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The purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.

For the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.

The experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.

To the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.

The purpose of this paper is to gain trajectory-tracking controllers for autonomous aircraft are optimized using a modified evolutionary, or genetic algorithm (GA).

The GA design utilizes real representation for the individual consisting of the collection of all controller gains subject to tuning. The initial population is generated randomly over pre-specified ranges. Alternatively, initial individuals are produced as random variations from a heuristically tuned set of gains to increase convergence time. A two-point crossover mechanism and a probabilistic mutation mechanism represent the genetic alterations performed on the population. The environment is represented by a performance index (PI) composed of a set of metrics based on tracking error and control activity in response to a commanded trajectory. Roulette-wheel selection with elitist strategy are implemented. A PI normalization scheme is also implemented to increase the speed of convergence. A flexible control laws design environment is developed, which can be used to easily optimize the gains for a variety of unmanned aerial vehicle (UAV) control laws architectures.

The performance of the aircraft trajectory-tracking controllers was shown to improve significantly through the GA optimization. Additionally, the novel normalization modification was shown to encourage more rapid convergence to an optimal solution.

The GA paradigm shows much promise in the optimization of highly non-linear aircraft trajectory-tracking controllers. The proposed optimization tool facilitates the investigation of novel control architectures regardless of complexity and dimensionality.

The addition of the evolutionary optimization to the WVU UAV simulation environment enhances significantly its capabilities for autonomous flight algorithm development, testing, and evaluation. The normalization methodology proposed in this paper has been shown to appreciably speed up the convergence of GAs.

The paper provides a flexible generalized framework for UAV control system evolutionary optimization. It includes specific novel structural elements and mechanisms for improved convergence as well as a comprehensive PI for trajectory tracking.

Trajectory tracking error of robotic manipulator has limited its applications in trajectory tracking control systems. This paper aims to improve the trajectory tracking accuracy of robotic manipulator, so a linear-extended-state-observer (LESO)-based prescribed performance controller is proposed.

A prescribed performance function with the convergence rate, maximum overshoot and steady-state error is derived for the output error transformation, whose stability can guarantee trajectory tracking accuracy of the original robotic system. A LESO is designed to estimate and eliminate the total disturbance, which neither requires a detailed system model nor a heavy computation load. The stability of the system is proved via the Lyapunov theory.

Comparative experimental results show that the proposed controller can achieve better trajectory tracking accuracy than proportional-integral-differential control and linear active disturbance rejection control.

In the LESO-based prescribed performance control (PPC), the LESO was incorporated into the PPC design, it solved the problem of stabilizing the complex transformed system and avoided the costly offline identification of dynamic model and estimated and eliminated the total disturbance in real-time with light computational burden. LESO-based PPC further improved control accuracy on the basis of linear-active-disturbance-rejection-control. The new proposed method can reduce the trajectory tracking error of the robotic manipulators effectively on the basis of simplicity and stability.

This paper aims to present an adaptive robust sliding mode tracking controller for a 6 degree-of-freedom industrial assembly robot with parametric uncertainties and external disturbances. The controller is used to achieve both stringent trajectory tracking, accurate parameter estimations and robustness against external disturbances.

The controller is designed based on the combination of sliding mode control, adaptive and robust controls and hence has good adaptation and robustness abilities to parametric variations and uncertainties. The unknown parameter estimates are updated online based on a discontinuous projection adaptation law. The robotic dynamics is first formulated in both joint spaces and workspace of the robot’s end-effector. Then, the design procedure of the adaptive robust sliding mode tracking controller and the parameter update law is detailed.

Comparative tests are also conducted to verify the effectiveness of the proposed controller, which show that the proposed controller achieves significantly better dynamic trajectory tracking performances as compared with conventional proportional derivative controller and sliding mode controller under the same conditions.

This is a new innovation for industrial assembly robot to improve assembly automation.

The purpose of this paper is to enhance the quadrotor’s capability of short-distance delivery to satisfy the large demand for quadrotor, which is used for goods distribution in huge warehouses, under time-varying payload and external wind disturbance.

A trajectory tracking controller design based on the combination of an adaptive sliding mode control (ASMC) method and the active disturbance rejection control (ADRC) technique is proposed. Besides, an inner–outer loop control system structure is adopted.

Simulation results of different trajectory tracking verify the effectiveness and robustness of the proposed tracking control method under various conditions, including parameter uncertainty and external wind disturbance. The proposed control strategy ensures that quadrotor UAV is capable of tracking linear and spiral trajectory well whether it loads or unloads goods in the presence of the external wind disturbance.

The proposed method of designing a trajectory tracking controller is based on an integral ADRC and ASMC scheme so as to deal with the trajectory tracking problem for a quadrotor with payload variation.

The aim of this paper is to propose a robust robot fuzzy logic proportional-derivative (PD) controller for trajectory tracking of autonomous nonholonomic differential drive wheeled mobile robot (WMR) of the type Quanser Qbot.

Fuzzy robot control approach is used for developing a robust fuzzy PD controller for trajectory tracking of a nonholonomic differential drive WMR. The linear/angular velocity of the differential drive mobile robot are formulated such that the tracking errors between the robot’s trajectory and the reference path converge asymptotically to zero. Here, a new controller zero-order Takagy–Sugeno trajectory tracking (ZTS-TT) controller is deduced for robot’s speed regulation based on the fuzzy PD controller. The WMR used for the experimental implementation is Quanser Qbot which has two differential drive wheels; therefore, the right/left wheel velocity of the differential wheels of the robot are worked out using inverse kinematics model. The controller is implemented using MATLAB Simulink with QUARC framework, downloaded and compiled into executable (.exe) on the robot based on the WIFI TCP/IP connection.

Compared to other fuzzy proportional-integral-derivative (PID) controllers, the proposed fuzzy PD controller was found to be robust, stable and consuming less resources on the robot. The comparative results of the proposed ZTS-TT controller and the conventional PD controller demonstrated clearly that the proposed ZTS-TT controller provides better tracking performances, flexibility, robustness and stability for the WMR.

The proposed fuzzy PD controller can be improved using hybrid techniques. The proposed approach can be developed for obstacle detection and collision avoidance in combination with trajectory tracking for use in environments with obstacles.

A robust fuzzy logic PD is developed and its performances are compared to the existing fuzzy PID controller. A ZTS-TT controller is deduced for trajectory tracking of an autonomous nonholonomic differential drive mobile robot (i.e. Quanser Qbot).

The purpose of this paper is to review the progress made in arc welding automation using trajectory planning, seam tracking and control methodologies.

This paper discusses key issues in trajectory planning towards achieving full automation of arc welding robots. The identified issues in trajectory planning are real-time control, optimization methods, seam tracking and control methodologies. Recent research is considered and brief conclusions are drawn.

The major difficulty towards realizing a fully intelligent robotic arc welding system remains an optimal blend and good understanding of trajectory planning, seam tracking and advanced control methodologies. An intelligent trajectory tracking ability is strongly required in robotic arc welding, due to the positional errors caused by several disturbances that prevent the development of quality welds. An exciting prospect will be the creation of an effective hybrid optimization technique which is expected to lead to new scientific knowledge by combining robotic systems with artificial intelligence.

This paper illustrates the vital role played by optimization methods for trajectory design in arc robotic welding automation, especially the non-gradient approaches (those based on certain characteristics and behaviour of biological, molecular, swarm of insects and neurobiological systems). Effective trajectory planning techniques leading to real-time control and sensing systems leading to seam tracking have also been studied.

The purpose of this paper is to present work which is a part of the Comprehensive Automation for Specialty Crops project (CASC). Desired trajectory tracking objective has been previously performed by using a non‐model based approach in this project. Long distance autonomous drive has been achieved; however the results haven't met the expectations of the project requirements. In order to provide these requirements, this study is conducted. In this study, long distance autonomous trajectory tracking for an orchard vehicle is studied. Besides longitudinal motion, lateral motion of the vehicle is also considered. The longitudinal and lateral errors are objected to keep into a region of less than 10 cm.

Car‐like robot kinematic modeling approach is used to create desired trajectory. In order to control longitudinal velocity and steering angle of the vehicle, a controller methodology is proposed. Stability of the controller proposed is shown by using Lyapunov stability approach.

The proposed model is adapted into a four‐wheeled autonomous orchard vehicle and tested in an experimental orchard for long distance autonomous drives. More than 15 km autonomous drive is successfully achieved and the details are presented in this paper.

In this study, long distance autonomous trajectory tracking for an orchard vehicle is focused. A model based control strategy, including the information about longitudinal and lateral motion of the vehicle, is constructed. A new approach to create steering angles for turning operations of the orchard vehicle is introduced. It is objected that the longitudinal and lateral errors should be less than 10 cm during the trajectory tracking task.

The purpose of this paper is to design a new trajectory error compensation method to improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction motion.

A trajectory error compensation method based on admittance-extended Kalman filter (AEKF) error fusion for human–exoskeleton interaction control. The admittance controller is used to calculate the trajectory error adjustment through the feedback human–exoskeleton interaction force, and the actual trajectory error is obtained through the encoder feedback of exoskeleton and the designed trajectory. By using the fusion and prediction characteristics of EKF, the calculated trajectory error adjustment and the actual error are fused to obtain a new trajectory error compensation, which is feedback to the knee exoskeleton controller. This method is designed to be capable of improving the trajectory tracking performance of the knee exoskeleton and enhancing the compliance of knee exoskeleton interaction.

Six volunteers conducted comparative experiments on four different motion frequencies. The experimental results show that this method can effectively improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction.

The AEKF method first uses the data fusion idea to fuse the estimated error with measurement errors, obtaining more accurate trajectory error compensation for the knee exoskeleton motion control. This work provides great benefits for the trajectory tracking performance and compliance of lower limb exoskeletons in human–exoskeleton interaction movements.

This study discusses the tracking trajectory issue of the exoskeleton under the bounded disturbance and designs an useful tracking trajectory control method to solve it. By using the proposed control method, the tracking error can be successfully convergence to the assigned boundary. Meanwhile, the chattering effect caused by the actuators is already reduced, and the tracking performance of the pneumatic artificial muscles (PAMs) elbow exoskeleton is improved effectively.

A prescribed performance sliding mode control method was developed in this study to fulfill the joint position tracking trajectory task on the elbow exoskeleton driven by two PAMs. In terms of the control structure, a dynamic model was built by conforming to the adaptive law to compensate for the time variety and uncertainty exhibited by the system. Subsequently, a super-twisting algorithm-based second-order sliding mode control method was subjected to the exoskeleton under the boundedness of external disturbance. Moreover, the prescribed performance control method exhibits a smooth prescribed function with an error transformation function to ensure the tracking error can be finally convergent to the pre-designed requirement.

From the theoretical perspective, the stability of the control method was verified through Lyapunov synthesis. On that basis, the tracking performance of the proposed control method was confirmed through the simulation and the manikin model experiment.

As revealed by the results of this study, the proposed control method sufficiently applies to the PAMs elbow exoskeleton for tracking trajectory, which means it has potential application in the actual robot-assisted passive rehabilitation tasks.