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.

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.

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.

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.

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.

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.

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.

Local Path Planning and Tracking Control of Vehicle Collision Avoidance System

Automotive collision avoidance technology can effectively avoid the accidents caused by dangerous traffic conditions or driver's manipulation errors.Moreover,it can promote the development of autonomous driving for intelligent vehicle in intelligent transportation.We present a collision avoidance system,which is composed of an evasive trajectory planner and a path following controller.Considering the stability of the vehicle in the conflict-free process,the evasive trajectory planner is designed by polynomial parametric method and optimized by genetic algorithm.The path following controller is proposed to make the car drive along the designed path by controlling the vehicle's lateral movement.Simulation results show that the vehicle with the proposed controller has good stability in the collision process,and it can ensure the vehicle driving in accordance with the planned trajectory at different speeds.The research results can provide a certain basis for the research and development of automotive collision avoidance technology.

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.

Tracking Control for a Cushion Robot Based on Fuzzy Path Planning With Safe Angular Velocity

This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived.The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.

Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅰ)

Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Car-tesian space mainly through increasing the number of knots on the path and the number of the path′s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot′s hand and does not change the number of the path′s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.

Path Recognition Algorithm of Tracking Robots Based on Image Sensor

Path recognition is an inevitable core technology in the development of tracking robot. In this paper,the path tracking system of tracking robot can be realized by image sensor module based on camera to obtain lane image information,and then extract the path through visual servo. The whole system can be divided into seven modules: micro control unit( MCU) processor module,image acquisition module,debugging module,motor drive module,servo drive module,speed sensor module,and voltage conversion module.In image pre-processing part,there is an introduction of binarization processing and the median filtering to strengthen the image information. About recognition algorithm,three key variables which are changed in the movement state are discussed and there are also many auxiliary algorithms that help to improve the path recognition.The experiment can verify that the whole system can accurately abstract the black guide lines from the white track and make the robot moving fast and stable by following the road parameters and conditions.

Modeling and Kinematics Simulation of Hydro-mechanical Split Path Steering Device of Tracked Vehicle Based on CATIA

Based on the working principle of hydro-mechanical split path of tracked vehicle, a operating gear was developed which was controlled by steering wheel and match with transmission case. Then CATIA software was used to build the three-dimensional model and carry out dynamic simulation of the mechanism. The result indicates that the design of the mechanism fulfills the request.

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.

Real-time accurate hand path tracking and joint trajectory planning for industrial robots(Ⅱ)

Previously, researchers raised the accuracy for a robot′s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the segments of the path. But, this method resulted in the heavier on line computational burden for the robot controller. In this paper, aiming at this drawback, the authors propose a new kind of real time accurate hand path tracking and joint trajectory planning method for robots. Through selecting some extra knots on the specified hand path by a certain rule, which enables the number of knots on each segment to increase from two to four, and through introducing a sinusoidal function and a cosinoidal function to the joint displacement equation of each segment, this method can raise the path tracking accuracy of robot′s hand greatly but does not increase the computational burden of robot controller markedly.

基于前馈非线性模型预测控制的类车机器人路径跟踪

类车机器人由于零件标准化程度低,侧偏刚度等轮胎力学参数难以准确获得,存在动力学建模十分困难的问题,因此现有研究工作通常以运动学模型作为类车机器人的控制模型,但由于其运动学模型存在模型失配,导致类车机器人与参考路径之间的误差、类车机器人的前轮转角和前轮转角速度出现剧烈振荡现象.针对前述问题,本文基于非线性模型预测控制(Nonlinear model predictive control,NMPC)的滚动优化原理,引入基于逆运动学模型的前馈转角信息,将前轮转向角作为预测模型的第四维,提出了一种基于前馈非线性模型预测控制(Feedforward NMPC,FNMPC)的类车机器人路径跟踪控制算法.并通过Simulink和CarSim进行了联合仿真,结果表明FNMPC有效减小了模型失配导致的振荡现象,同时具有较高的跟踪精度.其中前馈非线性模型预测控制器的位移误差幅值不超过0.1106 m,航向误差幅值不超过0.1253 rad.在相同工况下,线性模型预测控制、前馈线性模型预测控制、纯跟踪控制和Stanley控制误差发散,而本文提出的FNMPC相比已有NMPC跟踪精度更高,且控制增量绝对累计值相比NMPC控制器减小67.53%.通过线控类车机器人底盘作为实验平台完成的测试结果表明,NMPC系统在进入弯道时出现控制失控现象,在相同工况下,FNMPC系统能够有效完成对参考路径的跟踪,同时将位移误差幅值控制在0.1624 m以内,航向误差幅值控制在0.1138 rad以内.

麦克纳姆轮农业机器人路径跟踪——基于改进野马算法

针对麦克纳姆轮农业机器人在智能大棚中的路径跟踪问题,建立了运动学模型和动力学模型,设计了一种新型的双环比例微分-分数阶比例积分导数(Proportional Derivative-Fractional Order Proportional-Integral Derivative,PD-FOPID)控制器对全局路径进行动态跟踪控制。对于控制器参数多且整定困难的问题,首先采用帐篷映射初始化种群策略、精英主义记忆策略、动态余弦权重策略和柯西—高斯变异策略对原始野马算法进行改进,然后利用略改进野马算法(Improved Wild Horse Optimizer,IWHO)对控制器最优增益参数优化。实验结果表明:所开发的算法在探索和开发阶段方面性能优异,且PD-FOPID控制器在整定工作中表现突出。路径跟踪仿真证明,设计的双环PD-FOPID控制器比FOPID控制器更具显著的优势,能够避免动态误差累积,快速响应调整到规划路径,在提高农业大棚机器人路径跟踪控制质量方面具有巨大的潜力。

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.