triggered mechanism is proposed for a five-degree-of-freedom underactuated autonomous underwater vehicle (AUV) with unknown external disturbances and actuators saturated. First, a new self-adjusting prescribed performance function is designed to ensure that the tracking errors do not exceed the prescribed bounds and to solve the singularity problem of general prescribed performance control (PPC) due to actuator saturation. Second, a predefined-time $H_{\mathrm {\infty }}$ controller combined with a predefined-time dynamic surface control (DSC) method is proposed to guarantee that system signals converge to the neighborhood of zero in a predefined time without adjusting the control parameters and to improve system robustness to uncertain disturbances. Third, an improved dynamic relative threshold event-triggered method is designed to save the communication resources of an underactuated AUV system. Then, the Lyapunov stability proof indicates that all signals in the closed-loop system are predefined-time bounded, and the trajectory tracking errors can converge to the neighborhood of zero within the set desired time. Finally, the simulations not only demonstrate the performance of the proposed controller-controlled system but also verify the effectiveness of the proposed scheme.

This article presents an extensive comparison of collision avoidance systems with local path planning based on a mathematical model of an autonomous underwater vehicle (AUV) controlled by the trajectory tracking control system. In the study, six methods such as improved artificial potential field (APF), D* algorithm, dynamic course adjustment (DCA), genetic algorithm (GA), particle swarm optimization (PSO) and rapidly-exploring random tree (RRT) were tested, the efficiency of which was verified on 10 test maps with various types of obstacles’ configurations and shapes with taking into account real-time decision-making ability. Both obstacle detection system and collision avoidance systems were extensively fine-tuned to achieve a compromise between collision avoidance efficiency and minimization of computation time. Based on the prepared simulation framework and environment, the trajectory completion percentage, average trajectory deviation, trajectory energy consumption, computation time and percentage of collision trials were assessed. The best results in terms of AUV safety were achieved by the D* and DCA methods. Slightly worse results were obtained by GA and PSO. Considering real-time decision-making ability, the best results were obtained by DCA and APF methods. Based on a detailed analysis of the results, it can be concluded that the DCA method can be used in quick-react emergency systems, and D*, GA and PSO methods are reasonable to use in medium-range local collision avoidance systems.

In order to realize waypoint-based automatic berthing alongside or astern, a generation algorithm of dynamic virtual ships is proposed to guide the underactuated surface vehicle (USV). In this paper, a nonlinear model predictive control (NMPC) problem is set up with multiple shooting method, which lifts the system and improves convergency. Measuring error and disturbances are reduced by moving horizon estimation (MHE) where the weights of sensors are auto-tuned according to their variation. Simulations of berthing alongside and astern of ship BAY CLASS illustrates the position error is smaller than 0.6 m and course error is smaller than 0.5°. Compared to adaptive sliding mode control, proposed method has advantage on state smoothness and the control performance meets the requirements of berthing accuracy.

It is undeniable that the development of robot manipulators has gained significant attention due to its numerous applications in various sectors. In order to address and resolve several issues for robotic manipulators, this paper provides a review of recent control approaches that have been conducted. In the beginning, a succinct comprehensive introduction of the pertinent terminology, configurations, components, advantages/disadvantages, and applications is given. A state-of-the-art review of the various control strategies for robotic manipulator systems is then presented, along with potential solutions when the systems are faced with various obstacles and impediments. An analytical study is discussed showing percentages of the papers discussed in this study in terms of the different control strategies, link types, models, applications, and degrees of freedom of robotic manipulators. For academic, research, medical, and industrial uses, some off-the-shelf developments in robotic manipulators are also presented.

To address the challenges posed by nonlinear tire characteristics in trajectory tracking control of active four-wheel steering (4WS) vehicle or fire-fighting robot, a novel control method is proposed. This method incorporates time-varying corrected cornering stiffness to enhance adaptability. Initially, the impact of friction coefficient and vertical load on tire lateral force nonlinearity is analyzed. Key input features are identified, and a cornering stiffness estimation model is developed using a Back Propagation (BP) neural network. Subsequently, the trajectory tracking state equation is established based on the 2-degree-of-freedom (2-DOF) dynamic model and trajectory tracking error model. An active front-wheel steering (AFS) trajectory tracking sliding mode controller (SMC) is designed, augmented by a Radial Basis Function (RBF) neural network, forming an RBF-SMC AFS controller capable of real-time correction of cornering stiffness. Additionally, an active rear-wheel steering (ARS) controller is designed based on fuzzy control theory, considering the influence of center of gravity lateral deviation on vehicle stability. Finally, Simulation tests under varied speed conditions on icy and dry asphalt surfaces, using the Matlab/Simulink-Carsim co-simulation platform, demonstrate that the proposed method dynamically adjusts front and rear axle cornering stiffness, enhancing trajectory tracking accuracy and maneuvering stability, particularly in high-speed or low-friction road conditions.

A linear time-varying model predictive control (LTV-MPC) method based on $SE(3)$ is proposed, to enhance the control precision and reduce energy consumption of the spacecraft. First, left-invariant principle of Lie group, Lie algebra $SO(3)$ , and other differential geometry theories are applied to extend LTV-MPC to $SE(3)$ . Then, considering the obstacle avoidance problem of the spacecraft in space, a suitable optimization function is selected to ensure smooth tracking of the desired working trajectory. By controlling the incremental output with the fastest convergence rate, the controller enables effective trajectory tracking. Finally, the effectiveness and applicability of the controller are verified by simulation experiments. These simulations validate the controller’s ability to achieve constraint satisfaction, optimize transient processes, and enhance control accuracy. The results provide compelling evidence of the controller’s potential for real-world spacecraft control applications.

In response to the challenge of insufficient trajectory tracking accuracy and low solution efficiency of Mecanum wheel AGV (Automated Guided Vehicle) under complex and constrained working conditions, this paper proposes an efficient Model Predictive Control (MPC) method to achieve superior tracking performance and robustness. Initially, a linear error model of the mobile platform is established based on pose error, serving as the predictive model for the MPC controller. A target function is designed to transform the trajectory tracking control problem into an optimal control problem. To handle inequality constraints, penalty terms are introduced into the objective function, and the resulting constrained problem is subsequently solved to approximate the optimal solution for the original inequalities. To alleviate the computational burden associated with real-time optimization problem-solving, an efficient MPC algorithm. has been developed. To ensure closed-loop stability under the MPC control method, stability constraints are imposed on the new optimization problem. Simulation results demonstrate that, in comparison to traditional MPC methods, the proposed approach reduces the average solution calculation time by 5.1% and the maximum single calculation time by 13.7%, all while maintaining trajectory tracking accuracy. These results validate the algorithm’s feasibility, effectively addressing the challenges associated with solving MPC problems.

Trajectory tracking is one of the most important aspects of an unmanned aerial system (or quad-copter) for selecting the optimal path from the source to the destination. This article presents a mathematical framework and approach for addressing the challenge of nonlinear systems like quad-copter. A novel control system for the quad-copter’s positions $\left ({{z,y,x} }\right)$ and attitudes (roll ( $\phi $ ), yaw ( $\psi $ ), pitch ( $\theta $ )) has been proposed based on optimisation techniques that are integrated with proportional-integral (PI) controllers. Astute position update methods such as helical, circular, etc. have been introduced using different algorithms like particle swarm optimization (PSO), grey Wolf optimization (GWO), and the diversified grey wolf optimizer (DGWOA) algorithm. Following that, in an iterative procedure, a variety of leadership levels are used to update the individual’s position, and the leadership is modified through the use of an adaptive mechanism. For validation, the proposed algorithm’s effectiveness is evaluated based on the convergence rate compared to that of other meta-heuristic algorithms. Owing to its inadequate exploration, PSO leads to challenges with parameter selection, whereas GWO is easy to get to the local optimum. The concept and execution of DGWOA have been implemented to update the Unmanned Aerial Systems (UAS) controlled parameters in order to overcome these limitations. The proposed algorithm’s performance for path planning in a complex and cluttered environment is investigated. The simulation shows that the DGWOA algorithm has a faster response as compared to the reference and $\left ({{z,y,x}}\right)$ has been improved with (92.87, 96.95, and 99.69) percentage along with eliminating the shortcomings of PSO & GWO.

This paper focuses on the trajectory tracking problem of unmanned aerial vehicles (UAVs) under external disturbances, and a trajectory tracking method that combines model predictive control with dynamic neural networks was proposed. Firstly, the trajectory tracking problem is transformed into a constrained quadratic programming problem using the idea of model predictive control. Then, the kinematic constraints are taken into account, and control increment constraints and relaxation factors are designed in the objective function. A dynamic neural network is introduced to solve this quadratic programming problem in real-time. In addition, a disturbance compensation observer is designed to overcome external disturbances. Finally, numerical simulations are conducted to verify that the proposed tracking strategy reduces computational

Assistive care robots operate in cluttered, complex environments, akin to human residences, and need to face sensor and actuator faults during their operation without compromising safety. In these situations, the system must foresee and provide reactions that are beyond robust in addition to compensating for uncertainty and volatility in its functioning. We propose a new control design framework based on the principles of antifragility. In this work, we provide a formal concept of antifragile control and outline the design procedures for creating a mobile robot trajectory-tracking antifragile controller. An extended comparative evaluation against other controllers and a methodical investigation of the performance under parametrizable uncertainty and errors is also provided. Our findings demonstrate the effectiveness of antifragile closed-loop control in volatile and unanticipated circumstances.

This paper presents a framework to plan and execute autonomous parking maneuvers in complex parking scenarios. We formulate a minimum-time optimal control problem for trajectory planning, using an indirect optimal control approach. A novel smooth penalty function is devised for collision avoidance with optimal control, and an effective technique is adopted to compute an initial solution guess. The trajectory planning tasks are solved with low computational times, and a dense mesh is used to discretize the domain of the optimal control problems, resulting in accurate collision-free solutions. The planned parking maneuvers are tracked with an original pseudo-neural feedforward-feedback steering controller, which outperforms other techniques from the literature, and a feedback longitudinal controller, to drive a realistic 14-degree-of-freedom vehicle simulator. We validate the planning and tracking algorithms in challenging narrow parking scenarios, including reverse, parallel and angle parking, and unstructured environments. The framework robustness is assessed by changing the vehicle mass, the road adherence conditions, and by introducing measurement noise with realistic sensor models. A video of the trajectory planning and tracking results is available as supplementary material.

This work addresses the trajectory tracking problem for a non-holonomic differential drive mobile robot with a constant time delay $h$ at the input signal. To compensate for the adverse effects of the input time delay on the vehicle, a non-linear prediction-observer scheme based on a sub-prediction strategy that asymptotically estimates the future values of the state, $h$ units of time ahead was introduced, and, thanks to the characteristics of the system, a condition which depends only on the gains of the predictor-observer is obtained for the convergence of the predicted states. Non-linear feedback based on the estimated future state is proposed to tackle the trajectory tracking problem of a mobile robot. The closed-loop system describing the prediction strategy and trajectory tracking solution was formally analyzed, showing the asymptotic convergence of the prediction and tracking errors to the origin. Numerical and real-time experiments were performed to evaluate the prediction-based control scheme, which show adequate performance.

In this study, a Fractional-Order Sliding Mode Control scheme is proposed for trajectory tracking control of Delta parallel robot. The proposed controller is compared with both integer-order Proportional-Derivative controller and integer-order Sliding Mode Controller with Computed Torque Control method. The forward kinematics, inverse kinematics and dynamic of Delta parallel robot are described. A Solidworks/Matlab/SimScape/Multibody model of Delta parallel robot is generated and used for dynamic parameter estimation and validation of the proposed method. Particle Swarm Optimization algorithm is utilized for dynamic parameter estimation of Delta parallel robot. The validation of the proposed method is evaluated for three different trajectories. External disturbances, noise and also various payloads are considered in testing robustness of control techniques. The results of the robustness tests confirm higher performance of FOSMC than two other control schemes.

This paper deals with the quadrotor craft trajectory tracking problem subject to unknown disturbance and actuator constraints. A new adaptive sliding mode control (ASMC) with finite-time convergence characteristics is proposed to guarantee quadrotor hovering in spite of parametric uncertainties and external disturbances. Compared with conventional sliding mode controller (SMC), the proposed adaptive algorithm has been developed for the vehicle altitude and attitude control, with unknown bounded of lumped uncertainties. This approach is based on a dynamical adaptive control law to avoid the overestimation and to ensure the convergence in a finite time. In addition, to solve the actuator saturation problem an auxiliary system is used. Stability analysis is demonstrated via Lyapunov theory, exhibiting that the proposed control strategy ensures that all signals of the closed-loop system are bounded and that the tracking errors are bounded in finite time. Numerical simulations and experimental results are given to illustrate the effectiveness of the proposed method, in which a comparative study with conventional SMC found in literature has been made. Experimental validation of the control strategy is carried-out using the parrot mambo mini-UAV.

This paper focuses on a fixed-time prescribed performance-based Fault-tolerant controller that guarantees the global performance for the Trajectory tracking control of the air cushion vehicle (ACV). In the presence of faults, time-varying parameters and environmental disturbances, the proposed control system in this paper has good robustness and control performance. Firstly, an integrated observer for disturbances and faults is proposed to suppress all uncertainties in the system. Then a novel prescribed performance function is designed that does not need to be constrained by the initial value of the target errors while ensuring that it has fixed-time convergence performance. Global prescribed performance control has the advantage of separating the error initial conditions from the prescribed performance function. At the same time, combined with the global sliding mode control method, the fast convergence and robustness of the whole system are guaranteed. Finally, the simulation results verify the effectiveness of the control system.

Automated driving systems operated at SAE levels 4 and 5 require a far-reaching fault-tolerant design. To meet this need at the actuator level, we present an integrated vehicle motion control approach that is able to tolerate a wide range of different actuator degradations and failures as well as tire blowouts in vehicles featuring four wheel-individual steering, drive, and brake actuators. The approach, which is based on non-linear model predictive control (MPC), tracks a temporal sequence of reference poses. Fault tolerance is achieved by reconfiguration of the MPC’s constraints, weights, and prediction model, which consists of a double-track vehicle and a brush tire model. The evaluation of the approach is based on two reference trajectories. The example of a simple single lane change trajectory in IPG CarMaker demonstrates the basic functionality of the approach. The example of a demanding decelerated single lane change trajectory shows that the approach is subject to limitations when tolerating different degradations and failures. Still, the observed limitations can be explained by the interplay of the specific degradation or failure and the demanding nature of the trajectory. Therefore, the results indicate that the suitability of fault-tolerant vehicle motion control as part of a system-wide safety concept is strongly connected to the range of possible driving scenarios that an automated driving system can encounter.

The mowing robots work with a multivariable strong coupling underactuated system that is mostly troubled by difficulty controlling and unsatisfactory accuracy. Especially, the frequent external disturbances and parameter changes are likely to get missed and heavy cutting. In this paper, a new trajectory tracking control method based on extended state observer (ESO) is introduced with a particular focus on dual closed-loop sliding mode. Firstly, from the perspective of kinematics, a speed assistant controller was designed to generate the speed control quantity, and secondly, a sliding mode control algorithm based on the improved Fractional Power Rate Reaching Law (IFPRRL) was programmed to control the drive motor that tracked the speed control quantity. By means of comparison, our improved algorithm presented faster arrival time and better robustness along with similar jittering. At the same time, the robustness of the system was further enhanced with the help of an optimized ESO to tackle unmodeled disturbances and uncertain disturbances during the operation. Finally, the experimental analysis of the motor drive circuit and the trajectory tracking control system of the lawn mowing robot were both carried out respectively. The analysis shows that the performance of the proposed reaching law sliding mode control algorithm had some new pleasing changes, such as adjustment time and robustness. The circular trajectory and the detour mowing trajectory were respectively tracked in the double closed-loop sliding mode designed in this paper. The experimental goal was to ensure that the error vector $P_{e} =$ ( $x$ Axis position error $x_{e}$ , $y$ Axis position error $y_{e}$ , Angle error $\theta _{e}$ ) all remaining at (0.01m, 0.01m, 0.01rad) were 5.34s and 5.36s, respectively, and both could be finally converged to 0. The results show that the newly developed controller based on ESO presented smaller arrival time and stronger robustness. The dual-closed-loop control of sliding-mode trajectory tracking method was capable to meet the real-time and precision requirements of the lawnmower robot for quick trajectory tracking.

Numerous academic works have addressed the identification and control problem for complex dynamic systems. In recent decades, the use of control algorithms based on neural networks (NNs) has been highlighted, which have shown satisfactory results in the trajectory tracking control for a class of discrete-time nonlinear systems. The present work proposes an efficient learning law for discrete-time recurrent high order neural networks (RHONNs), using a training algorithm based on an unscented Kalman filter (UKF). This learning law is applied through a decentralized neural block control using UKF (DNBC-UKF), for trajectory tracking control of a class of discrete-time nonlinear systems. The proposed controller is experimentally evaluated by means of real-time tests in a two degrees of freedom (DOF) vertical direct-drive robotic manipulator against a decentralized neural block control using EKF (DNBC-EKF). The Lyapunov stability theory is used to show that the identification errors of RHONNs are semi-globally uniformly ultimately bounded (SGUUB), the RHONN weights remains bounded, and the closed-loop tracking errors go to zero.

This paper aims to develop a fractional control approach for quadrotor trajectory tracking. A fractional-order integrator (PI $^{\lambda} $ ) with a feedback derivative scheme is designed to control each state of the MIMO system. The designed feedback controller stabilizes the initially unstable decoupled states and widens the stability, while PI $^{\lambda} $ provides precise trajectory tracking capabilities. After a successful simulation study, the new PI $^{\lambda} $ -D controller is implemented in the hardware environment. The various performance and load disturbance analyses reveal the effectiveness of the proposed scheme compared with the classical PD/PID controllers. The real-time study also shows that this scheme is a simple yet robust solution.

Model Predictive Controller (MPC) is widely used as a technique for path tracking control since it allows for dealing with system constraints and future forecasts. However, the performance of MPC is directly affected by the adopted model. A complex dynamic model can guarantee accuracy in path tracking but may not be suitable in computational terms. On the other hand, a simplified model may not capture essential nonlinear aspects. Thus, to cope with these problems, this paper deals with data-driven tire modeling to improve autonomous ground vehicle path tracking control. The main contribution of the present work is to show that neural tires can capture the nonlinearities present in the interaction between lateral and longitudinal vehicle dynamics, with a reduced computational cost for predictive controllers. Simulated and experimental tire data are approximate to design data-driven tire models using radial basis function and multilayer perceptron neural networks. Then, based on ground vehicles with neural tires, model predictive controllers are designed to regulate wheel torque and steering angle inputs. Comparative tests were conducted to compare the proposed data-driven MPC approach with the classical nonlinear MPC controller. The results show that the neural tires approximate nonlinear tire models and experimental data with arbitrary precision in terms of accuracy and error-based metrics. The proposed methodology was successfully applied to perform trajectory and velocity tracking of ground vehicles. In addition, MPC with a neural tire model as prediction inference reduces the computational effort compared to traditional approaches.

To address the high-precision trajectory tracking task of uncertain robotic manipulators, a continuous sliding mode control (CSMC) scheme based on time-varying disturbance estimation and compensation is developed. The proposed control approach can not only avoid the chattering of the traditional sliding mode control (SMC) scheme and solve the problems existing in the application of the CSMC method but also make the robot obtain stronger disturbance rejection performance. Meanwhile, the stability of the closed-loop system under the recommended control approach is guaranteed by a defined Lyapunov function. Finally, the trajectory tracking and disturbance rejection performance of the 2-DOF robot under the action of the PID control, traditional SMC, CSMC, and present control methods are carried out, respectively. The results show the effectiveness and superiority of the proposed control method.

The demand for accurate and fast trajectory tracking for multirotor Unmanned Aerial Vehicles (UAVs) have grown recently due to advances in UAV avionics technology and application domains. In many applications, the multirotor UAV is required to accurately perform aggressive maneuvers in challenging scenarios like the presence of external wind disturbances or in-flight payload changes. In this paper, we propose a systematic controller tuning approach based on identification results obtained by a recently developed Deep Neural Networks with the Modified Relay Feedback Test (DNN-MRFT) algorithm. We formulate a linear equivalent representation suitable for DNN-MRFT using feedback linearization. This representation enables the analytical investigation of different controller structures and tuning settings, and captures the non-linearity trends of the system. With this approach, the trade-off between performance and robustness in design was made possible which is convenient for the design of controllers of UAVs operating in uncertain environments. We demonstrate that our approach is adaptive and robust through a set of experiments, where accurate trajectory tracking is maintained despite significant changes to the UAV aerodynamic characteristics and the application of wind disturbance. Due to the model-based system design, it was possible to obtain low discrepancy between simulation and experimental results which is beneficial for potential use of the proposed approach for real-time model-based planning and fault detection tasks. We obtained RMSE of 3.59 cm when tracking aggressive trajectories in the presence of strong wind, which is on par with state-of-the-art.

Trajectory tracking control is indispensable for a wheeled mobile robot to achieve successful navigation. The classical tracking control systems that are used in wheeled mobile robots do not compensate for the parameter uncertainties and external disturbances. For control strategy, this paper presents a novel hybrid approach, combining a neural network-based kinematic controller and a model reference adaptive control. The controller parameters are adaptively determined online using neural networks. The adaptively tuned kinematic controller ensures a fast convergence to the desired trajectory. The model reference adaptive controller retains the desired tracking performance when parameter and model uncertainties occur. The Lyapunov stability method is used to obtain the adaptive gains which guarantee the asymptotic stability of the error dynamics, where the error is the difference between the outputs of the reference model and the actual plant. The performance of the proposed controller is compared with that of the PID controller, kinematic controller, and adaptive dynamic controller using different performance analysis indices such as integral absolute error, integral squared error, and mean absolute error. Simulation studies demonstrate that the proposed controller achieves high tracking accuracy and fast convergence as compared to the PID, kinematic, and adaptive dynamic controllers considering parameter uncertainties and slip disturbances. The outcomes of the simulation studies also illustrate that the proposed controller achieves the best transient performance. Experiments using real-world tests based on a two-wheeled differential drive robot architecture have elucidated the feasibility of the developed controller regarding tracking accuracy, total control effort, and robustness against uncertainties.

In this paper, a novel event-triggered composite learning finite-time control scheme is presented for underactuated marine surface vehicles (MSVs) trajectory tracking under unknown dynamics and unknown time-varying disturbances. Line-of-sight (LOS) tracking control method is employed to address the underactuation problem of MSVs. The neural networks (NNs) are untilized to approximate unknown dynamics. The serial-parallel estimation model is employed to construct the prediction error, and the prediction errors and tracking errors are fused with construct the NN weights updating. Combining the result of approximation information, the disturbances observers can be created to achieve disturbance estimation. Fractional power technology is artistically introduced to realize the finite-time trajectory tracking control of MSVs based on composite learning. The proposed control scheme ensures the simultaneous realization of high precision tracking performance and unknown information approximation. Moreover, an event-triggered mechanism is introduced to reduce the transmission load and the execution rate of actuators. It is proved that the proposed control scheme ensures all error signals of the MSVs trajectory tracking control system can converge to the neighborhood of zero within a finite time. Finally, the simulation results on an MSV verify the effectiveness and superiority of the proposed control scheme.

Automatic train operation is an important part of the train control system. As train operating intervals continue to shorten and train speeds continue to increase, multiple train cooperative control is currently an important technology to further improve the efficiency of train operation and line passing capacity. However, considering various factors such as the nonlinearity and uncertainty of the train dynamics model and the complexity of the line conditions, this creates even greater demands on the design of the controller. In this study, we propose an adaptive cooperative tracking control method for multiple trains using adjacent information. For the multiple-train coordinated tracking control in the presence of model uncertainties, unknown parameters, and external disturbances, a distributed cooperative control scheme for multiple trains is designed using the displacement, velocity, and acceleration information of adjacent trains, combined with radial basis function neural networks and adaptive methods. A fast high-order sliding mode observer is used to estimate the train velocity and acceleration information. Stability and convergence are proved for single and multiple trains utilizing Lyapunov stability analysis. Simulation examples demonstrate the effectiveness of the proposed controller.

In this work, a new constrained numerical optimization approach is proposed for solving offline the Inverse Kinematics Problem (IKP) of articulated robots, which consists on optimizing the joint displacement while the end effector is positioned and oriented in a desired pose. The novelty of this approach is in the formulation of the optimization problem, where the objective function calculates the minimum joint displacement, with the position and orientation errors handled as equality constraints. This formulation may avoid configurations containing singularities. The IKP is solved for a defined trajectory in the dexterous workspace of the robot by using two versions of the Differential Evolution algorithm and considering two stages. First, DE/rand/1/bin is used for positioning and orienting the end effector at the first point of the trajectory regardless of its initial position. The second stage applies DE/best/1/bin in order to emphasize the exploitation process and minimize the computational time to obtain the inverse kinematics due to the closeness that exists between the consecutive points that make up the trajectory. This combination of DE versions is another contribution of the proposed approach that speeds up considerably the search process by first prioritizing the exploration and then the exploitation, and this sequential application can be used to the solution of diverse constrained numerical optimization problems. Finally, the IKP for the IRB-1600 robot was solved as a case study considering two trajectories in its dexterous workspace, circular and Lissajous. The results generated by the proposed approach for the case study were simulated in the RoboDK® industrial robot simulator.

In this paper, we propose a game-based coupling controller to solve the problem of autonomous vehicles in the trajectory tracking process. The controller ensures path tracking accuracy and shows good tracking performance for the desired speed profile that changes based on navigation while driving. Furthermore, it improves ride comfort and addresses the lateral stability problems that occur when applying classical model predictive control (MPC) controllers. We implemented this controller to plan the trajectory by considering the fundamental interaction between longitudinal and lateral vehicle dynamics, as well as to track the trajectory by using a receding horizon strategy. A comparative study was conducted to compare the proposed controller with the classical MPC controller. Based on CarMaker-Matlab/Simulink co-simulations, this controller outperformed the classical MPC in terms of trajectory tracking performance. Moreover, it exhibits excellent ride comfort and lateral stability that passengers will experience.

This paper proposed a finite-time prescribed performance control scheme for underactuated autonomous underwater vehicles (AUVs) based on adaptive neural networks and a tan-type barrier Lyapunov function. Even in the presence of output constraints and environmental disturbances, the AUV can also precisely track the desired trajectory in a finite time. By introducing a tan-type barrier Lyapunov Function (TBLF), the singularity problem in process design is solved and all output errors are guaranteed to satisfy the prescribed performance specifications. Dynamic surface control (DSC) and the minimal learning parameter (MLP) are employed to greatly simplify the complexity of the algorithm and enhance the robustness of the control system, respectively. Lyapunov stability analysis proves that the proposed controller guarantees all signals in the closed-loop system to be uniformly ultimately bounded (UUB), and that the tracking errors converge to a small neighborhood near the origin in a finite time. Finally, the simulation results demonstrate the effectiveness and feasibility of the proposed controller.

An obstacle avoidance algorithm was suggested in this study to handle the redundant manipulator’s end trajectory planning problem, with the accuracy of the end trajectory guaranteed to be within the projected error. To accomplish this goal, the calculation method of vector pseudo distance is used instead of the traditional Euclidean distance to express the minimum proximity between the robot arm and the obstacle. This method can express the constraint conditions between the obstacle and the robot arm more clearly and improve the obstacle avoidance efficiency. The virtual repulsion force is generated to make the end of the manipulator far away from the obstacle through the relationship between the velocity vector and the angle vector of the end motion, and the end recovers to the desired trajectory quickly and stably after avoiding the obstacle through the adjustment of the tangent velocity function. The error adjustment coefficient is intended to communicate back the actual trajectory of the end obstacle avoidance to the tracking function in real time, and to adaptively change the velocity and acceleration of the end-executor to reduce the end trajectory tracking error. The simulation results show that when an envelope body obstacle appears unexpectedly on the end executor’s expected mission locus, if the expected distance between the end-effector r and the obstacle is greater than or equal to 0.02m, the end of the actuator can avoid the obstacle and return to the expected track quickly and smoothly.

This paper presents the application of different approaches of intelligent controllers based on LAMDA (Learning Algorithm for Multivariate Data Analysis) to perform the trajectory tracking task of a mobile robot Pioneer 3-DX simulated in the Virtual Robot Experimentation Platform V-REP environment. The paper proposes the design of a cascade control strategy composed of two controllers, the external controller based on a feedback linearization for the robot kinematics and the internal controller applied to the robot dynamics where the LAMDA approaches are applied. In this work, it is considered an uncertain dynamic model. Thus, its identification and control are based on a reduced-order model for designing purposes. Finally, the dynamic controller is designed using different controllers based on LAMDA, such as LAMDA-PID, LAMDA-Sliding Mode Control, and Adaptive LAMDA. To perform a comparative analysis between them that includes a conventional PID, SMC, and Fuzzy-PID, different trajectories are examined to evaluate the methods. The obtained results are compared qualitatively and quantitatively to determine which proposal performs the most accurate control and presents the best results in terms of performance.

The tuning of the robot actuator represents many challenges to follow a predefined trajectory on account of the uncertainties of parameters and the model nonlinearity. Furthermore, the controller gains require proper optimization to achieve good performance. In this paper, the use of a modified neural network algorithm (MNNA) is proposed as a novel adaptive tuning algorithm to optimize the controller gains. Furthermore, a new mathematical modulation is introduced to promote the exploration manner of the NNA without initial parameters. Specifically, the modulation is formed by using a polynomial mutation. The proposed algorithm is applied to select the proportional integral derivative (PID) controller gains of a robot manipulator arms in lieu of conventional procedures of designer expertise. Another vital contribution is formulating a new performance index that guarantees to improve the settling time and the overshoot of every arm output simultaneously. The proposed algorithm is evaluated with different intelligent techniques in the literature, including the genetic algorithm (GA) and the cuckoo search algorithm (CSA) with PID controllers, where its superiority to follow various trajectories is demonstrated. To affirm the robustness and efficiency of the proposed algorithm, several trajectories and uncertainties of parameters are considered for assessing the response of a robotic manipulator.

New control procedures for finite-time stabilization of discrete-time nonlinear systems in the strict-feedback form are proposed. The proposed designs enjoy the properties of being dependent on one design parameter and the ability to bring the state vector to the origin in finite time. Moreover, the settling-time functions are estimated in terms of the initial state vector and the unique design parameter that regulates the rate of the finite-time convergence. Finally, a trajectory-tracking control algorithm is presented and approved by numerical simulations. The simulation results have shown the excellent performance of the closed-loop system for different values of the free design parameter.

For 4MIDEV with differential steering, the trajectory tracking multi-objective control method is studied. The dynamics model of the four-in-wheel motor independent-drive vehicle (4MIDEV) is established comprehensively considering the differential steering dynamics characteristics, longitudinal dynamics characteristics, and lateral dynamics characteristics. Takagi Sugeno (T-S) fuzzy method is adopted to deal with the nonlinear and time-varying characteristics of the model parameters such as vehicle longitudinal speed and the front steering wheel angle. The trajectory tracking control targets are divided into the kinematic control target considering the trajectory tracking accuracy and the dynamics control target considering longitudinal speed tracking as well as lateral stability performance. The generalized $H_{2}$ norm and $H_{\infty }$ norm are selected to constrain the kinematic control target and the dynamics control target respectively. The generalized $H_{2}/H_{\infty }$ trajectory tracking controller is designed to improve the trajectory tracking accuracy and longitudinal speed tracking as well as lateral stability performance. The hardware in the loop test (HIL) verified that the designed trajectory tracking multi-objective controller can improve the comprehensive performance of vehicle and balance the trajectory tracking accuracy between the longitudinal and lateral dynamics performance.

The nonlinearities of the robotic manipulators and the uncertainties of their parameters represent big challenges against the controller design. Moreover, the tracking of regular and irregular trajectories with fewer overshoots, short settling time, and small steady-state error is the main target for the robotic response. The model predictive control (MPC) is an efficient controller to handle the performance requirements. However, the conventional MPC requires the linearization of the system model. The linearization of the model does not cover all dynamics of the robotic system. Thus, this paper introduces the nonlinear MPC (NLMPC) as a proper control method for the nonlinear systems instead of the conventional MPC. Specifically, this work proposes the use of NLMPC for controlling robotic manipulators. However, the NLMPC gains need proper tuning to attain good performance rather than the conventional methods. The neural network algorithm (NNA) considers a sufficient adaptive intelligent technique that can be utilized for this purpose. The restriction in a local optimum reveals the main issue versus artificial intelligence techniques. This paper suggests a new improvement to reinforce the exploration behavior of the NNA to overcome the local restriction issue. This modification is carried out by utilizing the polynomial mutation as an effective method to promise the exploration manner of the intelligence techniques. The proposed system can estimate all states from only the output to reduce the cost of the required sensors to measure all states. The results confirm the superiority of the proposed systems with the estimator with negligible change in the output response. The proposed modified NNA (MNNA) is evaluated with the main NNA, genetic algorithm-based PID control scheme, besides the cuckoo search algorithm-based PID control scheme from other works. The results confirm the robustness and effectiveness of the suggested MNNA-based NLMPC to track regular and irregular trajectories compared with other techniques.

Steer-by-Wire (SBW) systems are an integral and essential component of intelligent electrified vehicles and are critical to ensure safe vehicle operations. In this paper, a fault-tolerant control method for SBW is proposed to mitigate the adverse influence of front wheel steering angle sensor faults based on the Kalman filtering technique. First, a linearized vehicle model is derived based on tire characteristics and is further combined with a steering actuator model to provide the modelling foundation for estimating the front wheel steering angle. Considering multi-source noises and their significant influence on the front wheel steering angle sensor, the Butterworth filter is employed to filter out the high-frequency noises. The front wheel steering angle estimation is realized by incorporating the measurements of the yaw rate and lateral acceleration of vehicle and the current of steering motor. In particular, a dynamic threshold mechanism is adopted to activate the fault diagnosis and fault-tolerant compensation based on the residual theory. Finally, a linear time-varying model predictive controller is presented to execute the trajectory tracking task for an intelligent electrified vehicle. The effectiveness of the proposed scheme is verified under the single lane change and double lane change maneuvers during the trajectory tracking.

For the parallel parking problem in narrow space, this paper proposes a trajectory tracking control method with a novel trajectory planning layer for autonomous parallel parking based on a numerical optimization algorithm and model predictive control. In the trajectory planning layer, the vehicle kinematics model suitable for the low-velocity parking scene is established. Considering the vehicle physical constraints, boundary condition constraints, and obstacle avoidance constraints during the parking process, the parking trajectory planning task is described as an optimal control problem, further transformed into a nonlinear programming problem by Gauss pseudo-spectral method. Taking the shortest parking completion time as the optimization objective function, the parking trajectories of the large, medium and small parking spaces are obtained, respectively. A parking trajectory tracking controller based on the model predictive control algorithm is designed in the trajectory tracking control layer. The linear error model is used as the prediction model, and the quadratic programming is adopted as the rolling optimization algorithm in the tracking controller. The velocity and front-wheel swing angle are obtained as control signals for parking trajectory tracking. Through CarSim and Simulink’s co-simulation, the feasibility and effectiveness of the proposed parallel parking trajectory planning and tracking control method are verified. The co-simulation results show that the maximum tracking errors of horizontal and longitudinal positions are less than 0.15m. The maximum tracking errors of heading angle are less than 2° under three different parking spaces. Real vehicle tests are carried out to verify the effectiveness of the proposed hierarchical control method. The test results show that the vehicle can park in the parking space safely, quickly and accurately when the actual parking space is detected. The proposed method can plan the parking trajectory with the constraints and the shortest time and control the vehicle to complete the parking operation accurately along the planned trajectory.

This article focuses on the trajectory-tracking of an underactuated surface vehicle (USV) considering model uncertainties and nonlinear environmental disturbances. For trajectory tracking in an actual USV sailing environment, both the inertia and damping matrixes are not diagonal, the velocities states are unmeasurable, and error constraints and input saturation are considered. A robust control strategy is proposed based on the backstepping method, state transformation, a super-twisting state observer, and neural networks. All the closed-loop signals are uniformly ultimately bounded, which is proved by the Lyapunov stability theory analysis. The advantages of the proposed method are as follows. (i) A super-twisting observer is constructed to solve the problem of the velocities being unmeasurable, and the error between the virtual and actual velocities converges to a small neighborhood around zero. (ii) Additional controllers are developed to address input saturation of the system control. (iii) A predefined function design is employed to guarantee the transient trajectory-tracking performance. Finally, simulation results verify the feasibility and effectiveness of the proposed USV trajectory-tracking control method.

In this paper, the problem of modeling and anti-disturbance control is studied for lightweight personal robotics (P-Robs) with a six-degree-of-freedom robot manipulator to solve the movement instability phenomenon caused by time-varying uncertain disturbances during the movement of the robot manipulator. The detailed dynamical equations of the P-Rob system are solved based on the Lagrange energy equation, and the actual dynamical model of the robot manipulator system is obtained. The disturbance observer is designed to estimate the disturbance effectively, and an integral sliding mode control algorithm is proposed to realize tracking control. Stability analysis of the system is carried out using the Lyapunov function. Finally, experiments are conducted on an actual P-Rob system model, and the experimental results show that the robot manipulator system tracks the desired trajectory effectively, which validates the effectiveness of the proposed control algorithm.

This paper deals with FeedBack/ FeedForward (FB/FF) control of double pendulum gantry crane systems with payloads taking values over arbitrarily large intervals. The new proposed 2DoF control architecture is aimed at: 1) to speed up the horizontal payload transportation while minimizing the tracking error with respect to a desired trajectory; 2) to minimize the sway angles amplitude. The main features of the control design procedure are: 1) the dynamic output FB control is designed in order to ensure the robust stability of the closed loop system and the steady-state exact payload positioning; 2) the FF control action is given by the optimally weighted sum of the two contributions due to FF Plant Inversion (FFPI) and FF Closed Loop Inversion (FFCLI) control schemes; 3) the optimal robust FF control input is obtained as the solution of a min max optimization problem that can be solved offline with numerically efficient procedures; 4) the provided analytical closed form of the FF input in terms of a linear combination of polynomial B-splines basis functions allows an easy implementation on commercial devices.

This paper addresses the spatial trajectory tracking problem for a stratospheric airship with state constraints, input saturation and unknown disturbances. First, a Laguerre-based model predictive kinematic controller (LMPC) is proposed to tackle the state constraints and generate the desired velocity signal. To reduce the complexity of online optimization, Laguerre functions are applied to decrease the number of optimization variables by approximating the predicted control sequence. Second, in the dynamic loop, a sliding mode controller (SMC) with fast power rate reaching law (FPRRL) is introduced to track the desired velocity signal. The unknown disturbances in the dynamic model of airship are estimated and compensated by reduced-order extended state observer (ESO). An anti-windup compensator is incorporated into the FPRRL-based SMC controller to deal with the input saturation. Stability analysis implies that the tracking errors converge to a small neighborhood of zero. Comparative simulations about spatial straight and curve trajectory tracking are provided to evaluate the effectiveness and robustness of the proposed control scheme.

We consider a small helicopter structure that is maneuvered through the control of moving masses. It is referred to as a swash mass helicopter (SMH). This paper addresses the trajectory tracking control problem for the SMH, with a specific focus on the decoupling change of coordinates of both rotational and translational dynamics. We propose a control scheme in which position tracking is the primary objective, while the attitude tracking task is considered as a secondary objective. The intermediate control signals related to the attitude dynamics exploit the structural properties of the SMH and are enhanced with terms that grant a more accurate tracking of the target trajectory. The closed-loop system stability under the trajectory tracking objective is obtained following the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) approach. In addition, the presence of external disturbances can diminish the trajectory tracking performance. For this reason, a nonlinear outer loop controller is added to the IDA-PBC to compensate the disturbances. Finally, the results of several simulations are reported to evaluate the performance of the control strategy.

For four-wheel independent drive intelligent vehicle, the Model Predictive Control (MPC) is adopted to design the trajectory tracking controller through active steering and four-wheel independent drive/brake. The control objective is to follow a desired trajectory while taking into account the control actuator constraints and vehicle dynamic stability constraints. To reduce the computational complexity, a linear time-varying model predictive controller is designed to linearize the nonlinear vehicle model locally at each sampling point. The co-simulation of CarSim/Simulink shows that the designed controller has high tracking accuracy on the basis of ensuring vehicle stability and strong robustness to vehicle velocity and road adhesion coefficient. The trajectory tracking accuracy based on MPC is better than that of the preview driver model (PDM).

This paper reports a flexible (or time-varying) multi-agent formation approach with average trajectory tracking for second-order integral multi-agent networks with single virtual leaders. The approach is developed by means of time-varying Olfati-Saber flocking algorithms, and sliding mode control (SMC) in terms of the leader-average dynamics. More precisely, SMC-specifying average trajectory tracking is combined with flexible multi-agent flocking driven by the Olfati-Saber flocking algorithms with time-varying weighting norm. Existence conditions and properties of the suggested multi-agent formation are examined rigorously, together with implementation formulas. It is shown that by designing the sliding surface and the time-varying weighting matrix appropriately, flexible formation with finite-time trajectory tracking can be achieved, free of control action chattering; moreover, the sliding mode control and formation control can be designed separately. Numerical examples are given to illustrate the main results.

A series of fractional robust trajectory tracking controls are proposed for the Delta parallel robot with uncertainty. For the high speed and heavy load, the Delta parallel robot could not ignore the influences of the high nonlinearity (by the dynamics of the multiple closed-loops mechanism and the nonlinear joints friction) and the various kinds of uncertainties (i.e., the unknown dynamic parameters and external disturbances caused by the residual vibration). By formulating the motion equation of the Delta parallel robot, the nonlinearity is settled by a norm model based control design. The uncertainty considered in the paper is time-varying but unknown. An online estimation with an exponential type leakage term and dead-zone is construct to investigate the realtime information of the uncertainty. In virtue of the estimated information, two fractional robust trajectory tracking controls with the joints friction compensation are designed. Under the proposed controls, the system performance of the Delta parallel robot can be deterministically guaranteed (which includes uniform boundedness and uniform ultimate boundedness).

Tracking control has been an important research topic in robotics. It is critical to design controllers that make robotic systems with smooth velocity commands. In addition, the robustness of the robotic system in the presence of system and measurement noises is an important consideration as well. This paper presents a novel tracking control strategy that integrates a biologically inspired backstepping controller and a torque controller with unscented Kalman filter (UKF) and Kalman filter (KF). The bioinspired backstepping controller and torque controller are capable of avoiding and reducing the velocity jumps and overshoots that occur in conventional backstepping control and provide smooth velocity commands. The integration of KF and UKF enables the proposed control strategy capable of providing accurate state estimates. The stability and convergence of tracking errors are guaranteed by Lyapunov stability analysis. The novelty of the proposed bioinspired tracking control strategy is to take the system and measurement noises and robot dynamic constraints into the consideration. The results show that the proposed control strategy provides accurate state estimates and avoids large velocity jumps and overshoot that occurs in conventional backstepping control. This tracking control strategy is suitable for autonomous mobile robots under hard conditions with system and measurement noises.

Being trajectory tracking key for safe mobile robot navigation, Fuzzy Logic (FL) has been useful in tackling uncertainty and imprecision to realize robust and smooth trajectory tracking. In this paper, we present the Z-number based Fuzzy Logic control for trajectory tracking of differential wheeled mobile robots. The unique point of our approach lies in the ability to encode constraint and reliability in multi-input and multi-output rules, whose antecedent universe considers only the instantaneous measurements of distance and the orientation gaps, and whose consequent universe is computed by the interpolative reasoning and the graded mean integration approach. As a consequence, not only our approach avoids the complexity of encoding error gradients, but also is advantageous to model versatile control rules able to cope with missing observations and noisy inducements on actuators. Our experiments using both physics-based simulations and real-world tests based on a Pioneer 3DX robot architecture have elucidated the superior efficacy and the feasibility of the proposed controller regarding accuracy, robustness, and smoothness compared to other well-known related frameworks such as Fuzzy Logic Type 1, Fuzzy Logic Type 2 and Fuzzy Logic with PID. Our results provide unique insights to realize generalizable algorithms aided by FL and Z-number towards robust trajectory tracking.