Trajectory Tracking Control Scheme Research Articles

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

A Walking Trajectory Tracking Control Based on Uncertainties Estimation for a Drilling Robot for Rockburst Prevention

A walking trajectory tracking control approach for a walking electrohydraulic control system is developed to reduce the walking trajectory tracking deviation and enhance robustness. The model uncertainties are estimated by a designed state observer. A saturation function is used to attenuate sliding mode chattering in the designed sliding mode controller. Additionally, a walking trajectory tracking control strategy is proposed to improve the walking trajectory tracking performance in terms of response time, tracking precision, and robustness, including walking longitudinal and lateral trajectory tracking controllers. Finally, simulation and experimental results are employed to verify the trajectory tracking performance and observability of the model uncertainties. The results testify that the proposed approach is better than other comparative methods, and the longitudinal and lateral trajectory tracking average absolute errors are controlled in 10.23 mm and 22.34 mm, respectively, thereby improving the walking trajectory tracking performance of the walking electrohydraulic control system for the coal mine drilling robot for rockburst prevention.

Trajectory Tracking Control Design for 4WS Vehicle Based on Particle Swarm Optimization and Phase Plane Analysis

With the rapid development of today’s society, the traffic environment has become more and more complex. As an essential part of intelligent vehicles, trajectory tracking has attracted significant attention for its stability and safety. It is prone to poor accuracy and instability in extreme working conditions like high speed. In this paper, a trajectory tracking control strategy to ensure lateral stability at a high speed and low attachment limit conditions is proposed for distributed drive vehicles. The model predictive controller (MPC) was used to control the front wheel angle, and the particle swarm optimization (PSO) algorithm was designed to optimize the MPC control parameters adaptively. The sliding mode controller controls the rear wheel angle, and the vehicle instability degree is judged by analyzing the β − β˙ phase plane. The controllers of different instability degrees are designed herein. Finally, a torque divider is designed to consider the actuation anti-slip. The designed controller is verified by Carsim and MATLAB-Simulink co-simulation. The results show that the trajectory tracking controller designed in this paper effectively improves the tracking accuracy under the premise of ensuring stability.

Optimal trajectory tracking for uncertain linear discrete‐time systems using time‐varying Q‐learning

SummaryThis article introduces a novel optimal trajectory tracking control scheme designed for uncertain linear discrete‐time (DT) systems. In contrast to traditional tracking control methods, our approach removes the requirement for the reference trajectory to align with the generator dynamics of an autonomous dynamical system. Moreover, it does not demand the complete desired trajectory to be known in advance, whether through the generator model or any other means. Instead, our approach can dynamically incorporate segments (finite horizons) of reference trajectories and autonomously learn an optimal control policy to track them in real time. To achieve this, we address the tracking problem by learning a time‐varying ‐function through state feedback. This ‐function is then utilized to calculate the optimal feedback gain and explicitly time‐varying feedforward control input, all without the need for prior knowledge of the system dynamics or having the complete reference trajectory in advance. Additionally, we introduce an adaptive observer to extend the applicability of the tracking control scheme to situations where full state measurements are unavailable. We rigorously establish the closed‐loop stability of our optimal adaptive control approach, both with and without the adaptive observer, employing Lyapunov theory. Moreover, we characterize the optimality of the controller with respect to the finite horizon length of the known components of the desired trajectory. To further enhance the controller's adaptability and effectiveness in multitask environments, we employ the Efficient Lifelong Learning Algorithm, which leverages a shared knowledge base within the recursive least squares algorithm for multitask ‐learning. The efficacy of our approach is substantiated through a comprehensive set of simulation results by using a power system example.

Predefined-Time Tracking Control of Unmanned Surface Vehicle under Complex Time-Varying Disturbances

Aiming at the unmanned surface vehicle (USV) trajectory tracking control under complex time-varying environment, a predefined-time convergence sliding mode disturbance observer (PTC-SMO) is introduced to effectively handle the internal parameter uncertainties and external environmental disturbances, thereby guaranteeing precise compensation of the lumped disturbance term within a set time. Then, in order to achieve precise tracking of the desired trajectory using USV under a predetermined time constraint, a novel fast trajectory tracking control strategy with predefined-time convergence (PTC-FTTCS) is established to improve tracking performance and ensure that the trajectory tracking error converges quickly in the predefined time. Through rigorous comparative simulation under ideal conditions and time-varying disturbances, the results demonstrate reliable trajectory tracking and disturbance handling effects, and the tracking performance and disturbance observation performance are significantly better than state-of-the-art methods.

State-constrained control strategy for safe navigation trajectory tracking of hovercraft based on improved barrier Lyapunov function

This study addresses the challenge of trajectory tracking control for underactuated hovercraft by utilizing an improved integral barrier Lyapunov function to ensure safe and efficient navigation in the presence of uncertain dynamics and environmental disturbances. The research introduces an improved barrier Lyapunov function tailored for both constrained and unconstrained systems by integrating prescribed performance control (PPC) with a log-type barrier Lyapunov function (LBLF). This function effectively limits tracking errors in both position and heading to within a predetermined range. To ensure the hovercraft's navigational stability at high speeds, the paper presents a novel, time-varying integral barrier Lyapunov function (IBLF) with both unilateral and bilateral asymmetric constraints, specifically designed to control surge speed and yaw angular velocity. This ensures the maintenance of surge speed above the critical resistance peak speed and keeps the yaw angular velocity within a secure operational band. The study also introduces a finite-time disturbance observer (FTDO) to estimate the system's uncertainties. Theoretical analysis confirms that the tracking errors are ultimately uniformly bounded, establishing Lyapunov stability. Simulation results substantiate the superiority and efficacy of the proposed control strategy.

Adaptive Terminal Sliding Mode Trajectory Tracking Control for Autonomous Vehicles Considering Completely Unknown Parameters and Unknown Perturbation Conditions

In the actual implementation of autonomous vehicle controller and related applications, it is difficult to obtain all the actual parameters of the vehicle. Considering factors such as uneven pavement and different pavement conditions, it is difficult to accurately establish the vehicle dynamic system model. Based on the non-singular terminal sliding mode and adaptive control theory, this paper establishes a trajectory tracking control strategy for an autonomous vehicle with unknown parameters and unknown disturbances. Firstly, the complex trajectory tracking problem is decoupled from the position and heading angle tracking problem, and the preview error equation is established. Secondly, a non-singular terminal sliding mode (NTSM) controller is established to stabilize the trajectory tracking error to the origin in a finite time, and adaptive laws are proposed to estimate the unknown vehicle parameters to adapt to environmental changes. Through the CarSim–Matlab platform, typical working conditions are implemented to verify the proposed controller. Our experimental outcomes affirm that the NTSM controller effectively guarantees the autonomous vehicle’s accurate following of the reference path, ensuring smooth control inputs throughout the entire process.

Disturbance Observer-Based Fixed-Time Tracking Control for a Tilt Trirotor Unmanned Aerial Vehicle

This paper proposed a new fixed-time trajectory tracking control strategy based on the disturbance observer (DOB) for a tilt trirotor unmanned aerial vehicle (TTUAV) which is subject to unknown external disturbances. To facilitate the TTUAV's trajectory tracking controller design, the dynamic model of the TTUAV is divided into two subsystems, the position subsystem (outer-loop) and the attitude subsystem (inner-loop). For the dynamics of the TTUAV's outer-loop, the unknown external disturbances consist of the unknown wind disturbances, the unknown aerodynamic frictions forces, the lateral force generated by the rear servo and the states coupling between the outer-loop and the inner-loop. Then, a nonlinear DOB is designed to estimate the unknown external disturbances, and a nonsingular terminal sliding-mode controller (NTSMC) is further developed to drive the TTUAV's position tracking errors to zero in a fixed time. For the dynamics of the TTUAV's inner-loop, the unknown external disturbances are mainly introduced by the aerodynamic frictions torques. Then, a modified sliding mode controller is designed to reject the unknown external disturbances, and to ensure that the attitude tracking errors converge to zero exponentially. In addition, a composite stability analysis based on Lyapunov stability theory is provided to guarantee the fixed-time convergence of the closed-loop dynamics of the TTUAV. Finally, the results of the real-time experiments are presented to verify the effectiveness of the proposed control strategy.

A fast dynamic pose estimation method for vision-based trajectory tracking control of industrial robots

Vision-based robotic trajectory tracking control is considered a promising technology. However, the slow sampling rate and latency of the vision sensor enormously limit the tracking performance. To conquer the issues, this paper proposes a dual-space error-state Kalman filter (DS-ESKF). By combining the encoder measurement with the vision measurement, the end-effector’s pose between adjacent vision measurements is restored, and the pose estimation cycle is synchronized with the control cycle. The critical distinguishing of DS-ESKF is that the encoder-driven error-state kinematics for the industrial robot is reconstructed. The experimental results on the Staubli TX60 industrial robot show that compared with the existing dual-rate Kalman filters (DR-KF), DS-ESKF can reduce estimation errors by about 50 % and have robust estimation performance. By applying the trajectory tracking control scheme combining DS-ESKF with a simple PID controller to Staubli TX60, the tracking accuracy is significantly improved (±0.11 mm for position and ± 0.05°for orientation).

Event-triggered trajectory tracking control for USV with prescribed performance and time delay based on differential flatness

This paper presents a trajectory tracking control scheme for underactuated surface vessels (USVs) with input delay. Firstly, the underactuated surface vessel system is transformed into a fully actuated system using differential flatness theory. To estimate the unknown nonlinear terms introduced in the transformation process, a fuzzy neural network (FNN) is employed. Secondly, to conserve control resources and communication bandwidth, the controller of the system under prescribed performance is designed using the backstepping method. This method updates the controller according to an event-triggered condition that is designed using a Lyapunov function. Finally, theoretical proof and simulation experiments are conducted to demonstrate the convergence and effectiveness of the proposed method.

A novel cascaded trajectory tracking control for UUVs under time-varying disturbances

In this paper, a novel cascaded trajectory tracking control strategy based on the characteristics of kinematics and dynamics is proposed for unmanned underwater vehicles (UUVs) under complex disturbances. A kinematic controller based on an improved model predictive control (MPC) is designed to solve the speed jump problem by considering system constraints. Moreover, an improved whale optimizer with elite strategy (EIWOA) is used to the rolling optimization process of MPC, ensuring that the global best solution is derived by obtaining the elite individuals in the population. Besides, a dynamic controller that consists of an adaptive disturbance observer and a fuzzy integral sliding mode control (ADO-FISMC) is proposed to obtain optimal thrust force under time-varying disturbances. The benefit of ADO lies in that it can estimate time-varying disturbances without specific information about disturbances. The fuzzy logic system is introduced to alleviate the chattering of sliding mode control. The simulation results demonstrate the great tracking performance of the cascaded trajectory tracking controller. The viability of the proposed algorithm is also confirmed by trials conducted in water pools.

Fixed‐time sliding mode trajectory tracking control for marine surface vessels under mismatched conditions and input saturation

SummaryThis paper addresses a trajectory tracking control problem for marine surface vessels (MSVs) in the presence of mismatched conditions and input saturation. Firstly, an MSV model under mismatched conditions is established to solve the problem of unreasonable modeling methods in the existing literature. Secondly, fixed‐time disturbance observers (FXDOs) are designed, where the designed FXDOs not only avoid selecting complicated parameters but also has simple structures, and the disturbance estimation errors can converge to the origin within a setting time. Thirdly, based on the FXDOs and an anti–saturation auxiliary dynamic system, a trajectory tracking control scheme in the presence of mismatched conditions and input saturation is constructed by virtue of fixed‐time integral sliding mode control (SMC), and the actual tracking error signals are uniformly fixed‐time bounded rather than finite‐time one. Fourthly, in order to decrease theoretical calculation values of the original setting time in fixed‐time control, the new setting time under three different parameter conditions is derived, and thus reducing the conservatism. Finally, the simulation results are provided to show the effectiveness and superiority of the designed tracking control scheme.

Event-triggered model predictive-preview control strategy for trajectory tracking of autonomous vehicle

This paper proposes an event-triggered model predictive-preview control strategy for autonomous vehicle trajectory tracking. First, the dynamic equation is established based on the preview road curvature and the vehicle’s 2 degree-of-freedom relationship. A model predictive tracking controller is designed by predicting the system dynamics in the future. Second, to reduce the computational burden of the controller, the triggering conditions are designed according to the system’s stability and feasibility. The proposed event-triggered model predictive-preview control strategy not only makes the autonomous vehicles maintain tracking accuracy but also reduces the number of online optimization. Then, asymptotically stable of closed-loop systems are proved by using Lyapunov’s theorem. Finally, simulation experiments show that the proposed strategy has some advantages over traditional model predictive control in terms of improving vehicle tracking accuracy and reducing algorithm complexity.

H[formula omitted] finite-time prescribed performance trajectory tracking control of MSVs with self-adjusting neural networks

The paper proposes a robust adaptive finite-time prescribed performance trajectory tracking control scheme for marine surface vessels (MSVs) under unknown external disturbance and model uncertainty, based on H∞ control and self-adjusting neural networks (SANN). Firstly, to tackle the challenge of unknown velocity, a high-gain observer is introduced. Secondly, SANN is designed to tackle model uncertainty, achieving a balance between the optimal number of neurons and the best expected performance, thus saving network resources. Simultaneously, finite-time (FT) auxiliary functions, error transformation functions, and H functions are introduced, ensuring a bounded expected decay level with L2 norm within FT. Finally, by combining backstepping, SANN, prescribed performance control and FTH∞ control methods, the system ensures the achievement of practically finite-time stable using fewer network resources under prescribed performance conditions. Simulation results validate the effectiveness of the proposed controller.

Fast Finite-Time Super-Twisting Sliding Mode Control with an Extended State Higher-Order Sliding Mode Observer for UUV Trajectory Tracking

This paper proposes a trajectory tracking control scheme consisting of a fast finite-time super-twisting sliding mode control (FSTSMC) approach and an extended state higher-order sliding mode observer (ESHSMO) for unmanned underwater vehicles (UUVs) with external disturbances and model uncertainties. Firstly, an extended state higher-order sliding mode observer with the finite-time convergence is designed based on the higher-order sliding mode technique and the extended state observer technique. Next, on the basis of disturbances and model uncertainties observation, a fast finite-time super-twisting sliding mode control approach is proposed, and the finite time stabilization property of the tracking errors is proved by Lyapunov theory. Finally, through numerical simulation and experiment in a water pool, it has been verified that the proposed control scheme has achieved the high control precision, the smaller chattering, the disturbance compensation and the fast finite-time convergence in UUV trajectory tracking.

An adaptive trajectory tracking control scheme for a novel fully actuated multirotor unmanned aerial vehicle without using velocity signals

SummaryThis paper introduces a novel fully actuated multirotor unmanned aerial vehicle (UAV) and develops an adaptive control scheme for it without relying on velocity signals. Conventional multirotors are limited by their strong coupling between translation and rotation motion, which makes it difficult to operate one motion without affecting the other. However, this novel multirotor's fully actuated design allows for independent translation and rotation motion, leading to better operational performance and expanded application scope. Additionally, velocity measurement signals can be prone to noise pollution and signal drift, making them unreliable for control purposes. Therefore, this proposed control scheme is developed without using velocity signals. The study utilizes a control performance improving method and guarantees stability of the closed‐loop system using the direct Lyapunov method. Finally, numerical simulations are employed to demonstrate the effectiveness of the proposed control scheme.

Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method

In order to better meet the practical application needs of mobile robots, this study innovatively designs an autonomous obstacle avoidance and trajectory planning control strategy with low computational complexity, high cost-effectiveness, and the ability to quickly plan a collision-free smooth trajectory curve. This article constructs the kinematic model of the mobile robot, designs a dual-loop trajectory tracking control strategy for position control law and attitude control law algorithms, and improves the traditional artificial potential field method to achieve a good obstacle avoidance strategy for mobile robots. Based on the dual-loop trajectory tracking control and the improved artificial potential field method, the autonomous obstacle avoidance and trajectory planning scheme of the mobile robot is designed, and closed-loop stability verification and analysis are conducted on the overall control system. And through the detailed simulation and experiments, the advantages of the proposed method in trajectory tracking accuracy and motion stability compared to the existing methods are verified, showing good effectiveness and feasibility and laying a good foundation for the application of mobile robots in practical complex scenes.

Research on trajectory tracking control of ocean unmanned aerial vehicles based on disturbance observer and nonlinear sliding mode

This paper aims to solve the problem of real time tracking of unmanned aerial vehicle (UAV) with external disturbances, model uncertainty, and multiple control parameter tuning during wave glider (WG) navigation. Firstly, the dynamic model of UAV and WG is instituted; Secondly, an Expanded State Observer (ADOB) is proposed to estimate the total perturbations in real time, including model uncertainties and external wind perturbations; Moreover, the ADOB is integrated with a nonlinear integral sliding mode control to generate a nonlinear sliding mode controller (ASMC) with a compound disturbance observer for the trajectory tracking control strategy; Finally, the bandwidth parameterization theory is used to tune the parameters of the ASMC controller. Simulation and experimental results show that the UAV trajectory tracking landing control scheme proposed in this paper can effectively solve the real-time tracking problem of the UAV during WG navigation.

Position and Attitude Tracking Controllers Using Lyapunov Transformations for Quadrotors

In this paper, a novel feedback control strategy for quadrotor trajectory tracking is designed and experimentally tested with proof of exponential stability, using the Lyapunov transformations theory. The controller is derived from an inner-outer loop control structure, namely by considering the position system coupled through an interconnection term with the attitude system. For the design of the position controller, the considered dynamics are worked on the body frame, which is uncommon in the literature, and its synthesis derives from theories such as Pontryagin’s maximum principle, Lyapunov theory, and Linear Quadratic Regulator (LQR), which ensure Input-to-state stability, steady-state optimality, and global exponential stability. The attitude system is based on an error quaternion parameterization via a nonlinear coordinate transformation matrix followed by a state input feedback, rendering the system linear and time-invariant. Under a correct transformation, LQR theory ensures almost exponential stability and steady-state optimality for the overall interconnected closed-loop systems. Experimental and simulation results illustrate the performance of the tracking system onboard a quadrotor.

A unified barrier function-based trajectory tracking control for hovercraft with asymmetric dynamic safety constraints

This paper addresses a trajectory tracking control scheme based on a unified barrier function for hovercraft subject to asymmetric dynamic safety constraints. Firstly, a non-affine model of hovercraft has been built and aims to estimate the lumped disturbance, an extended state observer is utilized. Secondly, for the sake of position constraints, virtual velocity control law is obtained by utilizing a unified barrier function (UBF). Thirdly, a constraint control scheme according to UBF is presented to address asymmetric safety constraint problems of hovercraft. The proposed method can transform the original constrained hovercraft control into an equivalent “non-constrained” one and guarantee the three velocities of hovercraft within asymmetric boundaries with requirements of safe performance during motion respectively. In addition, aims to handle the issue of the virtual control law's differential explosion, and considering that the output torque of the controller should be limited to a certain range, a bioinspired neurodynamic model (BNDM) is adopted. The total system is ultimately uniformly bounded (UUB) via Lyapunov stability theories and the stability lemma of the cascade system. Finally, obtained simulation results prove the effectiveness of the proposed control scheme.