Trajectory Tracking Control Method Research Articles

Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.

Fixed-time trajectory tracking for autonomous surface vehicles via output feedback under various constraints

This paper proposes a novel fixed-time output feedback trajectory tracking control method suitable for autonomous surface vehicles (ASVs). Firstly, various complex uncertainty terms, such as unknown external disturbances, unmodeled errors, and actuator faults are considered in this paper. And these terms are uniformly converted into the total uncertainty terms through model transformation for convenience. Then, a fixed-time extended state observer (FTESO) with the newly expanded state is designed to observe and estimate the total uncertainty terms. Next, the saturation dynamic filter (SDF) is adopted to address the input saturation, and the saturation factors of SDF are incorporated into the trajectory error calculation to reduce the torque mutation caused by an excessive error in the control input. Finally, a fixed-time control law is proposed by taking into account the ASV system error and FTESO estimation state. Simulation experiments show that this method has excellent control performance, and this conclusion is validated through stability proof and case comparison.

Intelligent vehicle trajectory tracking control based on physics-informed neural network dynamics model

In order to solve the accuracy problem of trajectory tracking control method based on data-driven model, an intelligent vehicle trajectory tracking control method based on physics-informed neural network (PINN) vehicle dynamics model is proposed. Aiming at the problem of poor interpretability of data-driven model, a vehicle dynamics model based on the PINN is established, and the physics-driven deep learning method is used instead of the data-driven deep learning method to obtain the dynamic characteristics of the intelligent vehicle, to benefit from both the physical-based method and the data-driven method. A sequential training method is also proposed to solve the coupling problem when training multiple PINNs simultaneously. The model takes the nonlinearity of the neural network model and physical interpretability into consideration compared to the standard neural network model. Then, based on the PINN vehicle dynamics model, a trajectory tracking controller based on the iterative linear quadratic regulator (ILQR) control algorithm is developed. The optimal control law is derived by optimizing the ILQR control algorithm to implement the intelligent vehicle’s precise and stable tracking for the desired trajectory. The Levenberg-Marquardt (LM) algorithm and line search technology are used and damping factor adjustment rules are set up to enhance the convergence performance of the ILQR control algorithm. In order to verify the effectiveness of the proposed method, the simulation is conducted under the condition of double lane change. The simulation results demonstrate that the proposed method can track the reference trajectory accurately under the limited conditions. Its control performance is much better than other algorithms.

Research on an Intelligent Vehicle Trajectory Tracking Method Based on Optimal Control Theory

This study aims to explore an intelligent vehicle trajectory tracking control method based on optimal control theory. Considering the limitations of existing control strategies in dealing with signal delays and communication lags, a control strategy combining an anthropomorphic forward-looking reference path and longitudinal velocity closure is proposed to improve the accuracy and stability of intelligent vehicle trajectory tracking. Firstly, according to the vehicle dynamic error tracking model, a linear quadratic regulator (LQR) transverse controller is designed based on the optimal control principle, and a feedforward control strategy is added to reduce the system steady-state error. Secondly, an anthropomorphic look-ahead prediction model is established to mimic human driving behavior to compensate for the signal lag. The double proportional–integral–derivative (DPID) control algorithm is used to track the longitudinal speed reference value. Finally, a joint simulation is conducted based on MatLab/Simulink2021b and CarSim2019.0 software, and the effectiveness of the control strategy proposed in this paper is verified by constructing a semi-physical experimental platform and carrying out a hardware-in-the-loop test. The simulation and test results show that the control strategy can significantly improve the accuracy and stability of vehicle path tracking, which provides a new idea for future intelligent vehicle control system design.

A trajectory tracking control method for autonomous vehicle based on adaptive model predictive control

A trajectory tracking control method for autonomous vehicle based on adaptive model predictive control

RBFNN-Based Adaptive Integral Sliding Mode Feedback and Feedforward Control for a Lower Limb Exoskeleton Robot

In this paper, an adaptive trajectory tracking control method combining proportional–integral–derivative (PID) control, Radial Basis Function neural network (RBFNN)-based integral sliding mode control (ISMC), and feedforward control, i.e., the PIDFF-ISMC method, is proposed. The PIDFF-ISMC method aims to deal with the dynamic uncertainties, disturbances, and slow response in lower limb exoskeleton robot systems. Firstly, the Lagrange function is utilized to establish dynamic models that include frictional force and unmodeled dynamics. Secondly, the feedback controller is composed of PID and RBFNN-based ISMC to improve tracking performance and decrease the chattering phenomenon. The feedforward controller is adopted to reduce the response time by employing inverse dynamic models. Finally, the Lyapunov function proves the stability of the proposed control method. The experimental results show that the proposed control method can effectively reduce the trajectory tracking error and response time at two different speeds while alleviating control input chattering.

Trajectory tracking control of autonomous space-based simulators for the on-orbit assembly of large space optical telescopes

To enhance the precision of on-orbit assembly for large space optical telescopes, the control of attitude motion in the Autonomous Space-based Simulator (ASS) is imperative. This paper presents a robust finite-time trajectory tracking control method aimed at improving the position and attitude tracking performance of ASS. Considering the dynamic characteristics inherent in ASS, we introduce an improved non-singular fast terminal sliding mode controller (INFTSMC) incorporating an adaptive fuzzy mechanism to attain finite-time error convergence and robust control. The adaptive fuzzy logic control (AFLC) method yields an equivalent gain, eliminating discontinuous switching in terminal sliding mode control (TSMC). This reduction minimizes chattering in control inputs and compensates for uncertainties and time-varying disturbances within the dynamic model. The proposed method’s effectiveness is validated through comprehensive simulation and experimental studies.

Distributed Dynamic Surface Control for a Class of Quadrotor UAVs with Input Saturation and External Disturbance

An adaptive dynamic surface trajectory tracking control method based on the Nussbaum function is proposed for a class of quadrotor UAVs encountering unknown external disturbances and unidentified nonlinearities. By transforming controller expressions into numerical solutions, the challenge of overly complex controller design expressions is addressed, simplifying the overall controller design process and enhancing the efficiency of simulation programs. Additionally, an adaptive controller based on Nussbaum gain is introduced to effectively resolve actuator saturation issues. This approach mitigates complexities associated with traditional control design and ensures smooth operation of the quadrotor UAVs. The proposed methodology offers promising prospects for enhancing the robustness and performance of quadrotor UAVs under uncertain operating conditions. Finally, to validate the effectiveness of the proposed control scheme, a hardware-in-the-loop experimental setup is constructed. The dynamic model of the quadrotor UAVs and the proposed controller scheme are implemented on the Rapid Control Prototype (RCP) and Real-Time Simulator (RTS), respectively. This facilitates a semi-physical simulation experiment, providing a basis for the subsequent application of the control scheme to actual aerial vehicles. The concluding experimental results affirm the effectiveness of the proposed control scheme and highlight its potential for practical applications.

An anti-disturbance lane-changing trajectory tracking control method combining extended Kalman filter and robust tube-based model predictive control

This paper proposes a trajectory tracking control method combining extended Kalman filter (EKF) and robust tube-based model predictive control (RTMPC) methods to improve the anti-disturbance capability during lane-changing maneuver of automated vehicles. A time-based quintic polynomial function is introduced for the implementation of trajectory planning to obtain the desired reference trajectory. The planned trajectory is input to the nominal system-oriented model predictive controller (MPC) in RTMPC for optimization to obtain the optimal control of the nominal system. The EKF collects the state measurements of the current instant and the optimal state estimates of the previous instant, and performs filtering to obtain the optimal state estimates of the current instant. The optimal estimate of the current state and the current state of the nominal system are input into the auxiliary control law of RTMPC to obtain the control of the actual system. Comparative numerical simulation experiments are conducted to analyze robustness and sensitivity of the proposed method. The results show that the control method combining EKF and RTMPC can optimize the trajectory tracking performance of the vehicle system, especially in the lateral displacement and the yaw-rate control. When the amplitude of measurement noise reaches the maximum, the optimization effect of lateral control is most significant in experiments. And the optimization effect in the control of lateral displacement and yaw angle continues to enhance with the increase of measurement disturbance. Therefore, this study can provide a reference for the anti-interference lane change trajectory tracking strategy of automated vehicles in the future.

Vision-Based Adaptive Trajectory Tracking Control of Wheeled Mobile Robot With Unknown Translational External Parameters

In this article, the vision-based trajectory tracking control problem of wheeled mobile robot is addressed, and different from the traditional vision-based adaptive control methods, the case that the camera is not installed in the center of the mobile robot is considered. In this case, the visual model needs to consider the influence of unknown translational external parameters. To solve this problem, a novel adaptive vision-based trajectory tracking control method is proposed, and a two-stage switching trajectory tracking control law is designed, where the adaptive control method is used to compensate the unknown external parameters. The asymptotic convergence of tracking errors are strictly proved by applying the Lyapunov method. Simulation and experimental results show that proposed approach can effectively control the mobile robot to track the desired trajectory in the presence of unknown external translational parameters.

Permanent magnet synchronous motor stator flux trajectory tracking control based on switching time correction

In this paper, aiming at the problems that the existing stator flux trajectory tracking control method often needs to design complex fundamental wave component observers and the switching time correction based on steady-state solution lacks accurate theoretical calculation equations, a permanent magnet synchronous motor stator flux trajectory tracking control method using optimal PWM (Pulse Width Modulation) is proposed. The outer loop is the speed regulator, whose output is combined with the flux linkage of the permanent magnet of the motor as the reference vector of the stator flux linkage. And the motor speed with the rotor position is combined to calculate the amplitude and phase angle of the reference stator voltage vector, which is used to optimize PWM pulse mode and to determine switching action. Meanwhile, the switching time of optimal PWM is corrected in real time through the stator flux deviation to eliminate the deviation between the stator flux reference value and the actual value. This method does not need to estimate the fundamental component of voltage, current or flux linkage. And unlike the traditional vector method, there is no current inner loop, which can significantly improve the dynamic response speed while simplifying the control structure. Simulation and experiments also fully verify the effectiveness of the proposed control method.

Adaptive Trajectory Tracking Control for the Quadrotor Aerial Transportation System Landing a Payload Onto the Mobile Platform

Recently, it is becoming increasingly possible to apply aerial transportation systems to real-world applications. However, current researches on cable-suspended transportation systems present practical limitations due to the fixed-length cable. With the introduction of the cable adjustment mechanism, various complicated tasks, such as limited space crossing, offshore sample collection, and even landing the payload on a mobile platform, can be accomplished by actively changing the distance between the quadrotor and the payload. In order to complete the aforementioned tasks, a trajectory tracking control method is in urgent need for the variable-length-cable-suspended aerial transportation systems. To this end, an adaptive tracking control approach with the consideration of unknown resistance coefficients is designed in this paper. Subsequently, Lyapunov techniques and Barbalat's Lemma are utilized to prove the convergence for the equilibrium point of the closed-loop system. Finally, hardware experiments are meticulously conducted based on a self-built experimental platform, which verify the satisfactory performance of the proposed method in anti-swing aerial transportation and payload landing onto the mobile platform.

Real-time Trajectory Planning and Tracking Control of Bionic Underwater Robot in Dynamic Environment.

In this article, we study the trajectory planning and tracking control of a bionic underwater robot under multiple dynamic obstacles. We first introduce the design of the bionic leopard cabinet underwater robot developed in our lab. Then, we model the trajectory planning problem of the bionic underwater robot by combining its dynamics and physical constraints. Furthermore, we conduct global trajectory planning for bionic underwater robots based on the temporal-spatial Bezier curves. In addition, based on the improved proximal policy optimization, local dynamic obstacle avoidance trajectory replanning is carried out. In addition, we design the fuzzy proportional-integral-derivative controller for tracking control of the planned trajectory. Finally, the effectiveness of the real-time trajectory planning and tracking control method is verified by comparative simulation in dynamic environment and semiphysical simulation of UWSim. Among them, the real-time trajectory planning method has advantages in trajectory length, trajectory smoothness, and planning time. The error of trajectory tracking control method is controlled around 0.2 m.

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.

Autonomous trajectory tracking control method for an agricultural robotic vehicle

Autonomous trajectory tracking control method for an agricultural robotic vehicle

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.

Prescribed performance control of a robotic manipulator with unknown control gain and assigned settling time

This paper presents a control method for trajectory tracking of a robotic manipulator, subject to practical constraints and uncertainties. The proposed method is established upon an adaptive backstepping procedure incorporating a tangent-type barrier Lyapunov function and it preserves some important metrics of trajectory tracking such as fast and user-defined settling time response and robustness against actuation faults and unknown control gain. The proposed design maintains the system trajectory within a prescribed performance bound and relaxes the assumption of the bounded initial condition. These salient features preserve the system within a safety bound and, consequently, guarantee the system stability and safety. The performance of the proposed control method is validated on a 3-DOF PUMA 560 robotic manipulator benchmark model, with different operation scenarios. The simulation results confirm the effectiveness and robustness of the proposed control method.

Passivity-Based Trajectory Tracking and Formation Control of Nonholonomic Wheeled Robots Without Velocity Measurements

This note proposes a passivity-based control method for trajectory tracking and formation control of nonholonomic wheeled robots without velocity measurements. Coordinate transformations are used to incorporate the nonholonomic constraints, which are then avoided by controlling the front end of the robot rather than the center of the wheel axle into the differential equations. Starting from the passivity-based coordination design, the control goals are achieved via an internal controller for velocity tracking and heading control and an external controller for formation in the port-Hamiltonian framework. This approach endows the resulting controller with a physical interpretation. To avoid unavailable velocity measurements or unreliable velocity estimations, we derive the distributed control law with only position measurements by introducing a dynamic extension. In addition, we prove that our approach is suitable not only for acyclic graphs but also for a class of non-acyclic graphs, namely, ring graphs. Simulations are provided to illustrate the effectiveness of the approach.

A dual-loop feedback trajectory tracking control for rock drilling hydraulically driven manipulator

This paper is devoted to proposing a feedback trajectory tracking control method for hydraulically driven rock drilling robotic manipulators. The rock drilling robot has a large-scale long boom and multiple joints (6R-2P), so the deformation of the arm may not be neglected. A kinematic model with the flexible deformation of the boom is developed by adding a modified coordinate transformation matrix to the general model. Each joint motion is determined by solving the inverse kinematic model in an optimization algorithm, which aims at minimizing the positional error and smoothing the motion. A dual-loop feedback controller is proposed to track the end-effector’s position and orientation. Based on the model predictive control (MPC) method, the inner-loop controller controls the cylinder motion by controlling the cylinder motion. The outer-loop controller uses the fuzzy-PID control to correct the position error which is caused by the inner-loop controller. Several reference trajectories are designed to validate the effectiveness of the proposed dual-loop control strategy, which demonstrates it has higher accuracy and lower control fluctuation than single-loop and other dual-loop controllers.

Adaptive Kinematic Control of Underwater Cable-Driven Parallel Robot

We previously proposed on the underwater cable-driven parallel robot (UCDPR), a system comprising multiple surface robots, and designed a modeling and trajectory tracking control method for it. However, the conventional trajectory tracking control of the UCDPR using the kinematic controller faced several issues. These included challenges in control gain tuning due to model uncertainty and a decline in trajectory tracking performance caused by changes in system characteristics due to environmental factors like current velocity. In response, this study focuses on the development of an adaptive kinematic controller. The aim is to mitigate the effects of uncertainties and other factors while ensuring effective trajectory tracking. This is achieved by incorporating an adaptive modification term into the conventional kinematic controller, which can be tuned adaptively in real-time. To validate the effectiveness of the adaptive kinematic controller, we conducted numerical simulations using a planar 2-DOF UCDPR.