Trajectory Tracking Control Algorithm Research Articles

A trajectory tracking control method for the discharge arm of the self-propelled forage harvester

The cooperative operation between the self-propelled forage harvester and the trailer aims to achieve precise and automatic forage unloading. The discharge arm serves as the core structure for conveying forage, and the precision and speed of its motion control are crucial factors influencing the efficiency of forage harvesting. In this context, we proposed a trajectory tracking control method for the discharge arm based on an improved particle swarm optimization (IPSO)-PID controller. Firstly, we utilized the Denavit-Hartenberg (D-H) model of the discharge arm for a positive kinematics solution and the geometric resolution and linear fitting method for the inverse kinematics solution. Secondly, we employed the polynomial interpolation method for trajectory planning on the joint space of the discharge arm, and the PSO algorithm for time-optimal trajectory planning. Then, we designed an IPSO-PID trajectory tracking control algorithm and built an Amesim-Simulink co-simulation model for multiple simulation experiments. Finally, we conducted several performance tests of the discharge arm automatic control system in the workstation and the field, respectively. The experiment results indicate that the performance of the IPSO-PID controller exceeds that of all other controllers, which can meet the discharge arm’s motion control accuracy and speed requirements. Our research results are of great significance for improving the productivity and automation process of the self-propelled forage harvester and provide valuable references for research on automatic and precise control of material loading in other agricultural cooperative harvesting.

PID Controller Based on Improved DDPG for Trajectory Tracking Control of USV

When navigating dynamic ocean environments characterized by significant wave and wind disturbances, USVs encounter time-varying external interferences and underactuated limitations. This results in reduced navigational stability and increased difficulty in trajectory tracking. Controllers based on deterministic models or non-adaptive control parameters often fail to achieve the desired performance. To enhance the adaptability of USV motion controllers, this paper proposes a trajectory tracking control algorithm that calculates PID control parameters using an improved Deep Deterministic Policy Gradient (DDPG) algorithm. Firstly, the maneuvering motion model and parameters for USVs are introduced, along with the guidance law for path tracking and the PID control algorithm. Secondly, a detailed explanation of the proposed method is provided, including the state, action, and reward settings for training the Reinforcement Learning (RL) model. Thirdly, the simulations of various algorithms, including the proposed controller, are presented and analyzed for comparison, demonstrating the superiority of the proposed algorithm. Finally, a maneuvering experiment under wave conditions was conducted in a marine tank using the proposed algorithm, proving its feasibility and effectiveness. This research contributes to the intelligent navigation of USVs in real ocean environments and facilitates the execution of subsequent specific tasks.

Fuzzy Adaptive Whale Optimization Control Algorithm for Trajectory Tracking of a Cable-Driven Parallel Robot

Fuzzy Adaptive Whale Optimization Control Algorithm for Trajectory Tracking of a Cable-Driven Parallel Robot

Nonlinear terminal sliding mode trajectory tracking control algorithm for industrial robots based on dung beetle optimizer

Abstract To enhance the precision of trajectory tracking control in industrial robots, a nonlinear end-to-end sliding mode trajectory tracking control algorithm for industrial robots based on the dung beetle algorithm is proposed. By employing nonlinear terminal sliding mode control to resolve the issue of inadequate trajectory tracking control performance in industrial robots, and integrating the dung beetle optimizer (DBO) algorithm for control parameter adjustment, significant enhancements are achieved in trajectory tracking accuracy.

Development of a digital twin system for snake endoscope manipulator in fusion reactors

Tokamak fusion is one of the solutions to the energy crisis. The environment of the vacuum chamber as a reaction site is extreme, so it needs to be observed during the operation period. This paper has developed a digital twin system for the snake endoscope manipulator (SEM) system, designed to observe of the fusion reactor vacuum chamber. The system includes a five-dimensional model of the SEM digital twin and a three-category architecture encompassing perception, data, and interaction. Additionally, a visualization and interaction system based on ROS-Unity has been developed to depict the working conditions of the SEM accurately. A terminal traction-based trajectory tracking control algorithm has been designed, enabling the SEM to maneuver flexibly within the confined space of the vacuum chamber to avoid collisions and prevent additional damage to the vacuum chamber. The system has integrated a Python-ROS-Unity-based algorithm for joint simulation channel development, which has been used for the virtual simulation experiments of SEM to validate the algorithms and collect data. Furthermore, a prototype has been constructed for virtual-to-real mapping experiments. Experiments show the digital twin system is feasible, with low latency, high sync, and stable operation, which verifies the feasibility of the system.

Backstepping-Based Quasi-Sliding Mode Control and Observation for Electric Vehicle Systems: A Solution to Unmatched Load and Road Perturbations

The direct current (DC) motor is the core part of an electrical vehicle (EV). The unmatched perturbation of load torque is a challenging problem in the control of an EV system driven by a DC motor and hence a deep control concern is required. In this study, the proposed solution is to present two control approaches based on a backstepping control algorithm for speed trajectory tracking of EVs. The first control design is to develop the backstepping controller based on a quasi-sliding mode disturbance observer (BS-QSMDO), and the other controller is to combine the backstepping control with quasi-integral sliding mode control (BS-QISMC). In the sense of Lyapunov-based stability analysis, the ultimate boundedness of the proposed controllers has been detailedly analyzed, assessed, and evaluated in the presence of unmatched perturbation. A modified stability analysis has been presented to determine the ultimate bounds of disturbance estimation error for both controllers. The determination of ultimate bound and region-of-attraction for tracking and estimation errors is the contribution achieved by the proposed control design. The performances of the proposed controllers have been verified via computer simulations and the level of ultimate bounds for the estimation and tracking errors are the key measures for their evaluation. Compared to BS-QISMC, the results showed that a lower level of ultimate boundedness with a higher convergent rate can be reached based on BS-QSMO. However, a higher control effort can be exerted by the BS-QSMO controller as compared to BS-QISMC; and this is the price to be paid by the BS-QSMO controller to achieve lower ultimate boundedness with a faster convergence rate.

Self-triggered fuzzy trajectory tracking control for the stratospheric airship

A self-triggered trajectory tracking control algorithm, which considers unknown disturbance and actuator saturation, has been studied to address the energy and onboard equipment life limitation problems of stratospheric airships. The controller is based on a backstepping-sliding mode method, utilizing the fuzzy logic systems and auxiliary systems to handle unknown disturbance and actuator saturation, respectively. Based on the continuity of the control law, the self-triggered condition is designed whose paradigm is used to build the fuzzy logic systems. Compared with the existing stratospheric airships event-triggered controller, continuous state detection and calculation are avoided. It is proved that the tracking errors and the weight matrix errors of the fuzzy logic system are uniformly ultimately bounded both at the trigger moment and within the trigger interval. Additionally, Zeno behavior is avoided without imposing additional parameter restrictions. Simulation results demonstrate the effectiveness of the proposed algorithm. Based on execution frequency, the proposed algorithm can conserve 98.3% of resources compared to the traditional algorithm and 97.5% of resources compared to the event-triggered algorithm.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Compliant variable admittance adaptive fixed-time sliding mode control for trajectory tracking of robotic manipulators

Abstract This paper presents a compliant variable admittance adaptive fixed-time sliding mode control (SMC) algorithm for trajectory tracking of robotic manipulators. Specifically, a compliant variable admittance algorithm and an adaptive fixed-time SMC algorithm are combined to construct a double-loop control structure. In the outer loop, the variable admittance algorithm is developed to adjust admittance parameters during a collision to minimize the collision time, which gives the robot compliance property and reduce the rigid collision influence. Then, by employing the Lyapunov theory and the fixed-time stability theory, a new nonsingular sliding mode manifold is proposed and an adaptive fixed-time SMC algorithm is presented in the inner loop. More precisely, this approach enables rapid convergence, enhanced steady-state tracking precision, and a settling time that is independent of system initial states. As a result, the effectiveness and improved performance of the proposed algorithm are demonstrated through extensive simulations and experimental results.

Research on two stage obstacle-avoidance trajectory planning and trajectory tracking control in curves

The existing obstacle-avoidance trajectory planning and trajectory tracking control algorithms have limitations such as long-time consumption, high failure rate in dynamic traffic environments, and insufficient trajectory tracking accuracy in curved roads. Based on the above problems, this paper designs a two stage obstacle-avoidance trajectory planner based on nonlinear optimization theory. In first stage Part-NLP, only considering the safety obstacle avoidance, a point mass model and linearization constraints are established to quickly solve the initial trajectory. In the second stage Full-NLP, considering smooth soft constraints comprehensively, the initial trajectory is optimized by establishing driving corridors and a lightweight iterative framework. In control module, this paper selects a linear quadratic form lateral trajectory tracking controller, and the parameters were optimized through the carnivorous plant algorithm. The joint simulation results show that in dynamic traffic environment of curved roads, the two stage planner proposed can accurately plan safe and smooth obstacle avoidance trajectories, and there is a significant reduction in time consumption compared to traditional NLP algorithms. The control strategy can accurately track the planned trajectories, with lateral error controlled within plus or minus 0.1 m, heading error controlled within plus or minus 0.15 rad, speed tracking error controlled within plus or minus 0.15 m/s, and vehicle yaw angle error controlled within plus or minus 0.04 rad; the hardware-in-loop test results indicate that the controller can achieve real-time and accurate trajectory tracking.

Quadrotor Modeling Approaches and Trajectory Tracking Control Algorithms: A Review

Quadrotor unmanned aerial vehicles are utilized in basically every sector of society, including the business, civil, and military industries. Popular applications include delivery, agriculture, target-acquisition, surveying, surveillance, and rescue. They are widely used due to their exceptional features such as accuracy, capability to perform swift inspections, simplicity in deploying perilous and uncertain missions, and additional praiseworthy attributes. This article presents a comprehensive analysis of the theoretical frameworks that have been proposed for the purpose of quadrotor modelling and control. Detailed examinations are conducted on every methodology that underpins the control algorithms, spanning from traditional linear to modern. The analysis looks at hybrid control technique models, which incorporate adaptive components across multiple controllers to improve overall performance and resilience by addressing individual algorithm shortcomings. This analysis also delves deeper into potential future research avenues. These include the development of learning-based or hybrid methodologies that employ machine learning and artificial intelligence to optimize performance and adaptability. For instance, model reference adaptive control systems can learn adaptation laws through machine learning techniques, as opposed to depending on predefined adaptation laws. By training neural networks or fuzzy logic controllers to forecast optimal adaptation parameters based on sensor data, the quadrotor can adjust to fluctuating conditions more effectively. A comparison table is provided to elaborate on the advantages, disadvantages, and hybrid versions of each control algorithm. This will serve as a concise guide that will promote innovation, facilitate the selection and integration of appropriate control algorithms, and enhance the functionality of quadrotor control systems.

Trajectory Tracking Control Algorithm of Two-wheel Rutting Model

In the development of unmanned two-wheeled self-balancing vehicle, it is very important to consider the trajectory tracking of unmanned two-wheeled self-balancing vehicle. In order to study the track tracking problem of unmanned two-wheeled self-balancing vehicle, the kinematic model of unmanned two-wheeled vehicle and the relation between its roll Angle and the kinematic model were established. The simulation platform is built to realize the unmanned two-wheeled vehicle and realize the circular track tracking at 5m/s, and the tracking performance of the track tracking controller under the circular track is verified.

Fast Trajectory Tracking Control Algorithm for Autonomous Vehicles Based on the Alternating Direction Multiplier Method (ADMM) to the Receding Optimization of Model Predictive Control (MPC).

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC.

Trajectory tracking control of unmanned marine vehicles with thruster faults based on broad learning system

The presence of unknown nonlinearities in the model of unmanned marine vehicles is inevitable. This paper proposes a new trajectory tracking control algorithm for nonlinear unmanned marine vehicles with model uncertainty, ocean disturbances and thruster faults. Broad learning system is first employed to approximate the nonlinear functions of the model, and an adaptive mechanism is used to estimate the unknown bounds of disturbances and thruster faults. And sliding mode controller is designed for unmanned marine vehicles with unknown nonlinearity and thruster faults to ensure the asymptotic stability of the tracking trajectory error system. It should be mentioned that the proposed approximator based on broad learning system can reduce the calculation time and decrease the estimation error arbitrarily. Finally, simulation studies have verified the effectiveness of the proposed control scheme.

A Self-Adaptive Double Q-Backstepping Trajectory Tracking Control Approach Based on Reinforcement Learning for Mobile Robots

When a mobile robot inspects tasks with complex requirements indoors, the traditional backstepping method cannot guarantee the accuracy of the trajectory, leading to problems such as the instrument not being inside the image and focus failure when the robot grabs the image with high zoom. In order to solve this problem, this paper proposes an adaptive backstepping method based on double Q-learning for tracking and controlling the trajectory of mobile robots. We design the incremental model-free algorithm of Double-Q learning, which can quickly learn to rectify the trajectory tracking controller gain online. For the controller gain rectification problem in non-uniform state space exploration, we propose an incremental active learning exploration algorithm that incorporates memory playback as well as experience playback mechanisms to achieve online fast learning and controller gain rectification for agents. To verify the feasibility of the algorithm, we perform algorithm verification on different types of trajectories in Gazebo and physical platforms. The results show that the adaptive trajectory tracking control algorithm can be used to rectify the mobile robot trajectory tracking controller’s gain. Compared with the Backstepping-Fractional-Older PID controller and Fuzzy-Backstepping controller, Double Q-backstepping has better robustness, generalization, real-time, and stronger anti-disturbance capability.

Research on Coupled Control Algorithm for Trajectory Tracking of Rear-Wheel Distributed Drive Vehicles

Research on Coupled Control Algorithm for Trajectory Tracking of Rear-Wheel Distributed Drive Vehicles

Collision-Free Model Predictive Trajectory Tracking Control for UAVs in Obstacle Environment

In this paper, we propose a collision-free model predictive trajectory tracking control algorithm for unmanned aerial vehicles (UAVs) in environments with both static obstacles and dynamic obstacles. Collision avoidance is ensured by obtaining outer polyhedral approximations of each interval of the dynamic obstacles trajectories based on MINVO basis, and then optimizing a plane to separate the polyhedra and the trajectory of the UAV. By incorporating the resulting computationally efficient collisionfree constraints and divers physical constraints, a model predictive control (MPC) optimization problem is formulated with a tailored terminal constraint set, which can be solved by a standard nonlinear programming solver. Moreover, the control theoretic properties are established, including recursive feasibility, the guarantee of collision avoidance, as well as closed-loop stability. Finally, the efficacy of the proposed algorithm is successfully evaluated by a simulation in a multi-obstacle environment.

A Survey of Intelligent Driving Vehicle Trajectory Tracking Based on Vehicle Dynamics

<div>Trajectory tracking control, as one of the core technologies of intelligent driving vehicles, determines the driving performance and safety of intelligent driving vehicles and has received extensive attention and research. In recent years, most of the research results of trajectory tracking control are only applicable to conventional working conditions; however, the actual operating conditions of intelligent driving vehicles are complex and variable, so the research of trajectory tracking control algorithm should be extended to the high-speed low-adhesion coefficient, large curvature, variable curvature, and other compound limit working conditions. This requires more consideration of the vehicle dynamics in the controller design. In this article, a comprehensive review of trajectory tracking control under extreme operating conditions is conducted from three levels: vehicle dynamics model, vehicle speed tracking (longitudinal motion control), and path tracking (transverse motion control), and the existing research results are analyzed and summarized to obtain the research trends and pain points and difficulties in each field. On this basis, the future outlook of trajectory tracking control is proposed, which is expected to provide some help and inspiration to the research workers in this field.</div>

Coupled lateral and longitudinal trajectory tracking control with a modified vehicle kinematics model for autonomous vehicles

Abstract The paper proposes a coupled lateral and longitudinal trajectory tracking control algorithm based on model predictive control (MPC) to enhance the precision and stability of trajectory tracking of autonomous vehicles. The coupled MPC controller is developed based on a modified vehicle kinematics model, which simultaneously takes the steering angle and the longitudinal speed as control variables. The modified vehicle model and the coupled MPC controller are verified by CarSim and MATLAB/Simulink co-simulation experiments. Simulation results demonstrate that, at the cost of 12 percent increase in average computational time, the proposed coupled MPC controller leads to an approximate 48 percent reduction in tracking error compared to the benchmarking coupled lateral and longitudinal MPC controller based on the classic kinematics model.

Adaptive Control Algorithm for Trajectory Tracking of Underactuated Unmanned Surface Vehicle (UUSV)

The ability to track the trajectory or path on the sea surface remains a key measurement in the control system of an unmanned surface vehicle (USV). In this research, the designed algorithm defines the path and minimizes the disturbances to zero. Underactuated USVs are ships or boats, which operate on the water surface without a crew and the underactuated system has low actuators than its degree of freedom (DOF). The adaptive control strategy is applied to the unbounded system as the ocean due to its high performance, while the robust control system attains high performance in the bounded system. To consider the trajectory tracking of UUSV and provide an optimal control strategy for a ship in the presence of external disturbances, the study presents a controller-based on model reference adaptive control with an integrator (MRACI), which guarantees the stability of a closed-loop system. The vehicle experiences variations in the system response due to external disturbance. This abovementioned scheme reduces the variations to nearly equal to zero making the vehicle stable. First, use computer-based simulation to verify the proposed controller under two different scenarios. Then, simulation results show that the designed scheme lowers the errors and performs well.