Trajectory Tracking Control Algorithm Research Articles

Tracking Control of Single-Axis Feed Drives Based on ADRC and Feedback Linearisation

The accuracy of manufacturing highly characterises the performance of industrial motion control. However, detrimental effects such as nonlinear coupling, model uncertainty and unknown external disturbances severely affect trajectory tracking performance. In this paper, we proposed an ADRC and feedback linearisation-based control algorithm for the high-precision trajectory tracking of feed drives. The controller was rigorously designed to ensure the convergence of observer states and tracking error. The applicability of the proposed approach was successfully demonstrated via high-fidelity simulation, and the numerical results based on different tracking methods were compared.

A Model Predictive Control with Preview-Follower Theory Algorithm for Trajectory Tracking Control in Autonomous Vehicles

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module could calculate reference lateral acceleration at the preview point by PFT to update state variables, and generate a reference yaw rate in each prediction point. Since the preview range is increased, PFT makes the calculation of yaw rate more accurate. Through physical constraints, the MPC controller can achieve the best tracking of the reference path. The MPC problem is formulated as a linear time-varying (LTV) MPC controller to achieve a predictive model from nonlinear vehicle dynamics to continuous online linearization. The MPC-PFT controller method performs well by increasing the effective length of the reference path. Compared with MPC and PFT controllers, the effectiveness and robustness of the proposed method are proved by simulations of two typical working conditions.

Toward Safe and Personalized Autonomous Driving: Decision-Making and Motion Control With DPF and CDT Techniques

In this article, a novel approach of decision-making and motion control is designed for realizing safe and personalized driving of autonomous vehicles. A new lane-change intention generation model and a new lane-change decision-making algorithm are proposed. The feature of the proposed decision-making module is that the interactions between the ego vehicle and other surrounding vehicles are represented by the dynamic potential field (DPF) and embedded in the gap acceptance model to ensure the safety and personalization during driving. In addition, an integrated trajectory planning and tracking control algorithm, which incorporates the artificial potential field and constrained Delaunay triangulation (CDT) into the model predictive control framework, is developed. The newly developed integrated controller allows efficient execution of the expected motion. The proposed approach is tested under different driving conditions and further compared with an existing baseline method. The results show that the proposed approach is able to make safe and personalized decisions, and execute motion control more efficiently for automated driving under dynamic situations, validating its feasibility and effectiveness.

Obstacle avoidance and model‐free tracking control for home automation using bio‐inspired approach

AbstractThis article proposes a control algorithm for obstacle avoidance and trajectory tracking for a redundant‐manipulator in smart‐homes. The redundancy provides dexterity and flexibility for the applications like picking, dropping, and transporting objects, tracking predefined paths while avoiding obstacles. The obstacle avoidance is one of the critical problems that need to be addressed. Our proposed algorithm, zeroing neural network with beetle antennae search (ZNNBAS), unifies these two problems into a single constrained optimization problem, which includes a penalty function to reward the optimizer on avoiding obstacles while tracking the reference trajectory. The penalty function is based on the principle of maximizing the minimum distance between the joints of the manipulator and the obstacles. Gilbert Johnson Keerthi (GJK) algorithm is used to calculate the distance between the manipulator and the obstacle as it uses the 3D geometry of the object and manipulator. To test the working of ZNNBAS, we simulated the model of the KUKA LBR robotic manipulator. We used two reference trajectories, that is, hypotrochoid and a character “M,” with an arbitrarily shaped obstacle. The simulation results show that ZNNBAS was able to trace the reference path while successfully avoiding the obstacle accurately.

Preliminary design of the control needed to achieve underwater vehicle trajectories

This paper presents a method for preliminary design of the control which is needed to achieve underwater vehicle trajectories. The proposed way allows one to evaluate dynamics of underwater vehicle using a trajectory tracking control algorithm. At the first stage, we propose the controller, and at the second, we test dynamics of the system based on the properties resulting from the transformed equations of motion and the selected indexes. The controller, which is applicable for fully actuated vehicles, contains the system dynamics in the control gains. It takes into account not only model of the vehicle but also model of disturbances. The way for the dynamics investigation uses the transformed equations obtaining from the inertia matrix decomposition. Consequently, thanks to the observed properties, it is possible to estimate dynamics using the criteria set. The method is useful before real experiment to test various models of the vehicle, disturbances, and the control task. The procedure is based on simulation tests and the proposed criteria. Effectiveness of the approach is shown on two examples of 6 DOF underwater vehicle model and its modifications.

A Novel Fixed-Time Control Algorithm for Trajectory Tracking Control of Uncertain Magnetic Levitation Systems

In this research, a new robust control method is developed, which achieves a fixed-time convergence, robust stabilization, and high accuracy for trajectory tracking control of uncertain magnetic levitation systems. A hybrid controller is a combination of an adaptive fixed-time disturbance observer and a fixed-time control algorithm. First, to estimate precisely the total uncertain component in fixed-time, an adaptive disturbance observer is constructed. Then, a new robust control method is designed from a proposed fixed-time sliding manifold, disturbance observer's information, and a continuous fixed-time reaching law. A global fixed-time stability and convergence time boundary of the control system is obtained by Lyapunov criteria in which the settling time can be arbitrarily set using design parameters regardless of the system's initial state. Finally, the designed control strategy is implemented for a magnetic levitation system and its control performance is compared with other existing finite-time control methods to evaluate outstanding features of the proposed system. Trajectory tracking experiments in MATLAB/SIMULINK environment have been performed to exhibit the effectiveness and practicability of the designed approach.

Finite-Time Stabilization Procedures for Discrete-Time Nonlinear Systems in Feedback Form

New control procedures for finite-time stabilization of discrete-time nonlinear systems in the strict-feedback form are proposed. The proposed designs enjoy the properties of being dependent on one design parameter and the ability to bring the state vector to the origin in finite time. Moreover, the settling-time functions are estimated in terms of the initial state vector and the unique design parameter that regulates the rate of the finite-time convergence. Finally, a trajectory-tracking control algorithm is presented and approved by numerical simulations. The simulation results have shown the excellent performance of the closed-loop system for different values of the free design parameter.

Robot dynamic trajectory tracking control algorithm based on steady-state closed-loop learning

In order to improve the stability control ability of flexible lower limb exoskeleton robot, a dynamic trajectory tracking control algorithm of flexible lower limb exoskeleton robot based on steady-state closed-loop learning is proposed. Gyroscope and rangefinder are used as information sensors of flexible lower limb exoskeleton robot to collect position information of flexible lower limb exoskeleton robot, fuse collected positioning information of flexible lower limb exoskeleton robot, fuse physical information and measure parameters of flexible lower limb exoskeleton robot by using dynamic information measurement method, and obtain mapping feature set of Cartesian space according to trajectory components of flexible lower limb exoskeleton robot. The pose information of the flexible lower limb exoskeleton robot is obtained through the forward kinematics, and the information is enhanced according to the spatial position information. The steady-state closed-loop learning method is adopted to realize the adaptive learning of the robot dynamic trajectory tracking control. The simulation results show that this method is adaptive to the dynamic trajectory tracking control of the robot, and the positioning control ability of the robot is strong.

A review of industrial tracking control algorithms

Advanced manufacturing is characterised by machines that move an end effector through a given trajectory to perform operations such as cutting, grinding and printing. In many industrial machines, properties such as structural flexibility, external disturbances as well as spatially separate actuator and end effector make the tracking problem challenging. In this paper, a literature survey on trajectory tracking control algorithms is conducted to examine representative features of existing methods. Then the major classes of algorithms are compared on a commercial single-axis test bench to provide practitioners with a direct insight into the trade-off between performance and implementation.

Research on intelligent vehicle trajectory tracking based on model predictive control

Intelligent vehicle trajectory tracking lateral control is the key technology to realize intelligent driving. Aiming at the problems that the existing control methods have a small effective control area and poor control effect under cornering conditions or small road adhesion coefficients, a model predictive control (MPC) algorithm is proposed for trajectory tracking control. Based on the two-degree-of-freedom vehicle model, a state space equation is established and discretized to obtain a predictive model that meets the conditions. Then, the corresponding objective function is designed based on the ideal yaw angular velocity under the optimal preview control theory, and the input-output constraints and side-slip angle constraints are designed according to the control and state quantities. The controller model is established in MATLAB / Simulink, and the road model is built in CarSim for joint simulation. Compared with CarSim’s own algorithm, the changes in side acceleration and steering wheel angle are smoother and less oscillating. The maximum lateral deviation and lateral acceleration are also smaller, and the lateral stability of the car is improved. It has better adaptability on pavement with lower adhesion coefficient, and can also maintain control stability. The real vehicle test results are consistent with the simulation results, with a maximum lateral error of 0.44m and a maximum heading angle deviation of 1.43 °. Therefore, the trajectory tracking control algorithm based on model predictive control designed in this paper has significantly improved control accuracy and stability, and can maintain control stability even when the road surface adhesion coefficient is low.

Longitudinal and lateral control of autonomous vehicles in multi‐vehicle driving environments

Lane changes in multi-vehicle driving environments are one of the most challenging manoeuvres for autonomous vehicles. The key innovation of this study is to develop an integrated longitudinal and lateral trajectory planning and tracking control algorithm under vehicle-to-vehicle communication. This algorithm includes two levels: trajectory planning and path-following control. In the upper level, considering riding comfort, a collision-free lane-changing trajectory cluster is generated under different lane change durations. Then, the most appropriate trajectory from this cluster is provided by selecting the optimal lane change duration considering vehicle dynamics safety, collision avoidance of surrounding vehicles and driver preference. At the bottom level, a multiple-input multiple-output triple-step non-linear approach is proposed in the longitudinal and lateral path-following controller design. The stability of the closed-loop system is rigorously proven based on the Lyapunov function. Finally, the effectiveness of the proposed algorithm is verified with a high-fidelity and full-car model on the veDYNA platform.

Robust 3D Tracking Control of an Underactuated Autonomous Airship

The paper presents a new, robust control algorithm for position trajectory tracking in a 3D space, dedicated to underactuated airships. In order to take into account real characteristics of such vehicles, and to reflect practically motivated constraints, the algorithm assumes a highly uncertain system dynamics model. The tracking problem is solved in a uniform way, without dividing it into subtasks considered in 2D spaces, thanks to the introduction of an auxiliary tracking error. The proposed controller is based on the sliding mode approach. Its stability is investigated using Lyapunov theorem. Numerical simulations are conducted in order to verify properties of a closed-loop system for a generic model of the airship. Performance of the control system is examined via experiments in various scenarios using a prototype airship. The obtained results indicate that the control objectives are satisfied in practice with a reasonable accuracy. Moreover, it is shown that the controller is robust to some bounded additive measurement perturbations and delays in the control loop.

Modeling and Trajectory Tracking Control for Magnetic Wheeled Mobile Robots Based on Improved Dual-Heuristic Dynamic Programming

In this article, a mathematical model of a magnetic-wheeled mobile robot (MWMR) used for wall climbing in some special industrial sites is established, and to realize the precise motion control of the robot, an intelligent discrete algorithm for trajectory tracking control of the MWMR is presented. The robot is subjected to nonholonomic constraints when moving on the wall. The discrete mathematical model of the MWMR is established with the description of the kinematics and dynamics, where the dynamics are described by the second-order Lagrange's equations. Improved dual-heuristic dynamic programming (DHP) where the actor-critic structure adopts random vector functional link neural networks (RVFL NNs) is the main configuration of the trajectory tracking control algorithm. Moreover, the tracking control algorithm is supplied by a PD controller and a supervisory element to generate overall control signals. The improved strategy is to optimize the input layer weights of RVFL NNs by a genetic algorithm to improve the approximation performance of DHP. Simulations are performed to test the trajectory tracking control algorithm for this wall-climbing robot, and the results are compared with those of neural network tracking control algorithm. Comparative analysis verifies the effectiveness and advancement of the proposed method.

Real-Time Optimal Trajectory Generation and Control of a Multi-Rotor With a Suspended Load for Obstacle Avoidance

This letter presents real-time optimization algorithms on trajectory generation and control for a multi-rotor with a suspended load. Since the load is suspended through a cable without any actuator, movement of the load must be controlled via maneuvers of the multi-rotor, which brings about difficulties in operating this system. Additionally, the highly nonlinear dynamics of the system exacerbates the difficulties. While trajectory generation and control are essential for safety, energy efficiency, and stability, the aforementioned characteristics of the system add challenges. With this in mind, the authors propose real-time path planning and optimal control algorithms for collision-free trajectory generation and trajectory tracking. For the dynamics, simplified dynamic models of the system are proposed by considering time delay in attitude control of the multi-rotor. For collision avoidance, the vehicle, cable, and load are considered as ellipsoids with different sizes and shapes, and collision-free constraints are expressed in an efficient and nonconservative way. The augmented Lagrangian method is applied to solve the nonlinear optimization problem with the nonlinear constraints in real-time. For control of the system, model predictive control with a sequential linear quadratic solver is used. Several simulations and experiments are conducted to validate the proposed algorithm.

Design, Implementation, and Validation of Robust Fractional-Order PD Controller for Wheeled Mobile Robot Trajectory Tracking

In this paper, a trajectory tracking control algorithm is proposed based on the fractional-order PD (FOPD) controller for a Wheeled Mobile Robot (WMR). Firstly, an improved flat phase property is put forward as a robust controller tuning specification. This specification is capable of guaranteeing the flatness of the phase curve in a frequency interval, so the controlled system robustness can be improved. Then, the stabilization process is discussed with respect to the parameters of the FOPD controller through a visualized 3-dimensional surface, so both the stability and robustness of the controlled system can be guaranteed under the proposed controller. Furthermore, the implementation of the proposed robust FOPD controller is presented, which makes the control algorithm easy to be realized. At last, the effectiveness of the proposed trajectory tracking control algorithm is verified by the simulation and experiment results.

Adaptive PID control of multi-DOF industrial robot based on neural network

The control system of parallel robot, especially industrial robot, is a very complex multi-modal nonlinear system, which has the characteristics of time-varying, strong coupling and strong nonlinearity. Trajectory tracking control algorithm is a very important part of industrial robot control system. It is required that the algorithm can realize the continuous tracking of each joint of the robot and the processing and tracking of the desired trajectory. However, due to the strong influence of acceleration and speed on the trajectory tracking of industrial robots, the corresponding control difficulty and control accuracy are seriously affected. Based on the core idea of fuzzy neural network algorithm, the functional relationship between control error and arrival degree is established to improve the control quality of industrial robots. At the same time, combining with the PID feedforward control algorithm, the self-adaptive adjustment of PID parameters is realized, and the accuracy of the tracking algorithm is improved. In order to verify the superiority of the proposed trajectory tracking control algorithm over the traditional PID algorithm, the model of industrial robot is established by using the virtual simulation system Adams. At the same time, the model is simulated by joint experiment. Experimental results show that the trajectory control algorithm based on the proposed trajectory control algorithm is effective. This method has good control accuracy and stability.

Intuitive Planning, Generation, and Tracking of Trajectory for WMR With Mobile Computing Device and Embedded System

With the intention of delivering an intuitive and simple platform to plan, generate, and track trajectories with a WMR, this paper presents a technological integration of hardware and software. This technological integration consists of a mobile computing device with an app developed by authors for the trajectory planning and a differential drive WMR that possesses an embedded system, in which a trajectory generation algorithm and a trajectory tracking control algorithm -both proposed by authors - are programmed. The mobile computing device wirelessly drives the WMR through the embedded system. The app is developed on the basis of the sketch approach, since it allows drawing sketches of the trajectory intuitively on the mobile device. Also, the app geometrically scales the sketch coordinates to match them with the real WMR workspace. For the trajectory generation, these scaled coordinates are wirelessly sent to the embedded system, where the trajectory generation algorithm joins them by using Bezier polynomials and concatenation of straight-lines. Hence, the tracking task is carried out with the control algorithm, which is proposed departing from the dynamic model of the WMR and whose asymptotic stability proof is performed with the Lyapunov method. Experimental results verify that the technological integration successfully plans, generates, and tracks trajectories, even when the WMR is far from the initial coordinate of the desired trajectory. These results, corroborate the good performance and robustness of the proposed control algorithm. Thus, the introduced technological integration is intuitive and simple since users only have to draw a sketch on the mobile device to carry out the trajectory tracking task.

A Vehicle Trajectory Tracking Method With a Time-Varying Model Based on the Model Predictive Control

The vehicle trajectory tracking algorithm is one of the key and difficult issues of intelligent driving technologies. In current control algorithms for the vehicle trajectory tracking, there are three main assumptions: the standard working condition for the driving path, the same control model used for the entire control process, and a fixed value for the longitudinal vehicle speed. However, the above determinations in current control algorithms are inconsistent with the actual vehicle driving conditions. To overcome those problems, a vehicle trajectory tracking method with a time-varying model is proposed. The time-varying model is developed by using a two-dimensional vehicle kinematics model. This method considers the influences of the longitudinal speed and road curvature on the vehicle trajectory tracking stability under the low-speed complex driving condition. Thus, the proposed method can improve the trajectory tracking accuracy when the unmanned vehicle is located at the road with a sharp curvature under the low-speed complex driving condition. Moreover, the proposed model can achieve the real time calculation. Meanwhile, the prediction accuracy of the vehicle kinematics model is ensured. The proposed approach with the above characteristics can complete the trajectory tracking for the route composed of arbitrary curves. The results show that the proposed method can effectively improve the trajectory tracking stability of the unmanned vehicle on the roads with different curvatures under complex driving conditions.

Trajectory Tracking Control Algorithm for Autonomous Vehicle Considering Cornering Characteristics

Trajectory tracking control is a key technology in the research and development of autonomous vehicles. With the aim of addressing problems such as low control accuracy and poor real-time performance, which can occur easily when an autonomous vehicle avoids obstacles, this research focuses on the trajectory tracking control algorithm for autonomous vehicle considering cornering characteristics. First, the vehicle dynamics model and tire model are established through appropriate simplification. Then, based on the basic principle of model predictive control, a linear time-varying model predictive controller (LTV MPC) that considers the cornering characteristics is designed and optimized. Finally, using CarSim and MATLAB/Simulink software, a joint simulation model is established and the trajectory tracking performance of the controlled vehicle under different vehicle speeds and road adhesion conditions are tested through simulation experiments in combination with the double-shift line reference trajectory. The simulation results show the LTV MPC controller that considers cornering characteristics has good self-adaptability under complicated and severe working conditions, and no cases, such as car sideslip or track departure, were observed. Compared with other controllers and algorithms, the designed trajectory tracking controller has remarkable comprehensive performance, exhibits superior robustness and anti-interference ability, and significant improvements in the trajectory tracking control accuracy and real-time performance. The proposed control algorithm is of great importance in improving the tracking stability and driving safety of autonomous vehicles under complex extreme conditions and conducive to the further development and improvement of the technological level of intelligent vehicle driving assistance.

A model-free fuzzy adaptive trajectory tracking control algorithm based on dynamic surface control

According to the robot’s dynamics, a high performance algorithm based on dynamic surface control is introduced to track desired trajectory, and simulations are conducted on a selective compliance assembly robot arm-type manipulator to verify the algorithm. The traditional dynamic surface control is designed based on dynamic model, which requires exact model information. Due to the model uncertainty and complex environments, the tracking performance of the controller can be significantly decreased. Therefore, a model-free fuzzy adaptive dynamic surface controller is designed, by adopting a fuzzy system with Lyapunov self-adaptation law. The new controller efficiently improves the dynamic quality. The simulation results prove that the designed model-free controller ensures that all the states and signals of the closed-loop system are bounded, the system has a faster response speed and smaller steady-state error comparing with the traditional dynamic surface control using the selective compliance assembly robot arm model, and the tracking error converge to a very small scale. Besides, the proposed algorithm can track the desired trajectory with high performance without the prior knowledge of specific parameters from the experimental manipulator, which simplifies the complexity of building the control system.