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ABSTRACT This article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The overtaking process for autonomous vehicles must prioritize both efficiency and safety, with safe distance being a crucial parameter. To address this, we propose an automatic overtaking path planning method based on minimal safe distance, ensuring both maneuvering efficiency and safety. This method combines the steady movement and comfort of the constant velocity offset model with the smoothness of the sine function model, creating a mixed-function model that is effective for planning lateral motion. For precise longitudinal motion planning, the overtaking process is divided into five stages, with each stage's velocity and travel time calculated. To enhance the control system, the model predictive control (MPC) algorithm is applied, establishing a robust trajectory tracking control system for overtaking. Numerical simulation results demonstrate that the proposed overtaking path planning method can generate smooth and continuous paths. Under the MPC framework, the autonomous vehicle efficiently and safely performs automatic overtaking maneuvers, showcasing the method's potential to improve the performance and reliability of autonomous driving systems. [ABSTRACT FROM AUTHOR]

Trajectory tracking control of input-constrained systems is an essential problem in many control applications, including robotics. In this paper, we propose a constrained tracking controller for input affine nonlinear systems with convex input constraints based on tracking control Lyapunov functions (TCLFs). To deal with general convex input constraints, we first solve a convex optimization problem that minimizes the time derivative of TCLFs subject to convex input constraints; we refer to its optimal solution as minimizing input. Then, the proposed trajectory tracking is constructed by using the minimizing input and an appropriate scaling function. We prove that the proposed controller locally achieves trajectory tracking and satisfies the given convex input constraints. Finally, we demonstrate the effectiveness of the proposed controller by numerical simulations of a wheeled mobile robot. [ABSTRACT FROM AUTHOR]

Intelligent vehicle trajectory tracking exhibits problems such as low adaptability, low tracking accuracy, and poor robustness in complex driving environments with uncertain road conditions. Therefore, an improved method of adaptive model predictive control (AMPC) for trajectory tracking was designed in this study to increase the corresponding tracking accuracy and driving stability of intelligent vehicles under uncertain and complex working conditions. First, based on the unscented Kalman filter, longitudinal speed, yaw speed, and lateral acceleration were considered as the observed variables of the measurement equation to estimate the lateral force of the front and rear tires accurately in real time. Subsequently, an adaptive correction estimation strategy for tire cornering stiffness was designed, an AMPC method was established, and a dynamic prediction time-domain adaptive model was constructed for optimization according to vehicle speed and road adhesion conditions. The improved AMPC method for trajectory tracking was then realized. Finally, the control effectiveness and trajectory tracking accuracy of the proposed AMPC technique were verified via co-simulation using CarSim and MATLAB/Simulink. From the results, a low lateral position error and heading angle error in trajectory tracking were obtained under different vehicle driving conditions and road adhesion conditions, producing high trajectory-tracking control accuracy. Thus, this work provides an important reference for improving the adaptability, robustness, and optimization of intelligent vehicle tracking control systems. [ABSTRACT FROM AUTHOR]

This paper presents an improved motion controller based on the backstepping method to address nonlinear control challenges in unmanned aerial–aquatic vehicles (UAAVs), enabling them to navigate between two different media. The nonlinear control approach is applied to UAAV motion control, incorporating filters to improve stability. The study designs motion controllers for three UAAV phases: underwater, in the air, and transitioning between media. Fluid simulations of the emergence process of the UAAV for future field experiments were conducted. By fine-tuning the simulations, a comprehensive understanding of the vehicle's performance is obtained, offering crucial insights for the development of subsequent control systems. Simulation results confirm the controller's ability to achieve target trajectory tracking with control system responses that meet practical requirements. The controller's performance in attitude control and trajectory tracking is verified in underwater gliding, transmedia transitions, and airborne phases, demonstrating its effectiveness. [ABSTRACT FROM AUTHOR]

Due to the characteristics of good concealment ability and strong mobility, multiple, small spherical underwater robot formations play an important role in near coast defense missions, such as cruising, reconnaissance, surveillance, and sensitive target capturing. Referring to the formation problem for underwater small spherical robots with limited energy, perception, and computation abilities, a trajectory tracking-based formation strategy that transforms the complex formation tracking problem into a simple trajectory tracking problem of a single robot is provided. Two layers are designed in the formation tracking strategy. The upper layer is a virtual structure-based formation algorithm. The bottom layer is a tracking controller based on model predictive control (MPC). The formation algorithm is in charge of calculating reference trajectory for each robot in the formation according to the global formation path. The MPC-based dynamic controller for each robot is designed to track the self reference trajectory. Compared with the model predictive control method used for the traditional trajectory tracking problem of a single robot, this paper additionally considers the formation constraints and the internal collision avoidance. In addition, the extended state observer (ESO) is utilized to estimate the lumped disturbance composed of environment disturbance and the inaccurate dynamic model of a small spherical robot. Not only are the numerical simulations based on MATLAB v.2015a, but physical simulations based on self-building multi-spherical robot formation platform are also carried out. Furthermore, through using two small spherical robots, a formation tracing experiment is conducted. All of the results prove that the proposed formation method is feasible and practical for small spherical robots. [ABSTRACT FROM AUTHOR]

Backstepping-based fixed-time tracking control is proposed for a robotic arm system to solve the problem of trajectory tracking control under system uncertainties, which ensures the robotic arm system can realize stable tracking control within a fixed time independent of the initial state of the system. In addition, to address the uncertainties in the robotic arm system, a control strategy based on disturbance observer compensation is designed, which provides feed-forward compensation through the accurate estimation of the system uncertainties and enhances the system's robustness. Finally, a two-link robotic arm model is used for simulation experiments, and the comparison results show that the control scheme designed in this article can effectively improve the robotic arm's tracking accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC. [ABSTRACT FROM AUTHOR]

The large-range uncertainties of specific impulse, mass flow per second, aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles (SLVs) ascending leads to the deviation of the actual trajectory from the reference one. One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer (ESO) and then modify the control commands. However, ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large, which reduces the guidance accuracy. This paper introduces differential inclusion (DI) and designs a controller to solve the large-range parameter uncertainties problem. When above uncertainties have large ranges, it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set. If the DI system is stabilized, all the subsets are stabilized. Different from the traditional controllers, the parameters of the designed controller are calculated by the uncertain boundaries. Therefore, the controller can solve the problem of large-range parameter uncertainties of in ascending. Firstly, the ascent deviation system is obtained by linearization along the reference trajectory. The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation, which is called DI system. A DI adaptive saturation tracking controller (DIAST) is proposed to stabilize the DI system. Secondly, an improved barrier Lyapunov function (named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations. Compared with traditional barrier Lyapunov function, it can dynamically adjust the boundary of deviation convergence, which improve the convergence rate and accuracy of altitude, velocity and LTIA deviation. In addition, the correction amplitudes of angle of attack (AOA) and angle of sideslip (AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight. In this paper, a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate, which eliminates the adverse effects caused by the saturation. Finally, it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller. Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values. The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm. Compared with Robust Gain-Scheduling Control method, the robustness to the engine parameters are greatly improved and the control variable is smoother. [ABSTRACT FROM AUTHOR]

This paper focuses on the trajectory planning and trajectory tracking control of articulated tracked vehicles (ATVs). It utilizes the path planning method based on the Hybrid A-star and the minimum snap smoothing method to obtain the feasible kinematic trajectory. To overcome the highly non-linearity of ATVs, we proposed a linear-parameter-varying (LPV) kinematic tracking-error model. Then, the kinematic controller was formulated as the adaptive model predictive controller (AMPC). The simulation of the path planning algorithm showed that the proposed planning strategy could provide a feasible trajectory for the ATVs passing through the obstacles. Moreover, we compared the AMPC controller with the developed controller in four scenarios. The comparison showed that the AMPC controller achieved satisfactory tracking errors regarding the lateral position and orientation angle errors. The maximum lateral distance error by the AMPC controller has been reduced by 72.4% compared to the standard-MPC controller. The maximum orientation angle error has been reduced by 55.53%. The simulation results confirmed that the proposed trajectory planning and tracking control system could effectively perform the automated driving behaviors for ATVs. [ABSTRACT FROM AUTHOR]

With the in-depth development of high-tech industries, especially in the fields of production, manufacturing, aviation, and medical care, most of the work needs to be accomplished with the help of machines. As a high-tech product, a robotic arm plays an irreplaceable role in high-risk and high-precision engineering, such as arc welding, spraying, and assembly. At the same time, with the increasing requirements of scientific and technological production processes, robotic arm tasks are becoming increasingly complicated. Robotic arm trajectory tracking control in industry also has increasingly higher standards. Furthermore, external interference sources invariably affect the robotic arm control system when it is in operation. Therefore, existing manipulator control systems can no longer meet the requirements of industrial production. This paper aims to realize the tracking control of the trajectory of a robotic arm through a neural network algorithm. This research offers an adaptive neural network control method to solve the manipulator trajectory tracking control problem. To increase the control effect and overall performance of the manipulator, a neural network is employed to address the uncertainty in the control system as well as the interference of external elements. Experiments reveal that a neural network-based manipulator trajectory control and tracking system can effectively regulate the manipulator's operation and improve its overall performance. [ABSTRACT FROM AUTHOR]

This paper develops a reinforcement learning (RL)‐based optimal trajectory tracking control scheme of surface vessels with unknown dynamics, unknown disturbances, and input saturations of surface vessels. The control scheme is designed by combining the optimal control theory, adaptive neural networks, and the RL method in a unified actor‐critic NN framework. A hyperbolic‐type penalty function of the control input is designed so as to deal with the input saturations of surface vessels. An actor‐critic NN‐based RL mechanism is established to learn the optimal trajectory tracking control law without the knowledge of the surface vessel dynamics and disturbances, where NN weights are tuned online on the basis of devised tuning laws. Theoretical analysis and simulation results prove that the proposed RL‐based optimal trajectory tracking control scheme can ensure surface vessels track the desired trajectory, while guaranteeing the boundedness of all signals in the surface vessel optimal trajectory tracking closed‐loop control system. [ABSTRACT FROM AUTHOR]

This paper discusses the robust trajectory tracking control of an autonomous tractor-trailer in agricultural applications. Firstly, considering the model parameter uncertainties and various disturbances, the kinematic and dynamic models of the autonomous tractor-trailer system are established. Moreover, the coordinate transformation is adopted to convert the trajectory tracking error into a new unconstrained error state space model. On this basis, the prescribed performance control (PPC) technique is designed to ensure the convergence speed and final tracking control accuracy of the tractor-trailer control system. Then, this paper designs a double closed-loop control structure. The posture control level adopts the model predictive control (MPC) method, and the dynamic level adopts the sliding mode control (SMC) method. At the same time, it is worth mentioning that the nonlinear disturbance observer (NDO) is designed to estimate all kinds of system disturbances and compensate for the tracking control system to improve the system's robustness. Finally, the proposed control strategy is validated through comparative simulations, demonstrating its effectiveness in achieving robust trajectory tracking of the autonomous tractor-trailer system. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The dynamics model of the unmanned underwater vehicle (UUV) system is highly nonlinear, multi-degree-of-freedom, strongly coupled, and time-varying. Its motion control has been a complex problem due to the unknown information about and the uncertainty of the working environment. To improve the performance and reliability of UUV trajectory tracking control, a trajectory tracking method based on nonlinear model predictive control is designed, and an improved gray wolf optimization (IGWO) is proposed for the optimization of nonlinear model predictive control. The convergence factor of IGWO is designed as a nonlinear attenuation function, and the memory function is added to the position update equation to enhance the effect of trajectory tracking control. Through the simulation in the ROS environment, the influence of the convergence factor on the convergence rate of trajectory tracking error and tracking control performance is obtained. By comparing the tracking effects of several groups of reference trajectories, it is shown that the proposed method is universally applicable and effective to the trajectory tracking control of UUV. Compared with traditional gray wolf optimization (GWO), SQP, and other optimization algorithms, the reliability of the proposed method for UUV trajectory tracking control is demonstrated. [ABSTRACT FROM AUTHOR]

Trajectory tracking is a fundamental task of the dynamic positioning (DP) system. This paper studies the problem of trajectory tracking of DP ships constrained by control inputs under environmental disturbances. To solve this problem, we develop a novel anti-disturbance Lyapunov-based model predictive control (ADLMPC) scheme. Firstly, an extended state observer (ESO) is designed to estimate environmental disturbances. By combining the ESO with Lyapunov-based model predictive control, the ADLMPC scheme is devised. Secondly, a virtual controller which satisfies input constraints is developed by backstepping and the auxiliary dynamic system, and it is integrated into the Lyapunov contraction constraint in ADLMPC. We show that if the parameters for the virtual controller are appropriately determined, the recursive feasibility of ADLMPC is theoretically guaranteed, and the uniform ultimate boundedness of all signals in the trajectory tracking control system is achieved. Finally, the simulation results display the efficacy and superiorities of the ADLMPC scheme. [ABSTRACT FROM AUTHOR]

Trajectory tracking is a critical problem in the field of mobile robotics. In this paper, a control scheme combined with backstepping and fractional-order PID is developed for the trajectory tracking of the differential-drive mobile robot. The kinematic and dynamic models of the mobile robot are described in detail for the trajectory tracking controller design. Then, based on the model of the mobile robot, the design of the trajectory tracking control system is addressed by combining backstepping with fractional-order PID. Moreover, to obtain an optimal control system, an improved beetle swarm optimization algorithm is presented to tune the parameters of the kinematic and dynamic controllers simultaneously. Finally, several simulations are implemented to the trajectory tracking of mobile robots in the cases with and without skidding and sliding, and the results can confirm the effectiveness and superiority of the combined control scheme. Abbreviations: FOPID: fractional-order PID; FOPD: fractional-order PD; DDMR:differential-drive mobile robot; BAS: beetle antennae search; BA: beetle antennae; PSO:particle swarm optimization; BSO: beetle swarm optimization. [ABSTRACT FROM AUTHOR]

This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS)method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on anMSV verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In the field of automated technology research and development, trajectory tracking plays a crucial role in the energy consumption of the vehicle's power battery. Reducing the deviation between the actual trajectory and the reference trajectory is the focus of trajectory tracking research. This paper proposes the use of the model predictive control (MPC) method to reduce the deviation of lateral and longitudinal position between the actual driving trajectory and the reference trajectory. First, the driving conditions of the vehicle are reflected by establishing the vehicle dynamics model. Then, the MPC trajectory tracking controller is built by designing the objective function with constraints; Finally, the feasibility of this approach was verified by a joint Carsim-Simulink simulation. The simulation results show that the MPC controller designed in this paper can track the trajectory better, and reduce the lateral and longitudinal position deviation. To a certain extent, the battery energy consumption is reduced and the accuracy of the tracking trajectory and the safety of vehicle driving are improved. [ABSTRACT FROM AUTHOR]

Multi‐degree‐of‐freedom permanent magnet spherical actuators (PMSAs) are highly nonlinear, coupled, and multivariable systems that are subject to different types of disturbances including unknown payloads, unmodelled dynamics, frictions, and other external disturbances, which adversely affect the trajectory tracking performance of a system. In this paper, a disturbance‐observer‐based continuous non‐singular terminal sliding‐mode control (NDOB‐CNTSMC) strategy is developed for a PMSA to enhance its trajectory tracking performance. Firstly, a nonlinear disturbance observer (NDOB) with a parameter design method is proposed to suppress uncertainty and reject disturbance in a PMSA trajectory tracking control system. Secondly, a continuous non‐singular terminal sliding‐mode controller (CNTSMC) is presented to compensate for the effect of the disturbance observation error and unobservable disturbances. The stability of the proposed control strategy is proved by the Lyapunov theorem. Both simulation and experimental results have shown that the control strategy proposed in this research can effectively address the issues of the inaccuracy of modelling and various disturbances and improve the trajectory tracking precision of the PMSA. [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]

To maintain the vibrations of the gyroscope proof mass, a trajectory tracking control system using a neural network estimator is proposed. The proposed control system incorporates a fractional controller based on the terminal sliding-mode and a recurrent Chebyshev fuzzy neural network using a self-evolving mechanism. The fractional-order terminal sliding-mode control can guarantee the tracking error exponential stable, and a self-evolving recurrent Chebyshev fuzzy neural network (SERCFNN) is introduced to relax the requirement of nonlinear functional certainty. In addition, the SERCFNN develops the advantages of the self-evolving fuzzy neural network (SEFNN), recurrent fuzzy neural network (RFNN), and Chebyshev function network (CFN). The SEFNN can adaptively update the dynamic structure through generating and adjusting fuzzy logic rules. The RFNN improves the performance for coping with a temporal problem with the capability to store prior information. The CFN is capable to enlarge the dimensionality of the input variables. Moreover, the asymptotic stability of the proposed control system can be proved by the Lyapunov stability theory. The effectiveness and superiority of the performance are exhibited with simulation studies and comprehensive comparisons. [ABSTRACT FROM AUTHOR]

This paper addresses trajectory planning and control for a dual-arm free-floating space robot (FFSR) based on predefinedtime stability. Firstly, a class of general nonsingular terminal sliding mode control strategy is proposed to achieve global predefined-time stability by switching a control parameter in a form of function. Then, a high-precision trajectory planning method is proposed for a FFSR using the proposed predefined-time stability theorem, which can make the end-effector and the base reach the desired pose within a prespecified time, and reduce the adverse effect on planning accuracy resulted from the singularity avoidance algorithm and the obstacle avoidance one. Subsequently, a trajectory tracking control strategy is proposed for a FFSR employing the proposed general nonsingular predefined-time terminal sliding mode, and the tracking errors can converge within a predefined time to an arbitrarily small neighborhood of zero in the presence of persistent disturbances. The proposed trajectory planning method has the advantage of pose feedback, so can be combined with the trajectory tracking controller in the control process to further enhance the control performance for the FFSR. Simulation results validate the effectiveness of the proposed methodologies. [ABSTRACT FROM AUTHOR]

Autonomous ground vehicles (AGVs) are receiving increasing attention, and the motion planning and control problem for these vehicles has become a hot research topic. In real applications such as material handling, an AGV is subject to large uncertainties and its motion planning and control become challenging. In this article, we investigate this problem by proposing a hierarchical control scheme, which is integrated by a model predictive control (MPC)-based path planning and trajectory tracking control at the high level, and a reduced-order extended state observer (RESO)-based dynamic control at the low level. The control at the high level consists of an MPC-based improved path planner, a velocity planner, and an MPC-based tracking controller. Both the path planning and trajectory tracking control problems are formulated under an MPC framework. The control at the low level employs the idea of active disturbance rejection control (ADRC). The uncertainties are estimated via a RESO and then compensated in the control in real time. We show that, for the first-order uncertain AGV dynamic model, the RESO-based control only needs to know the control direction. Finally, simulations and experiments on an AGV with different payloads are conducted. The results illustrate that the proposed hierarchical control scheme achieves satisfactory motion planning and control performance with large uncertainties. [ABSTRACT FROM AUTHOR]

To improve the accuracy of tracking the trunk center-of-mass (CoM) trajectory and foot-end trajectory in a fully electrically driven quadruped robot, an efficient and practical new trajectory tracking control method is designed. The proposed trajectory tracking method is mainly divided into trunk balance controller (TBC) and swing leg controller (SLC). In TBC, a quadruped robot dynamics model is developed to find the optimal foot-end force that follows the trunk CoM trajectory based on the model predictive control (MPC) principle. In SLC, the Bessel curve is planned as the desired trajectory at the foot-end, while the desired trajectory is tracked by a virtual spring-damping element driving the foot-end, meanwhile, the radial basis function neural network (RBFNN) is applied for supervisory control to improve the control performance for the system. The experimental results show that the control method can modify the robot's foot-end trajectory tracking effect, so that the stability error can be eliminated and the robustness of the controller can be improved, meanwhile, the linear and circular trajectory for CoM can be tracked accurately and quickly. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive backstepping sliding mode control (ABSMC) scheme for autonomous underwater vehicles (AUVs) subject to the dynamic uncertainty, external disturbance and quantization error. The control input signals including control forces and moment are quantized by a hybrid quantizer which is the combinination of a logarithmic quantizer and a uniform quantizer. The kinematic controller is designed by the backstepping control technique and the dynamic controller is developed using the sliding mode control method. In order to further improve the robustness of the closed‐loop system, an adaptive law is employed to estimate the upper bound of the total uncertainties in real time. The stability of the closed‐loop system is proved based on the Lyapunov theory and indicates that the proposed control method can force the AUV to track the desired trajectory. Simulation results demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, S E (3) . We formulate a finite-time stable (FTS) tracking control scheme for this underactuated system in discrete time. This scheme is based on our recently developed theory for finite-time stability for discrete-time systems using discrete Lyapunov analysis. The proposed scheme here is developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. This scheme guarantees a stable convergence of translational and rotational tracking errors to the desired trajectory in finite time. Furthermore, the advantages of finite-time stabilisation in discrete-time over finite-time stabilisation of a sampled continuous-time tracking control system is addressed here through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned aerial vehicle model. [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]

An underactuated unmanned surface vessel (USV) is a nonholonomic system, in which trajectory tracking is a challenging problem that has drawn more and more attention from researchers recently. The control of trajectory tracking is of critical importance since it determines whether the task can be carried out successfully. In this paper, a non-singular terminal sliding model (NTSM) controller is proposed for the trajectory tracking control of the underactuated USV, with a nonlinear disturbance observer which is designed to measure complex environmental disturbances such as wind, waves, and currents. Exploratory simulations were carried out and the results show that the proposed controller is effective and robust for the trajectory tracking of underactuated USVs in the presence of environmental disturbances. [ABSTRACT FROM AUTHOR]

This work proposes a new kind of trajectory tracking controller for the differential drive mobile robot (DDMR), namely, the nonlinear neural network fractional-order proportional integral derivative (NNFOPID) controller. The suggested controller's coefficients comprise integral, proportional, and derivative gains as well as derivative and integral powers. The adjustment of these coefficients turns the design of the proposed NNFOPID control further problematic than the conventional proportional-integral-derivative control. To handle this issue, an Enhanced Fruit Fly Swarm Optimization algorithm has been developed and proposed in this work to tune the NNFOPID's parameters. The enhancement achieved on the standard fruit fly optimization technique lies in the increased uncertainty in the values of the initialized coefficients to convey a broader search space. subsequently, the search range is varied throughout the updating stage by beginning with a big radius and declines gradually during the course of the searching stage. The proposed NNFOPID controller has been validated its ability to track specific three types of continuous trajectories (circle, line, and lemniscate) while minimizing the mean square error and the control energy. Demonstrations have been run under MATLAB environment and revealed the practicality of the designed NNFOPID motion controller, where its performance has been compared with that of a nonlinear Neural Network Proportional Integral Derivative controller on the tracking of one of the aforementioned trajectories of the DDMR. [ABSTRACT FROM AUTHOR]

The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out. [ABSTRACT FROM AUTHOR]

Copyright of Journal of East China University of Science & Technology is the property of Journal of East China University of Science & Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Realisation of high-precision trajectory tracking is the key technology to achieve unmanned driving, which has an important impact on vehicle handling stability, safety and comfort. However, many confounding factors seriously restrict tracking performance and pose a great challenge to the design of the controller for tracking the desired trajectory. A comprehensive method that combines feedforward and backstepping sliding mode control is proposed for a four-wheel independent driving–four-wheel independent steering (4WID-4WIS) vehicle, which has the advantages of over-coupling, multiple degrees of freedom and flexible operation. The desired value is the target for the feedforward output of the controller, and the backstepping sliding mode control is used to overcome all kinds of disturbances. A mature and reliable Luenberger observer is designed to achieve good trajectory tracking performance for reducing some sensors. The proposed method is verified via MATLAB/Simulink simulation, which proved that the method has an excellent trajectory tracking performance. [ABSTRACT FROM AUTHOR]

This paper investigates concentrates on the trajectory tracking control problem of dynamic positioning (DP) ship, in the presence of the time-varying disturbance and input saturation. Firstly, a simplified mathematical model of three degrees of freedom is established. According to the characteristics of the DP ship, an adaptive backstepping controller which combine the prescribed performance function with disturbance observer is proposed. The control scheme can guarantee the transient and steady state performance of the trajectory tracking and meet the prescribed performance criteria. In addition, an auxiliary dynamic system is introduced into the controller to deal with the input saturation problem of the actuator, so that the DP ship can accomplish the task of trajectory tracking under the condition of actuator constraint. Subsequently, in combination of barrier Lyapunov function (BLF), it is proved that the DP system can stabilize and converge rapidly to the small neighborhood of the equilibrium point, which can achieve the prescribed performance. Finally, the effectiveness of the DP control law is demonstrated by a series of simulation experiments. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low control precision and poor anti-disturbances ability of permanent magnet spherical actuator (PMSA), an active disturbance rejection trajectory tracking control method based on nonlinear extended state observer (NESO) is proposed in this paper. Firstly, the multivariable and strong coupling mathematical model of the PMSA is obtained by rigid body rotation coordinate transformation and the Lagrange dynamic equation. Then, the tracking differentiator is used to reduce the influence caused by the expected trajectory jump. In addition, NESO is designed to observe and calculate coupling of the system, external disturbance, and model error online. Finally, the nonlinear control law is used to compensate for the observed disturbance, and the stability is proved based on the Lyapunov equation. Simulation and experimental results show that the proposed control scheme can achieve decoupling and tracking control of the complex system in the presence of model error, random disturbance, and other uncertain factors, has good control accuracy and response speed, and has strong robustness to uncertain disturbances. [ABSTRACT FROM AUTHOR]

This paper proposed a novel disturbance observer‐based control state‐error port‐controlled Hamiltonian (DOBC‐SEPCH) control strategy for optimization of energy consumption and enhancement of tracking performance for unmanned surface vehicle (USV) with unknown environmental disturbances via the PCH system techniques. Firstly, an observer is constructed to estimate disturbances. Then, an energy‐based controller is constructed by using the SEPCH system method. In addition, the SEPCH controller provided that the tracking errors converged exponentially to zero. The SEPCH technique is augmented by a disturbance observer. Due to the controller need to be designed in two stages, the stability of the whole system will be difficult to be discussed. We give the proof of the stability of the desired target dynamic system. The robustness and control performance of the system are enhanced. The simulation and comparison results illustrate the performance of this controller. [ABSTRACT FROM AUTHOR]

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This research presents an adaptive energy-saving H2 closed-form control approach to solve the nonlinear trajectory tracking problem of autonomous mobile robots (AMRs). The main contributions of this proposed design are as follows: closed-form approach, simple structure of the control law, easy implementation, and energy savings through trajectory tracking design of the controlled AMRs. It is difficult to mathematically obtained this adaptive H2 closed-form solution of AMRs. Therefore, through a series of mathematical analyses of the trajectory tracking error dynamics of the controlled AMRs, the trajectory tracking problem of AMRs can be transformed directly into a solvable problem, and an adaptive nonlinear optimal controller, which has an extremely simple form and energy-saving properties, can be found. Finally, two test trajectories, namely circular and S-shaped reference trajectories, are adopted to verify the control performance of the proposed adaptive H2 closed-form control approach with respect to an investigated H2 closed-form control design. [ABSTRACT FROM AUTHOR]

This article investigates the postcapture control problem for the combined spacecraft formed after a service spacecraft captures a noncooperative target by manipulators. Two concurrent learning adaptive finite-time controllers are developed to achieve trajectory tracking and inertia parameter identification simultaneously. As a very common uncertainty affecting the spacecraft motion, the external disturbance should be considered, but it is ignored in most studies identifying inertia parameters. In this article, the presented controllers are designed according to the specific knowledge of the external disturbance: one controller is designed based on the disturbance bound that is assumed to be known; the other identifies the disturbance parameters together with the inertia parameters, presupposing that the nonlinearities involved in the external disturbance are known. Both of the two controllers require no a priori knowledge of the mass and inertia matrix of the combined spacecraft and take the input saturation into account. Sufficient conditions to identify inertia parameters are also given with no need of persistent excitation. The convergence of the closed-loop system is proved within the Lyapunov framework. Numerical results show that the proposed controllers can track the desired position and attitude trajectories in finite time, and, at the same time, the inertia parameters converge to their real values. [ABSTRACT FROM AUTHOR]

In this article, the eye-in-hand visual trajectory tracking control problem of wheeled mobile robots (WMRs) is considered. Different from the conventional vision-based approaches, the monocular camera is not required to be mounted at the center of WMR, and thus the derived visual model is subject to not only the nonholonomic constraint but also the unknown camera extrinsic parameters. To ensure the WMR can track a desired trajectory effectively, a combined observation/control strategy is proposed. First, a concurrent learning observer is designed to identify the camera extrinsic parameters with measurable visual signals. Then, with the aid of the estimated parameters, a nonlinear controller is presented to achieve the tracking task. The closed-loop system stability is analyzed with Lyapunov methods, showing that both the estimation and tracking errors are asymptotically convergent to zero. Simulation and experimental results are provided to validate the developed approach. [ABSTRACT FROM AUTHOR]

This article mainly investigates the problem of tracking the flight trajectory for a quadrotor aircraft with uncertain parameters and external disturbances. Combined with the model structure, the quadrotor aircraft system can be divided into position system and attitude system. Firstly, for the position system with unknown parameters, some adaptive finite‐time position tracking controllers are designed based on the homogeneous system theory and finite‐time parameter estimators. For the attitude system, the uncertain parameters and external disturbances are regarded as lumped disturbances. Based on the homogeneous system theory and sliding‐mode observers, some adaptive finite‐time attitude controllers are proposed. Finally, some numerical simulation results are given to verify the control performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The problem of trajectory tracking control for a blended-wing-body (BWB) large aircraft with model parameter uncertainties and unknown disturbances is considered. A linear parameter-varying (LPV) model is derived from the nonlinear dynamics of the BWB aircraft from which a robust linear parameter-varying controller is designed to track a desired trajectory. Using a single quadratic Lyapunov function (SQLF) and an infinite number of linear matrix inequalities to be evaluated at all vertices, a pair of positive definite symmetric matrix solutions are determined via Lyapunov stability theory and linear matrix inequality technique. Furthermore, a disturbance-observer is designed to process the unknown disturbances. Considering the plant exists some model errors except for disturbances, a radial basis function neural network approximation is embedded into the SQLF LPV controller to improve tracking performances, and a composite disturbance-observer based neural network single quadratic Lyapunov function (NNSQLF) controller can realize desired trajectory tracking of the linear parameter-varying system through regulating performance weighting functions. The closed-loop system of trajectory tracking control is proved to be asymptotically stable by using Lyapunov theory. Simulation results of forward flight speed and altitude tracking control of the BWB aircraft show that the proposed disturbance-observer based NNSQLF control can robustly stabilize the LPV system and precisely track the desired trajectory by comparing with conventional SQLF control and parameter-dependent Lyapunov function control, even in unknown exterior disturbances and model uncertainties. [ABSTRACT FROM AUTHOR]

This paper proposes the impact of the Dynamic model in Input-Output State Feedback Linearization (IO-SFL) technique for trajectory tracking of differential drive mobile robots, which has been restricted to using just the kinematics in most of the previous approaches. To simplify the control problem, this paper develops a novel control approach based on the velocity and position control strategy. To improve the results, the dynamics are taken into account. The objective of this paper is to illustrate the flaws unseen when adopting the kinematics-only controllers because the nonlinear kinematic model will suffice for control design only when the inner velocity (dynamic) loop is faster than the slower outer control loop. This is a big concern when using kinematic controllers to robots that don't have a low-level controller, Arduino robots for example. The control approach is verified using the Lyapunov stability analysis. MATLAB/SIMULINK is carried out to determine the impact of the proposed controller for the trajectory tracking problem, from the simulation, it was discovered that the proposed controller has an excellent dynamic characteristic, simple, rapid response, stable capability for trajectory-tracking, and ignorable tracking error. A comparison between the presence and absence of the dynamic model shows the error in tracking due to dynamic system that must be taken into account if our system doesn't come with a built-in one, thus, confirming the superiority of the proposed approach in terms of precision, with a neglectable difference in computations. [ABSTRACT FROM AUTHOR]

A stabilization control can be used to maintain the position and attitude of the ship, mooring manipulation, and tracking control can force ships to enter the preplanned route from any initial position and finally reach the destination along the route. In this article, both the prespecifiable fixed-time stabilization control and adaptive trajectory tracking control are considered for a kind of fully actuated ocean surface ship under output constraints. Barrier Lyapunov function (BLF) is utilized to remedy with the output limitation constraints. By combining the fixed-time control and switching techniques, and choosing the appropriate symmetric Lyapunov function, the control algorithm of fixed-time stabilization is designed guaranteeing that the closed-loop system state trajectories tend to zero in a fixed time and meanwhile not going beyond the preset operating range in the control process. The adaptive tracking control law is proposed by using the asymmetric BLF and adaptive control technologies. Under the adaptive controller, the output constraints are also achieved, and the tracking errors are adaptively converge to steady zero states, respectively, while keeping all the signals bounded in the control process. The simulations are carried out to demonstrate the effectiveness of the presented control methods. [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]

In this article, a novel robust observer-based nonlinear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based nonlinear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness. [ABSTRACT FROM AUTHOR]

In this paper, we develop a hybrid iterative learning controller (HILC) for a non-holonomic wheeled mobile platform to achieve trajectory tracking with actual complex constraints, such as physical constraints, uncertain parameters, and initial errors. Unlike the traditional iterative learning controller (ILC), the control variable selects the rotation speed of two driving wheels instead of the forward speed and the rotation speed. The hybrid controller considers the physical constraints of the robot's motors and can effectively handle the uncertain parameters and initial errors of the system. Without the initial errors, the hybrid controller can improve the convergence speed for trajectory tracking by adding other types of error signals; otherwise, the hybrid controller achieves trajectory tracking by designing a signal compensation for the initial errors. Then, the effectiveness of the proposed hybrid controller is proven by the relationship between the input, output, and status signals. Finally, the simulations demonstrate that the proposed hybrid iterative learning controller effectively tracked various trajectories by directly controlling the two driving wheels under various constraints. Furthermore, the results show that the controller did not significantly depend on the system's structural parameters. [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]