Trajectory Tracking Control Of Manipulator Research Articles

A Two-Layer Trajectory Tracking Control Scheme of Manipulator Based on ELM-SMC for Autonomous Robotic Vehicle

With the development of autonomous driving technology, some special vehicles should also be developed into autonomous driving vehicles. The robotic vehicles are widely used in engineering operations, and the robotic manipulator is a common tool mounted on robotic vehicles. The autonomous driving of robotic vehicles requires not only automatic movement, but also the automation of the robotic manipulator drive system. Therefore, this paper proposes an adaptive trajectory tracking control of manipulator based on sliding mode control (SMC), which can more accurately describe the joint space movement of the manipulator system under multi task coupling and external interference. Considering the multi-tasking situation, the influence of obstacle avoidance and base tilt on the trajectory of manipulator is investigated by using extreme learning machine (ELM), and the framework of machine learning is established. The output based on ELM-SMC is used as the bottom-layer control. Then an effective trajectory compensation method is proposed as the top-level control to avoid the error accumulation in the periodic repeated operation of the manipulator. Finally, the application effect of trajectory error tracking and compensation of manipulator in complex tasks of dynamic environment is verified by simulation and experiments, which lays a foundation for the stability control of manipulator in practical complex engineering applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to solve the problem of poor trajectory tracking control accuracy of the manipulator caused by the change of the direction of the manipulator base. It is suitable for the high-precision position control of the manipulator assembled on the mobile robotic vehicle. Nowadays, the autonomous driving technology is developing rapidly, and the automation of traffic will be widely popularized in the future. Therefore, we should not only pay attention to the autonomous driving function of passenger vehicles, but also give consideration to the autonomous driving technology of robotic vehicles applied in engineering. It not only needs to complete the driving function, but also needs to ensure the reliable operation of the manipulator. In this paper, we mathematically deduce the control model of the manipulator. Then, we use SMC as the trajectory tracking control method of the manipulator, and use ELM to estimate the trajectory error caused by the end trajectory of the manipulator in the non-horizontal state of the base. Furthermore, we propose an optimization algorithm to optimize the compensation coefficient of cubic spline and give a reasonable compensation scheme. Through simulation and experiments, it is preliminarily verified that the schemes proposed in this paper are feasible, but they lack the application verification in the actual robotic vehicles, and the model fitting part of machine learning is completed with the help of the host computer, and the calculation ability of the controller of the actual manipulator may also be the limitation of completing this scheme.

Adaptive radial basis function neural network sliding mode control of robot manipulator based on improved genetic algorithm

ABSTRACT Since the trajectory-tracking control performance of multi-joint robot manipulator may be degraded due to modeling errors and external disturbances, this paper designs a new adaptive robot manipulator trajectory tracking control method through improved genetic algorithm and radial basis function neural network sliding mode control (IGA-RBFNNSMC). Firstly, the genetic algorithm (GA) is improved by establishing superior populations centered on individuals with high fitness values and selecting individuals in the superior populations for crossover and variation. Secondly, the improved genetic algorithm (IGA) is used for the optimization of the center vector and width vector of the Gaussian basis function in radial basis function (RBF) neural network. Then, based on the dynamics model of the robot manipulator, the modeling errors are approximated by RBF neural network and eliminated by sliding mode control (SMC), and the Lyapunov theorem is used to prove the stability and convergence of the control system. Finally, a two-joint robot manipulator is taken as the research objective and the simulation results show that IGA can significantly reduce the solution time on the basis of guaranteed accuracy and IGA-RBFNNSMC can make the trajectory tracking control accurate and more efficient, which proves the effectiveness of the proposed control method.

Cooperative game-oriented optimal robust control for an uncertain wheeled mobile robot with position constraints

The trajectory tracking control performance of the wheeled mobile robot (WMR) is subject to position constraints, system uncertainties, and external disturbances. This paper explores the mechanism of the position constraints (equality and inequality) and considers the system uncertainties to be time-varying but bounded with fuzzy prescribed bounds. To solve the position constraints and uncertainties problems, a cooperative game-oriented optimal robust control method is proposed to provide high-precision, fast-response performance and robustness for WMR. First, a creative diffeomorphism transformation is proposed to convert the bounded state variables (subject to inequality constraints) into unbounded state variables. Accordingly, a restructured WMR system with the new state variables is established, which is free from inequality constraints. The uncertainties’ bound is described as a fuzzy number by employing fuzzy set theory, which builds the fuzzy dynamic system of the WMR. Second, the control goal for this study is to drive the WMR to follow the position constraints despite uncertainties. An optimal robust control is developed to guarantee that the tracking errors of the WMR converge to a predefined neighborhood of origin. Using Lyapunov stability analysis, a fuzzy performance index is constructed, including steady-state performance, time performance, and control effort. The fuzzy performance index is employed as the cost function based on the cooperative game theory. The optimal control design is formulated to seek the Pareto-optimal solution of control parameters. Finally, the stability analysis and comparative experiments demonstrate that the proposed control algorithm can ensure the WMR’s superior trajectory tracking convergence performance and strong robustness against uncertainties/disturbances.

Extended state observer based dynamic iterative learning for trajectory tracking control of a six-degrees-of-freedom manipulator

With the development of industrial automation comes an ever, broadening number of application scenarios for manipulators along with increasing demands for their precise control. However, manipulator trajectory tracking control schemes often exhibit problems such as those related to high levels of coupling, complex calculations, and in various difficulties in application for industrial environments. For the problems of low accuracy in control and poor robustness of multiple-jointed robotic trajectory tracking, iterative learning control (ILC) with model compensation (MC) based on extended state observer (ESO) has been proposed for the trajectory tracking control of six-degrees-of-freedom (six-DOF) manipulators. The scheme has excellent features to overcome uncertainties in repetitive tasks, including unknown bounded perturbations that are external to the model or dynamic perturbations that are internal to the model. The proposed control strategy combines ESO, iterative learning, and MC, for precise control of trajectory tracking. Here, ESO is used to estimate disturbances, iterative learning allows fast and accurate control in repeated tasks, and the model-compensated control algorithm alleviates the necessary for many inverse operations. The convergence of our proposed control scheme is proved through Lyapunov function and time-varying approximation theory. Simulation and experimental results verify the validity of the proposed scheme.

Fault-tolerant control allocation for a bio-inspired underactuated AUV in the presence of actuator failures: Design and experiments

In this paper, we present the mathematical design and implementation of a fault-tolerant control scheme for a bio-inspired underwater robot with four flexible fins. The proposed active fault-tolerant control scheme re-configures the force allocation matrix using the elimination of column method, depending on which fin actuator is faulty. The proposed method allows to decouple the 6-DOF controllable underwater vehicle using the remaining three fins. The efficacy of the proposed method is assessed experimentally for trajectory tracking of an ellipsoidal-shaped trajectory using two different controllers, namely PID control and Sliding Mode control. The obtained results show that the combination of a sliding mode controller with the proposed fault-tolerant control allocation approach ensures an efficient trajectory tracking control performance when faults occur.

MPC-based trajectory tracking control of unmanned underwater tracked bulldozer considering track slipping and motion smoothing

The trajectory tracking control strategy of unmanned tracked underwater bulldozer (UUTB) can improve the efficiency of trenching and dredging. The soft sediment increases the running difficulties while UUTB is operating on the river bed. The operation of UUTB will cause track slip between the tracks and soft sediment, resulting in the heading deviation of UUTB. A MPC-based trajectory tracking controller is developed. The effect of track slip rate on the deviation of trajectory tracking control is analyzed. The MPC-based strategy considering slipping and smoothing (MPC-CSS) is proposed in this paper to improve the anti-interference ability of track slipping in the process of trajectory tracking. The simulation results show that the lateral stability of UUTB can be improved by 72.5% with the proposed MPC-CSS strategy. A reduced-scale model prototype of UUTB based on a robot operating system (ROS) is designed. The trajectory tracking control performance on different artificial roads built in the lab is verified. The experimental results indicate that the proposed MPC-CSS strategy follows the desired trajectory compared with pure pursuit control (PPC) and MPC strategy. The effectiveness of the proposed MPC-CSS strategy of reduced-scale model prototype UUTB is verified, which effectively reduces the track slipping and improves the operating stability.

Intelligent-PID with PD Feedforward Trajectory Tracking Control of an Autonomous Underwater Vehicle

This paper investigates the model-free trajectory tracking control problem for an autonomous underwater vehicle (AUV) subject to the ocean currents, external disturbances, measurement noise, model parameter uncertainty, initial tracking errors, and thruster malfunction. A novel control architecture based on model-free control principles is presented to guarantee stable and precise trajectory tracking performance in the complex underwater environment for AUVs. In the proposed hybrid controller, intelligent-PID (i-PID) and PD feedforward controllers are combined to achieve better disturbance rejections and initial tracking error compensations while keeping the trajectory tracking precision. A mathematical model of an AUV is derived, and ocean current dynamics are included to obtain better fidelity when examining ocean current effects. In order to evaluate the trajectory tracking control performance of the proposed controller, computer simulations are conducted on the LIVA AUV with a compelling trajectory under various disturbances. The results are compared with the two degrees-of-freedom (DOF) i-PID, i-PID, and PID controllers to examine control performance improvements with the guaranteed trajectory tracking stability. The comparative results revealed that the i-PID with PD feedforward controller provides an effective trajectory tracking control performance and excellent disturbance rejections for the entire trajectory of the AUV.

Performing trajectory tracking control of an unmanned ground vehicle using fractional order terminal sliding mode controller

In this paper, fractional order terminal sliding mode control (FOTSMC) method is used for trajectory tracking control performance of an unmanned ground vehicle (UGV). Firstly, a kinematic controller is designed to estimate the linear and angular velocities of the vehicle. Then, a FOTSMC design is carried out to track the vehicle reference velocities. Terminal sliding mode control (TSMC) and sliding mode control (SMC) methods are also used to demonstrate the performance of the proposed controller. The simulation results show that the proposed controller improves the tracking error by about 13% over SMC and 6.146% compared to TSMC.

Robust state and output feedback prescribed performance interval type‐3 fuzzy reinforcement learning controller for an unmanned aerial vehicle with actuator saturation

AbstractThis paper presents a novel adaptive reinforcement learning control method with interval type‐3 fuzzy neural networks to improve the trajectory tracking control performance of quadrotor unmanned aerial vehicles in challenging flight conditions. The proposed reinforcement learning controller is independent of the system's dynamics, and only relies on measurable signals of the system. An adaptive robust controller in collaboration with the suggested reinforcement learning method is designed to significantly improve the robustness of the control system. The maximum overshoot/undershoot, convergence rate and final tracking accuracy are ensured a priori by the prescribed performance control methodology. To develop the proposed controller and to achieve a high‐performance closed‐loop system, a high‐gain observer is employed in order to estimate the velocity and acceleration of the quadrotor unmanned aerial vehicles system. The uniform ultimate boundedness stability of the proposed control algorithm is achieved by a Lyapunov‐based stability analysis. Finally, in the simulation section, it is shown that the presented intelligent controller with the proposed learning algorithm result in a better performance in contrast to the other kind of conventional control techniques.

A robust zeroing neural network and its applications to dynamic complex matrix equation solving and robotic manipulator trajectory tracking.

Dynamic complex matrix equation (DCME) is frequently encountered in the fields of mathematics and industry, and numerous recurrent neural network (RNN) models have been reported to effectively find the solution of DCME in no noise environment. However, noises are unavoidable in reality, and dynamic systems must be affected by noises. Thus, the invention of anti-noise neural network models becomes increasingly important to address this issue. By introducing a new activation function (NAF), a robust zeroing neural network (RZNN) model for solving DCME in noisy-polluted environment is proposed and investigated in this paper. The robustness and convergence of the proposed RZNN model are proved by strict mathematical proof and verified by comparative numerical simulation results. Furthermore, the proposed RZNN model is applied to manipulator trajectory tracking control, and it completes the trajectory tracking task successfully, which further validates its practical applied prospects.

Clonal selection algorithm based control for two-wheeled self-balancing mobile robot

In this study, we propose adaptive control approaches based on optimization for a two-wheeled mobile robot. The mathematical model of the self-balancing vehicle based on the inverted pendulum principle, is derived from the Lagrange method and the vehicle model is simulated within MATLAB/Simulink environment. Five different optimization-based controller models (Model 1–5) are developed based on common control methods, which are the Pole Placement Design Method, PID, and LQR. Besides the stability control of the robot, speed control and trajectory tracking control are also provided with these models. While improving the optimization-based controller models, the CSA, an artificial immune optimization methods, is adapted for use with the system. The benefits of the study are given as follows: 1) The balancing control and trajectory tracking control performance of the two-wheeled vehicle is improved using the proposed optimization-based control approach; 2) A comprehensive study is introduced with different control models based on Pole Placement Design Method, PID, and LQR Method; 3) Since parameter tuning of multiple PID controllers is challenging for a two-wheeled vehicle constructed by using the inverted pendulum principle, one of the proposed control models is developed using multiple PIDs. To alleviate the difficulties of parameter tuning for multiple PIDs, the CSA method is adapted for a self-balancing two-wheeled vehicle for the first time; 4) To exhibit the optimization effect of the CSA, the simulation results are compared with five other optimization methods, namely PSO, ABC, DE, GoldSa-II, and CS; 5) The effectiveness of the proposed optimization-based control approaches and optimization method are demonstrated through analyses and simulation studies. In this concept, it has been also analyzed effects of the external disturbances and uncertain parameters on the proposed control method.

Backstepping Adaptive Trajectory Tracking Control of Manipulator with Uncertainties of Model and State

In this paper, a backstepping adaptive control method based on Kalman data fusion (KDF-BAC) is proposed to solve parametric and non-parametric as well as state variables in manipulator dynamics model. Firstly, the non-parametric uncertainties are regarded as internal disturbances to simplify the dynamics model of the manipulator. Secondly the backstepping control law is derived using the idea of recursive design, and the adaptive method is used to identify the uncertain parameters to provide the estimated value of unknown parameters for the backstepping control law. Finally, the Kalman data fusion method is used to reduce the uncertainty of the velocity information, and the most reliable estimate value is obtained, which is fed back to the controller. The simulation results show that the proposed KDF-BAC can reduce the influence of manipulator uncertainties on trajectory tracking performance, and has better control effect than adaptive control and backstepping control.

Constraint-following control design for the position tracking of a permanent magnet linear motor with inequality constraints

Abstract. In this paper, we mainly solve the problem of the trajectory following the control and boundary transfinite control of the permanent magnet linear motor (PMLM). Using the Udwadia–Kalaba (U–K) method, the explicit equation of the complete nonholonomic constraint equation is first established, and then the new input constraint equation is obtained by integrating the inequality constraint and the original equation constraint through tangent-state transformation mapping. This constraint equation can make the motor move along the ideal trajectory in a limited range, thus solving the control problem of equality and inequality creatively. The simulation results and PMLM experiment results, based on control Signal Processing And Control Engineering (cSPACE), show that the proposed control method can obtain better motion performance, and the motion displacement does not exceed the boundary while satisfying the trajectory tracking control performance, which proves the effectiveness and feasibility of the proposed method.

Nonsingular fast terminal sliding mode control for manipulator based on combinatorial reaching law

Aiming at the problems of external disturbance, modeling errors, tracking speed and chattering in manipulator trajectory tracking control, a nonsingular fast terminal sliding mode control strategy for manipulator based on combinatorial reaching law was proposed. First, the nonlinear disturbance observer was used to observe the system’s external disturbance and modeling errors. Then, on the basis of the nonsingular fast terminal sliding mode surface, an improved nonsingular fast terminal sliding mode surface was proposed, which improves the convergence speed in the sliding motion process of sliding mode control. At the same time, a combinatorial reaching law combining the power reaching law and the variable speed reaching law was proposed, which improved the approach speed of the system under the premise of weakening the chattering. The simulation results verified the effectiveness of this control strategy.

SMCSPO-Based Robust Control of AUV in Underwater Environments including Disturbances

In the underwater environment, robust control algorithms are required to control autonomous underwater vehicles (AUVs) at high speed while preventing large nonlinearities and disturbances. Sliding mode control (SMC) is a well-known robust control theory and has been widely used not only in AUV control but also in systems such as industrial robots which have high nonlinearity in their system dynamics. However, SMC has the disadvantage of causing chattering on the control input, and it is difficult to apply this method to the control fins of an AUV system that cannot move its fins at high speed underwater. In this work, a design for a sliding mode control with sliding perturbation observer (SMCSPO) algorithm is applied to AUVs, and the simulation results under underwater disturbance conditions are discussed. From simulation using MATLAB, it is confirmed that AUV control using SMCSPO shows better trajectory tracking control performance without chattering than PID control.

Optimal Tuning of the SMC Parameters for a Two-Link Manipulator Co-Simulation Control

This paper presents the trajectory tracking control of a two-link planar robot manipulator using MSC Adams and MATLAB co-simulation which enables the innovative virtual prototyping of the systems without any mathematical expressions. Firstly, the tracking control performance of the planar manipulator is investigated using the Sliding Mode Control (SMC) controller and the Proportional Integral Derivative (PID) controller in terms of the performance analysis. As a result, the SMC demonstrates effective control performances compared to the PID controller according to the required trajectory, settling time, and end position of the system. Then, the SMC controller parameters are determined using the different optimization methods offered as open source by MATLAB/Response Optimization Toolbox and compared to each other. In the virtual co-simulation, the trajectory tracking control performance is observed to be improved by optimizing the parameters of the SMC controller using Simplex Search (SS) method. All control results are examined and presented with graphics and international error standards.

Research on trajectory tracking control of 7-DOF picking manipulator.

In order to solve the problem of poor robustness of the traditional method of calculating torque in the mechanical model of 7-DOF picking manipulator, this paper proposes a control strategy of calculating torque plus fuzzy compensation by using adaptive fuzzy logic system to compensate the uncertain part of the mechanical model of 7-DOF picking manipulator. By using Lagrange method, the dynamic model of 7-DOF manipulator is established, and the relationship between joint motion and applied torque (force) is obtained. Using ADAMS and MATLAB to establish a co-simulation platform, the manipulator and trajectory tracking control system are simulated. The results show that the trajectory tracking error of each joint in the algorithm is obviously reduced and the convergence trend is obvious. The average trajectory tracking accuracy of joint 1 to joint 7 was improved by 70.22%, 94.78%, 0.62%, 74.23%, 89.78%, 86.45%, and 67.15%, respectively. In this control scheme, the control force (moment) of each joint changes regularly, and the output force (moment) does not appear chattering and mutation when the disturbance signal is added. The research results can provide support for the further study of picking manipulator trajectory tracking control system.

RETRACTED: Rapid iterative learning algorithm of nonlinear time-delay system with initial deviation

A rapid iterative learning control algorithm with variable forgetting factor is applied for a class of nonlinear system with initial error and time-delay. This algorithm eliminats the limitation that the initial state should be reset to the expected one or fixed value at the start of iteration in the learning process of conventional algorithms. The error and the differences between two adjacent error is adopted to correct the controller avoiding the unstable influence of the derivative for PD type algorithm and the available information is fully used to increase convergence rate. Furthermore variable forgetting factor introduced guaranteed a fast convergence of trajectory tracking error Then, with applying the rapid algorithm to the trajectory tracking control of manipulator, the learning speed and tracking performance are both greatly improved. Meanwhile, the control strategy is proposed for the limitation of each joint rotation. The convergence of the method is also proved theoretically. Finally, simulation results illustrates the effectiveness and the real-time ability of the proposed way.

Adaptive Fuzzy Sliding Mode and Robust Tracking Control for Manipulators with Uncertain Dynamics

In response to the issue of the trajectory tracking control problem of manipulators with uncertain parameters and external disturbance, an adaptive fuzzy sliding mode robust control algorithm is proposed. Sliding mode control (SMC) is adopted to perform robotic manipulator trajectory tracking control. Then, a fuzzy logic system is used for adaptive adjustment of switching gain of the SMC and to reduce the buffeting problem. Next, compensation is made by using the robust controller in consideration of the impacts of unmodeled dynamics and external disturbance. The simulation experiment on a two axes robotic manipulator shows that, with the proposed control method, the sliding mode control input signal is kept smooth, and the manipulator has high trajectory tracking precision.

Expected yaw rate-based trajectory tracking control with vision delay for intelligent vehicle.

Accurate and real-time position of preview point is significant to trajectory tracking control of vision-guided intelligent vehicle. The unavoidable delay of road automatic identification system weakens trajectory tracking control performance, and even deteriorates the vehicle stability. Therefore, a compensator for the delay of road automatic identification system was proposed which combines the current statistical model and adaptive Kalman predictor to estimate the state of preview point position. The trajectory tracking sliding mode controller of intelligent vehicle is established through a 2-degrees of freedom vehicle dynamic model and motion model by using MATLAB/Simulink and CarSim. The trajectory tracking performance under 20-100 ms delay is analyzed. The simulation results show that the trajectory tracking performance of intelligent vehicle will be affected by the delay of road automatic identification system, reducing tracking accuracy. And when the delay is too large, it will deteriorate the vehicle stability and safety. In addition, the simulation results also verify the effectiveness of current statistical-adaptive Kalman predictor compensator at different delays.