Adaptive recursive sliding mode based trajectory tracking control for cable-driven continuum robots

To improve the transient response, accuracy and robustness of trajectory tracking control for cable-driven continuum robots (CDCRs), a recursive integral terminal sliding mode control combined with an adaptive disturbance observer (ADO-RITSMC) is proposed. The recursive integral terminal sliding mode control (RITSMC) guarantees fast transient response and high tracking accuracy with a fast zero convergence of the tracking error without chattering. To attenuate the effect of uncertain dynamics, an adaptive disturbance observer (ADO) is constructed to derive uncertain dynamics. Particularly, an improved grey wolf optimizer (IGWO) is merged into the ADO to enhance the estimating accuracy of uncertain dynamic factors. Simulation and experiment results demonstrate the superiority of the ADO-RITSMC in enabling fast transient response, high accuracy and strong robustness of trajectory tracking control.

Observer-based finite-time control for trajectory tracking of wheeled mobile robots with kinematic disturbances

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

Multi-stage trajectory tracking of robot manipulators under stochastic environments

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

Adaptive control of a nonaffine nonlinear system using self-organising kernel extreme learning machine

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

Modeling of PID controlled 3DOF robotic manipulator using Lyapunov function for enhancing trajectory tracking and robustness exploiting Golden Jackal algorithm

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

Finite-time adaptive super-twisting sliding mode control for autonomous robotic manipulators with actuator faults

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study.

Unlocking the Potential of Zebrafish Research with Artificial Intelligence: Advancements in Tracking, Processing, and Visualization

Zebrafish have become a widely accepted model organism for biomedical research due to their strong cortisol stress response, behavioral strain differences, and sensitivity to both drug treatments and predators. However, experimental zebrafish studies generate substantial data that must be analyzed through objective, accurate, and repeatable analysis methods. Recently, advancements in artificial intelligence (AI) have enabled automated tracking, image recognition, and data analysis, leading to more efficient and insightful investigations. In this review, we examine key AI applications in zebrafish research, including behavior analysis, genomics, and neuroscience. With the development of deep learning technology, AI algorithms have been used to precisely analyze and identify images of zebrafish, enabling automated testing and analysis. By applying AI algorithms in genomics research, researchers have elucidated the relationship between genes and biology, providing a better basis for the development of disease treatments and gene therapies. Additionally, the development of more effective neuroscience tools could help researchers better understand the complex neural networks in the zebrafish brain. In the future, further advancements in AI technology are expected to enable more extensive and in-depth medical research applications in zebrafish, improving our understanding of this important animal model. This review highlights the potential of AI technology in achieving the full potential of zebrafish research by enabling researchers to efficiently track, process, and visualize the outcomes of their experiments.

Robust adaptive three-dimensional trajectory tracking control scheme design for small fixed-wing UAVs

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

Neural network-based adaptive second-order sliding mode control for uncertain manipulator systems with input saturation

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

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

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

Disturbance observer-based prescribed performance super-twisting sliding mode control for autonomous surface vessels

This paper proposes a disturbance observer-based prescribed performance super-twisting sliding mode control (DOB PPSTSMC) for trajectory tracking of the autonomous surface vessels (ASVs) subject to unknown external disturbances and modeling errors. Both unknown external disturbances and system modeling errors are approximated by the disturbance observer, thus eliminating most of the effect caused by lumped disturbances in the control performance. Based on this, a prescribed performance super-twisting sliding mode controller is explored to further suppress the residual error of disturbance compensation. Prescribed performance constraints are considered in the coming up with the super-twisting sliding mode controller, so that ASVs not only achieve effective tracking of time-varying desired trajectories, but also improve the transient performance of the control system. In addition, the controller is continuous and chatter-free, which has greater practical value. The excellence of the control project design is highlighted through the simulation and comparison results.

EMPC with adaptive APF of obstacle avoidance and trajectory tracking for autonomous electric vehicles

In this paper, event-triggered model predictive control (EMPC) with adaptive artificial potential field (APF) is designed to realize obstacle avoidance and trajectory tracking for autonomous electric vehicles. An adaptive APF cost function is added to achieve obstacle avoidance and guarantee stability. The optimization problem for MPC is feasible by considering a special obstacle avoidance constraint. An event-triggered mechanism is proposed to reduce computational burden and ensure effectiveness of obstacle avoidance. Input and state constraints of autonomous electric vehicles are considered in both feasibility and stability by a robust terminal set. Effectiveness of both obstacle avoidance and trajectory tracking is shown by experimental results on autonomous electric vehicles.

Determination of trajectories using IKZ/CF inertial navigation: Methodological proposal

Nowadays, there are different methods used in the autonomous navigation task; current solutions include inertial navigation systems (INS). However, these systems present drift errors that are attenuated by the integration of absolute reference systems such as GPS, and antennas, among others. Consequently, few works concentrate efforts on developing a methodology to reduce drift errors in INS due to the widespread practice of incorporating absolute references into their systems. However, absolute references must be placed beforehand, which is not always possible. This work presents an improvement on our methodological proposal IKZ for tracking and localization of moving objects by integrating a complementary filter (CF). The main contribution of this paper is the methodological proposal in the integration between IKZ and CF, maintaining the restrictive properties to the drift error and significantly improving the handling characteristics of the system in real applications. Furthermore, the IKZ/CF was tested with raw data from an MPU-9255 in order to analyze the results between tests.

Optimal adaptive barrier-function super-twisting nonlinear global sliding mode scheme for trajectory tracking of parallel robots

Compared to serial robots, parallel robots have potential superiorities in rigidity, accuracy, and ability to carry heavy loads. On the other hand, the existence of complex dynamics and uncertainties makes the accurate control of parallel robots challenging. This work proposes an optimal adaptive barrier-function-based super-twisting sliding mode control scheme based on genetic algorithms and global nonlinear sliding surface for the trajectory tracking control of parallel robots with highly-complex dynamics in the presence of uncertainties and external disturbances. The globality of the proposed controller guarantees the elimination of the reaching phase and the existence of the sliding mode around the surface right from the initial instance. Moreover, the barrier-function based adaptation law removes the requirement to know the upper bounds of the external disturbances, thus making it more suitable for practical implementations. The performance and efficiency of the controller is assessed using simulation study of a Stewart manipulator and an experimental evaluation on a 5-bar parallel robot. The obtained results were further compared to that of a six-channel PID controller and an adaptive sliding mode control method. The obtained results confirmed the superior tracking performance and robustness of the proposed approach.

Global fixed-time trajectory tracking control of underactuated USV based on fixed-time extended state observer

This paper studies the trajectory tracking problem of unmanned surface vehicle subject to unmeasurable velocities and unknown disturbances. By combining a fixed-time extended state observer (FESO) and a fixed-time differentiator, a fixed-time sliding mode control (FTSMC) law is proposed, in which a saturation function is adopted to make the terminal sliding mode surface leave the singularity area. The value of this paper can be described: first, this paper designs a novel guidance law that can converge in a fixed time to reduce the convergence time of the error. Then, unmeasurable velocities and lumped disturbances are estimated by applying a FESO. Meanwhile, a fixed-time differentiator is used to obtain real-time differential signals, thus reducing the difficulty of controller design. Subsequently, a novel auxiliary dynamic system is designed to address actuator saturation. According to Lyapunov's theory, the entire closed-loop control system has uniformly global fixed-time stability (UGFTS). The superiority of the designed controller is demonstrated through numerical simulations.

3D High-Resolution Modeling of Aircraft-Induced NO x Emission Dispersion in CAEPport Configuration Using Landing and Take-Off Trajectory Tracking

Pollutant emissions from aircraft operations contribute to the degradation of air quality in and around airports. Meeting the ICAO's environmental certification standards regarding both gaseous and particulate aircraft engine emissions is one of the main challenges for air-transportation development over the coming years. To increase the accuracy of airport air pollution monitoring and prediction, advanced decision-making tools need to be developed. In this context, the present study aimed at demonstrating the modeling capabilities of an innovative methodology that accounts for the microscale evolution of aircraft emissions, both spatially and temporally. For this purpose, 3D high-resolution CFD simulations were carried out in the CAEPport configuration (medium-size mock airport) as defined by the Committee on Aviation Environmental Protection (CAEP/8) for local air-quality assessment. The modeled domain extends up to 8 km around the airport. A spatial resolution down to 1 m was used around buildings to refine the prediction of pollutant-emission concentrations. The model accounts for ambient meteorological conditions along with the background chemical composition. NO _x emissions from main engines and auxiliary power units (APUs) were individually tracked along LTO trajectories with a time resolution down to 1 s. The impact of atmospheric stability was investigated in three cases, i.e., stable, neutral, and unstable. The results show NO₂ dominating in apron areas due to the low power setting of main engines along APU contribution during extended parking. Conversely, a domination of NO emissions was observed at the runway threshold due to the high power setting of the main engines. Stable atmospheric conditions promoted higher NO and NO₂ concentrations as compared to both neutral and unstable cases. The use of APUs contributed to higher concentrations of both NO and NO₂ emissions and especially of NO₂ in terminal areas.

Practical fixed-time trajectory tracking control of constrained wheeled mobile robots with kinematic disturbances

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

Output feedback based adaptive composite nonlinear flight control design for a small-scale un-crewed helicopter

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.

Robust cooperative trajectory tracking control for an unactuated floating object with multiple vessels system

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.

Neural network for 3D trajectory tracking control of a CMG-actuated underwater vehicle with input saturation

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

Composite learning tracking control for underactuated marine surface vessels with output constraints

In this paper, a composite learning control scheme was proposed for underactuated marine surface vessels (MSVs) subject to unknown dynamics, time-varying external disturbances and output constraints. Based on the line-of-sight (LOS) approach, the underactuation problem of the MSVs was addressed. To deal with the problem of output constraint, the barrier Lyapunov function-based method was utilized to ensure that the output error will never violate the constraint. The composite neural networks (NNs) are employed to approximate unknown dynamics. The prediction errors can be obtained using the serial-parallel estimation model (SPEM). Both the prediction errors and the tracking errors were employed to construct the NN weight updating. Using approximation information, the disturbance observers were designed to estimate unknown time-varying disturbances. The stability analysis via the Lyapunov approach indicates that all signals of unmanned marine surface vessels are uniformly ultimate boundedness. The simulation results verify the effectiveness of the proposed control scheme.

Kinematic and dynamic control model of wheeled mobile robot under internet of things and neural network

This study aims to solve the issues of nonlinearity, non-integrity constraints, under-actuated systems in mobile robots. The wheeled robot is selected as the research object, and a kinematic and dynamic control model based on Internet of Things (IoT) and neural network is proposed. With the help of IoT sensors, the proposed model can realize effective control of the mobile robot under the premise of ensuring safety using the model tracking scheme and the radial basis function adaptive control algorithm. The results show that the robot can be controlled effectively to break the speed and acceleration constraints using the strategy based on the model predictive control, thus realizing smooth movement under the premise of safety. The self-adapting algorithm based on the IoT and neural network shows notable advantages in parameter uncertainty and roller skidding well. The proposed model algorithm shows a fast convergence rate of about 2 s, which has effectively improved performances in trajectory tracking and robustness of the wheeled mobile robot, and can solve the difficulties of wheeled mobile robots in practical applications, showing reliable reference value for algorithm research in this field.

Robust forward\backward control of wheeled mobile robots

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.

Trajectory tracking of a quadrotor using a robust adaptive type-2 fuzzy neural controller optimized by cuckoo algorithm

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.

Robust adaptive PD-like control of lower limb rehabilitation robot based on human movement data

The combination of biomedical engineering and robotics engineering brings hope of rehabilitation to patients with lower limb movement disorders caused by diseases of the central nervous system. For the comfort during passive training, anti-interference and the convergence speed of tracking the desired trajectory, this paper analyzes human body movement mechanism and proposes a robust adaptive PD-like control of the lower limb exoskeleton robot based on healthy human gait data. In the case of bounded error perturbation, MATLAB simulation verifies that the proposed method can ensure the global stability by introducing an S-curve function to make the design robust adaptive PD-like control. This control strategy allows the lower limb rehabilitation robot to track the human gait trajectory obtained through the motion capture system more quickly, and avoids excessive initial output torque. Finally, the angle similarity function is used to objectively evaluate the human body for wearing the robot comfortably.

Trajectory tracking controller for unmanned helicopter under environmental disturbances

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

On the stability of ADRC for manipulators with modelling uncertainties

The Active Disturbance Rejection Control (ADRC) is an object of the ever growing interest in the latest years due to its limited requirements concerning knowledge of a plant's mathematical model. In this paper, a problem of system stability in presence of modelling uncertainties is investigated. Precisely, imperfect knowledge of the manipulator dynamics and an inertia matrix is considered by the means of the Lyapunov analysis and conditions are formulated which guarantees convergence of the errors in the system to some finite boundary. Influence of the unknown inertia matrix is thoroughly investigated. It is shown, that if the third derivative of the desired trajectory is small enough then an intentional increase of the input matrix estimation error may lead to a reduction of the tracking error boundary. Obtained results are supported by presented simulations and experiments.

Adaptive tracking control of an unmanned aerial system based on a dynamic neural-fuzzy disturbance estimator

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

Adaptive trajectory tracking control for remotely operated vehicles considering thruster dynamics and saturation constraints

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

Adaptive output-feedback control with prescribed performance for trajectory tracking of underactuated surface vessels

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

Fixed-time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties

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

Force and electromyography responses during isometric force release of different rates and step-down magnitudes

This study investigated motor responses of force release during isometric elbow flexion by comparing effects of different ramp durations and step-down magnitudes. Twelve right-handed participants (age: 23.1 ± 1.1) performed trajectory tracking tasks. Participants were instructed to release their force from the reference magnitude (REF; 40% of maximal voluntary contraction force) to a step-down magnitude of 67% REF or 33% REF and maintain the released magnitude. Force release was guided by ramp durations of either 1 s or 5 s. Electromyography of the biceps brachii and triceps brachii was performed during the experimental task, and the co-contraction ratio was evaluated. Force output was recorded to evaluate the parameters of motor performance, such as force variability and overshoot ratio. Although a longer ramp duration of 5 s decreased the force variability and overshoot ratio than did shorter ramp duration of 1 s, higher perceived exertion and co-contraction ratio were followed. Force variability was greater when force was released to the step-down magnitude of 33% REF than that when the magnitude was 67% REF, however, the overshoot ratio showed opposite results. This study provided evidence proving that motor control strategies adopted for force release were affected by both duration and step-down magnitude. In particular, it implies that different control strategies are required according to the level of step-down magnitude with a relatively short ramp duration.

Active nonlinear partial-state feedback control of contacting force for a pantograph-catenary system

In this paper, a nonlinear partial-state feedback control is designed for a 3-DOF pantograph-catenary system by using backstepping approach, such that the contacting force of the closed-loop system is capable of tracking its reference profile. In the control design, the pantograph-catenary model is transformed into a triangular form, facilitating the utilization of backstepping. Derivatives of virtual controls in backstepping are calculated explicitly. A high-order differentiator is designed to estimate the unknown time derivatives of elasticity coefficient; and an observer is proposed to reconstruct the unmeasurable states. It can be proved theoretically that, with the proposed nonlinear partial-state feedback control, the tracking error of the contacting force is ultimately bounded with tunable ultimate bounds. Theoretical results are demonstrated by numerical simulations.

Adaptive second-order fast nonsingular terminal sliding mode control for robotic manipulators

This paper presents an adaptive chattering-free sliding mode controller for trajectory tracking of robotic manipulators in the presence of external disturbances and inertia uncertainties. To achieve fast convergence and desirable tracking precision, a second-order fast nonsingular terminal sliding mode (SOFNTSM) controller is designed to guarantee system performance and robust stability. Chattering is eliminated using continuous control law due to high-frequency switching terms contained in the first derivative of actual control signals. Meanwhile, uncertainties are compensated by introducing the adaptive technique, whose prior knowledge about upper bound is not required. Finally, simulation results validate the effectiveness of the proposed control scheme.

Dynamic path planning and trajectory tracking using MPC for satellite with collision avoidance

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

Adaptive fixed-time trajectory tracking control of a stratospheric airship

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

On-line confidence monitoring during decision making

Humans can readily assess their degree of confidence in their decisions. Two models of confidence computation have been proposed: post hoc computation using post-decision variables and heuristics, versus online computation using continuous assessment of evidence throughout the decision-making process. Here, we arbitrate between these theories by continuously monitoring finger movements during a manual sequential decision-making task. Analysis of finger kinematics indicated that subjects kept separate online records of evidence and confidence: finger deviation continuously reflected the ongoing accumulation of evidence, whereas finger speed continuously reflected the momentary degree of confidence. Furthermore, end-of-trial finger speed predicted the post-decisional subjective confidence rating. These data indicate that confidence is computed on-line, throughout the decision process. Speed-confidence correlations were previously interpreted as a post-decision heuristics, whereby slow decisions decrease subjective confidence, but our results suggest an adaptive mechanism that involves the opposite causality: by slowing down when unconfident, participants gain time to improve their decisions.

Time-scaling based sliding mode control for Neuromuscular Electrical Stimulation under uncertain relative degrees

This paper addresses the application of the sliding mode approach to control the arm movements by artificial recruitment of muscles using Neuromuscular Electrical Stimulation (NMES). Such a technique allows the activation of motor nerves using surface electrodes. The goal of the proposed control system is to move the upper limbs of subjects through electrical stimulation to achieve a desired elbow angular displacement. Since the human neuro-motor system has individual characteristics, being time-varying, nonlinear and subject to uncertainties, the use of advanced robust control schemes may represent a better solution than classical Proportional-Integral (PI) controllers and model-based approaches, being simpler than more sophisticated strategies using fuzzy logic or neural networks usually applied in this control problem. The objective is the introduction of a new time-scaling base sliding mode control (SMC) strategy for NMES and its experimental evaluation. The main qualitative advantages of the proposed controller via time-scaling procedure are its independence of the knowledge of the plant relative degree and the design/tuning simplicity. The developed sliding mode strategy allows for chattering alleviation due to the impact of the integrator in smoothing the control signal. In addition, no differentiator is applied to construct the sliding surface. The stability analysis of the closed-loop system is also carried out by using singular perturbation methods. Experimental results are conducted with healthy volunteers as well as stroke patients. Quantitative results show a reduction of 45% in terms of root mean square (RMS) error (from 5.9° to [Formula: see text] ) in comparison with PI control scheme, which is similar to that obtained in the literature.

Singularity-free backstepping controller for model helicopters

This paper develops a backstepping controller for model helicopters to achieve trajectory tracking without singularity, which occurs in the attitude representation when the roll or pitch reaches ±π2. Based on a simplified model with unmodeled dynamics, backstepping technique is introduced to exploit the controller and hyperbolic tangent functions are utilized to compensate the unmodeled dynamics. Firstly, a position loop controller is designed for the position tracking, where an auxiliary dynamic system with suitable parameters is introduced to warrant the singularity-free requirement for the extracted command attitude. Then, a novel attitude loop controller is proposed to obviate singularity. It is demonstrated that, based on the established criteria for selecting controller parameters and desired trajectories, the proposed controller realizes the singularity-free trajectory tracking of the model helicopter. Simulations confirm the theoretical results.

Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload

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

A composite controller for trajectory tracking applied to the Furuta pendulum

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