Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution

Parking difficulties have become a social issue that people have to solve.Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents.The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method(RF-LNMPC)in order to improve the overall path tracking accuracy in parking conditions.Firstly,A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively.Secondly,the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization,of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution.Thirdly,the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented.The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically.Finally,the proposed RF-LNMPC is implemented on a selfdriving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions.The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.

Observer-Based Path Tracking Controller Design for Autonomous Ground Vehicles With Input Saturation

This paper investigates the problem of path tracking control for autonomous ground vehicles(AGVs),where the input saturation,system nonlinearities and uncertainties are considered.Firstly,the nonlinear path tracking system is formulated as a linear parameter varying(LPV)model where the variation of vehicle velocity is taken into account.Secondly,considering the noise effects on the measurement of lateral offset and heading angle,an observer-based control strategy is proposed,and by analyzing the frequency domain characteristics of the derivative of desired heading angle,a finite frequency H_∞index is proposed to attenuate the effects of the derivative of desired heading angle on path tracking error.Thirdly,sufficient conditions are derived to guarantee robust H_∞performance of the path tracking system,and the calculation of observer and controller gains is converted into solving a convex optimization problem.Finally,simulation examples verify the advantages of the control method proposed in this paper.

MPC-based path tracking with PID speed control for high-speed autonomous vehicles considering time-optimal travel

In order to track the desired path as fast as possible,a novel autonomous vehicle path tracking based on model predictive control(MPC)and PID speed control was proposed for high-speed automated vehicles considering the constraints of vehicle physical limits,in which a forward-backward integration scheme was introduced to generate a time-optimal speed profile subject to the tire-road friction limit.Moreover,this scheme was further extended along one moving prediction window.In the MPC controller,the prediction model was an 8-degree-of-freedom(DOF)vehicle model,while the plant was a 14-DOF vehicle model.For lateral control,a sequence of optimal wheel steering angles was generated from the MPC controller;for longitudinal control,the total wheel torque was generated from the PID speed controller embedded in the MPC framework.The proposed controller was implemented in MATLAB considering arbitrary curves of continuously varying curvature as the reference trajectory.The simulation test results show that the tracking errors are small for vehicle lateral and longitudinal positions and the tracking performances for trajectory and speed are good using the proposed controller.Additionally,the case of extended implementation in one moving prediction window requires shorter travel time than the case implemented along the entire path.

Intelligent PID guidance control for AUV path tracking

Based on rational behavior model of three layers, a tracking control system is designed for straight line tracking which is commonly used in underwater survey missions. An intelligent PID control law implemented as planning level during the control system using transverse deviation is came up with. Continuous tracking of path expressed by a point sequence can be realized by the law. Firstly, a path tracking control system based on rational behavior model of three layers is designed, mainly satisfying the needs of underactuated AUV. Since there is no need to perform spatially coupled maneuvers, the 3D path tracking control is decoupled into planar 2D path tracking and depth or height tracking separately. Secondly, planar path tracking controller is introduced. For the reason that more attention is paid to comparing with vertical position control, transverse deviation in analytical form is derived. According to the Lyapunov direct theory, control law is designed using discrete PID algorithm whose parameters obey adaptive fuzzy adjustment. Reference heading angle is given as an output of the guidance controller conducted by lateral deviation together with its derivative. For the purpose of improving control quality and facilitating parameter modifying, data normalize modules based on Sigmoid function are applied to input-output data manipulation. Lastly, a sequence of experiments was carried out successfully, including tests in Longfeng lake and at the Yellow sea. In most challenging sea conditions, tracking errors of straight line are below 2 m in general. The results show that AUV is able to compensate the disturbance brought by sea current. The provided test results demonstrate that the designed guidance controller guarantees stably and accurately straight route tracking. Besides, the proposed control system is accessible for continuous comb-shaped path tracking in region searching.

Ribbon model based path tracking method for autonomous ground vehicles

To resolve the path tracking problem of autonomous ground vehicles,an analysis of existing path tracking methods was carried out and an important conclusion was got.The vehicle-road model is crucial for path following.Based on the conclusion,a new vehicle-road model named "ribbon model" was constructed with consideration of road width and vehicle geometry structure.A new vehicle-road evaluation algorithm was proposed based on this model,and a new path tracking controller including a steering controller and a speed controller was designed.The difficulties of preview distance selection and parameters tuning with speed in the pure following controller are avoided in this controller.To verify the performance of the novel method,simulation and real vehicle experiments were carried out.Experimental results show that the path tracking controller can keep the vehicle in the road running as fast as possible,so it can adjust the control strategy,such as safety,amenity,and rapidity criteria autonomously according to the road situation.This is important for the controller to adapt to different kinds of environments,and can improve the performance of autonomous ground vehicles significantly.

Adaptive Coordinated Path Tracking Control Strategy for Autonomous Vehicles with Direct Yaw Moment Control

It is a striking fact that the path tracking accuracy of autonomous vehicles based on active front wheel steering is poor under high-speed and large-curvature conditions.In this study,an adaptive path tracking control strategy that coordinates active front wheel steering and direct yaw moment is proposed based on model predictive control algorithm.The recursive least square method with a forgetting factor is used to identify the rear tire cornering stiffness and update the path tracking system prediction model.To adaptively adjust the priorities of path tracking accuracy and vehicle stability,an adaptive strategy based on fuzzy rules is applied to change the weight coefficients in the cost function.An adaptive control strategy for coordinating active front steering and direct yaw moment is proposed to improve the path tracking accuracy under high-speed and large-curvature conditions.To ensure vehicle stability,the sideslip angle,yaw rate and zero moment methods are used to construct optimization constraints based on the model predictive control frame.It is verified through simulation experiments that the proposed adaptive coordinated control strategy can improve the path tracking accuracy and ensure vehicle stability under high-speed and largecurvature conditions.

Fuzzy robust path tracking strategy of an active pelagic trawl system with coordinated ship and winch regulation

A fuzzy robust path tracking strategy of an active pelagic trawl system with ship and winch regulation is proposed.First,nonlinear mathematic model of the pelagic trawl system was derived using Lagrange equation and further simplified as a low order model for the convenience of controller design.Then,an active path tracking strategy of pelagic trawl system was investigated to improve the catching efficiency of the target fish near the sea bottom.By means of the active tracking control,the pelagic trawl net can be positioned dynamically to follow a specified trajectory via the coordinated winch and ship regulation.In addition,considering the system nonlinearities,modeling uncertainties and the unknown exogenous disturbance of the trawl system model,a nonlinear robust H2 /H∞ controller based on Takagi-Sugeno(T-S) fuzzy model was presented,and the simulation comparison with linear robust H2 /H∞ controller and PID method was conducted for the validation of the nonlinear fuzzy robust controller.The nonlinear simulation results show that the average tracking error is 0.4 m for the fuzzy robust H2 /H∞ control and 125.8 m for the vertical and horizontal displacement,respectively,which is much smaller than linear H2 /H∞ controller and the PID controller.The investigation results illustrate that the fuzzy robust controller is effective for the active path tracking control of the pelagic trawl system.

Particle path tracking method in two- and three-dimensional continuously rotating detonation engines

The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.

Path tracking for vehicle parallel parking based on ADRC controller

A novel path tracking controller for parallel parking based on active disturbance rejection control （ADRC） was presented in this paper. A second order ADRC controller was used to solve the path tracking robustness, which can estimate and compensate model uncertainty caused by steering kinematics and disturbances caused by parking speed and steering system delay. Collision-free path planning technology was adopted to generate the reference path. The simulation results validate that the performance of the proposed path tracking controller is better than the conventional PID controller. The actual vehicle tests show that the proposed path tracking controller is effective and robust to model uncertainty and disturbances.

Target Path Tracking Method of Intelligent Vehicle Based on Competitive Cooperative Game

To improve intelligent vehicle drive performance and avoid vehicle side-slip during target path tracking,a linearized four-wheel vehicle model is adopted as a predictive control model,and an intelligent ve-hicle target path tracking method based on a competitive cooperative game is proposed.The design variables are divided into different strategic spaces owned by each player by calculating the affecting factors of the design variables with objective functions and fuzzy clustering.Based on the competitive cooperative game model,each game player takes its payoff as a mono-objective to optimize its own strategic space and obtain the best strategy to deal with others.The best strategies were combined into the game strategy set.Considering the front wheel angle and side slip angle increment constraint,tire side-slip angle,and tire side slip deflection dynamics,it took the path tracking state model was used as the objective,function and the calculation was validated by competitive cooperative game theory.The results demonstrated the effectiveness of the proposed algorithm.The experimental results show that this method can track an intelligent vehicle quickly and steadily and has good real-time per-formance.

Path Tracking Control for Autonomous Truck with Dual Modular Chassis

This study focuses on enhancing the agility and path tracking capabilities of autonomous trucks equipped with dual 4WIS-4WID modular chassis.To address the challenges associated with these versatile vehicles,a comprehensive approach is presented.Firstly,a communication framework is devised,utilizing a hierarchical combination of two fieldbus systems.This framework facilitates adaptive marshalling,allowing effective communication and coordination among the various modular components of the autonomous truck.Secondly,a reference path generation strategy is proposed.This strategy relates the motion paths of the truck's body to its modular chassis.Reference paths for the modular chassis are derived based on the center of mass,effectively resolving the issue of differing motion paths.To tackle the path tracking problem for dual modular chassis,a cooperative path tracking controller is developed.This controller is designed using the kinematic model of the autonomous truck,enabling adaptive control through online adjustments of controller parameters based on measured input–output data.Simulation and real vehicle testing validate the proposed path tracking controller.In the dual modular chassis path tracking simulation,the maximum lateral position error and the maximum yaw angle error of truck body at different speeds are 0.082 m and 0.007 rad,respectively.In the real vehicle test,the maximum lateral position error is 0.194 m,and the maximum yaw angle error is 0.071 rad.These results demonstrate the practicality and effectiveness of the controller in real-world applications.

Cascade Optimization Control of Unmanned Vehicle Path Tracking Under Harsh Driving Conditions

Under ultra-high-speed and harsh conditions,conventional control methods struggle to ensure the path tracking accuracy and driving stability of unmanned vehicles during the turning process.Therefore,this study proposes a cascade control to solve this problem.Based on the new vehicle error model that considers vehicle tire sideslip and road curvature,the feedforward-parametric adaptive linear quadratic regulator(LQR)and proportional integral control-based speed-keeping controllers are used to compose the path-tracking cascade optimization controller for unmanned vehicles.To improve the adaptability of the unmanned vehicle path-tracking control under harsh driving conditions,the LQR controller parameters are automatically adjusted using a back-propagation neural network,in which the initial weights and thresholds are optimized using the improved grey wolf optimization algorithm according to the driving conditions.The speed-keeping controller reduces the impact on the curve-tracking accuracy under nonlinear vehicle speed variations.Finally,a joint model of MATLAB/Simulink and CarSim was established,and simulations show that the proposed control method can achieve stable entry and exit curves at ultra-high speeds for unmanned vehicles.Under strong wind and ice road conditions,the method exhibits a higher tracking accuracy and is more adaptive and robust to external interference in driving and variable curvature roads than methods such as the feedforward-LQR,preview and pure pursuit controls.

Path Planning and Tracking for Vehicle Parallel Parking Based on Preview BP Neural Network PID Controller

In order to diminish the impacts of extemal disturbance such as parking speed fluctuation and model un- certainty existing in steering kinematics, this paper presents a parallel path tracking method for vehicle based on pre- view back propagation （BP） neural network PID controller. The forward BP neural network can adjust the parameters of PID controller in real time. The preview time is optimized by considering path curvature, change in curvature and road boundaries. A fuzzy controller considering barriers and different road conditions is built to select the starting po- sition. In addition, a kind of path planning technology satisfying the requirement of obstacle avoidance is introduced. In order to solve the problem of discontinuous curvature, cubic B spline curve is used for curve fitting. The simulation results and real vehicle tests validate the effectiveness of the proposed path planning and tracking methods.

Wireless positioning and path tracking for a mobile platform in greenhouse

In order to realize intelligent greenhouse,an automatic navigation method for a mobile platform based on ultra-wideband(UWB)positioning technology was proposed and validated in this study.The time difference of arrival(TDOA)approach was used to monitor and track the UWB positioning to obtain the localization information of the mobile platform working in a greenhouse.After applying polynomial fitting for positioning error correction,the system accuracy was within 5 mm.A fuzzy controller model was constructed by incorporating the lateral and heading deviations as input variables and the steering angle of front wheel as the output variable.A fuzzy rule was established based on domain knowledge,as well as the steering angle of front wheel offline query table,which was applied to alleviate the calculative load of the controller.Experimental results confirmed that the automatic navigation method proposed in this study performed satisfactorily,with a steady-state error ranging from 41 mm to 79 mm when tracking straight line,and an average error of 185 mm and an average maximum error of 532 mm when tracking polygon.In addition,the maximum error occurred at the polygonal corner which could meet the needs of driving on the narrow road in the greenhouse.The method proposed in this study provides a new systematic approach for the research of greenhouse automatic navigation.

Implementation of MPC-Based Path Tracking for Autonomous Vehicles Considering Three Vehicle Dynamics Models with Different Fidelities

Model predictive control(MPC)algorithm is established based on a mathematical model of a plant to forecast the system behavior and optimize the current control move,thus producing the best future performance.Hence,models are core to every form of MPC.An MPC-based controller for path tracking is implemented using a lower-fidelity vehicle model to control a higher-fidelity vehicle model.The vehicle models include a bicycle model,an 8-DOF model,and a 14-DOF model,and the reference paths include a straight line and a circle.In the MPC-based controller,the model is linearized and discretized for state prediction;the tracking is conducted to obtain the heading angle and the lateral position of the vehicle center of mass in inertial coordinates.The output responses are discussed and compared between the developed vehicle dynamics models and the CarSim model with three different steering input signals.The simulation results exhibit good path-tracking performance of the proposed MPC-based controller for different complexity vehicle models,and the controller with high-fidelity model performs better than that with low-fidelity model during trajectory tracking.

Tractor path tracking control based on binocular vision

In the process of field operation management,determining how to accurately realize crop row identification and path tracking control is an essential part of tractor automatic navigation.According to the linear operation in the process of cotton field management,the tractor path tracking control system was designed based on binocular vision and the pure pursuit model.A new crop row detection method based on the Census transform and the PID control algorithm with dead zone were used.First,the upper computer software was developed by C++with the functions of parameter setting and image acquisition and processing.Second,an automatic steering controller was developed based on microprocessor MC9S12XS128 of Freescale.The control program was developed based on modular design using CodeWarrior during development of the PID-based automatic steering control strategy.Finally,a field experiment platform of tractor path tracking control was built,and field experiments under the actual cotton were conducted.The optimal visibility distance was determined by several previous experiments.When the tractor tracks the path with the optimal visibility distance in the growth environment of actual cotton crops,the mean absolute deviation of course angle was 0.95°,and the standard deviation was 1.26°;the mean absolute deviation of lateral position was 4.00 cm,and the standard deviation was 4.97 cm;the mean absolute deviation of front wheel angle was 2.99°,and the standard deviation was 3.67°.The experimental results show that(1)the crop row detection method based on Census transform can identify the crop line and plan the navigation path well,and(2)the tractor path tracking control system based on binocular vision has good stability and high control precision;thus,the control systemcan realize the automatic path tracking control of cotton line operation and meets the agricultural requirements of cotton field operation management.

Robust H_(∞)path tracking control of autonomous vehicles with delay and actuator saturation

The path tracking control problem is investigated in this paper for autonomous vehicles(AVs)with time-varying input delay and actuator saturation.Based on the Lyapunov-Krasovskii function and the characteristic of the saturation nonlinearity,a robust H_(∞)state-feedback path tracking controller is presented,and the corresponding control gain can be obtained by solving the linear matrix inequalities(LMIs).The asymptotic stability and prescribed H_(∞)performance conditions are studied for the closed-loop control system.To reduce the cost of control system,a static robust H_(∞)output-feedback controller is also proposed.In addition,the uncertainty effects of the cornering stiffness and external disturbances are included to improve the robustness of the control scheme.Simulation results are given to verify the effectiveness of the proposed theoretical results.

Study on multiple maneuvering targets tracking based on JPDA algorithm

A tracking algorithm for multiple-maneuvering targets based on joint probabilistic data association（JPDA）is proposed to improve the accuracy for tracking algorithm of traditional multiple maneuvering targets.The interconnection probability of the two targets is calculated,the weighted value is processed and the target tracks are obtained.The simulation results show that JPDA algorithm achieves higher tracking accuracy and provides a basis for more targets tracking.

Implementation of MPC-Based Trajectory Tracking Considering Different Fidelity Vehicle Models

In order to investigate how model fidelity in the formulation of model predictive control(MPC)algorithm affects the path tracking performance,a bicycle model and an 8 degrees of freedom(DOF)vehicle model,as well as a 14-DOF vehicle model were employed to implement the MPC-based path tracking controller considering the constraints of input limit and output admissibility by using a lower fidelity vehicle model to control a higher fidelity vehicle model.In the MPC controller,the nonlinear vehicle model was linearized and discretized for state prediction and vehicle heading angle,lateral position and longitudinal position were chosen as objectives in the cost function.The wheel step steering and sine wave steering responses between the developed vehicle models and the Carsim model were compared for validation before implementing the model predictive path tracking control.The simulation results of trajectory tracking considering an 8-shaped curved reference path were presented and compared when the prediction model and the plant were changed.The results show that the trajectory tracking errors are small and the tracking performances of the proposed controller considering different complexity vehicle models are good in the curved road environment.Additionally,the MPC-based controller formulated with a high-fidelity model performs better than that with a low-fidelity model in the trajectory tracking.

Design of intelligent controller for mobile robot based on fuzzy logic

In order to improve a mobile robot＇s autonomy in unknown environments, a novel intelligent controller is designed. The proposed controller is based on fuzzy logic with the aim of assisting a multi-sensor equipped mobile robot to safely navigate in an indoor environment. First, the designs of two behaviors for a robot＇s autonomous navigation are described, including path tracking and obstacle avoidance, which emulate human driving behaviors and reduce the complexity of the robot＇s navigation problems in unknown environments. Secondly, the two behaviors are combined by using a finite state machine （FSM）, which ensures that the robot can safely track a predefined path in an unknown indoor environment. The inputs to this controller are the readings from the sensors. The corresponding output is the desired direction of the robot. Finally, both the simulation and experimental results verify the effectiveness of the proposed method.