Path Tracking Error Research Articles

Control Strategy of Vehicle Anti-Rollover Considering Driver’s Characteristic

In the process of vehicle anti-rollover, the driver’s behavioral characteristics have a great influence on the vehicle rollover stability. However, the existing researches on anti-rollover rarely consider the driver in the human-vehicle-road closed loop system, which may directly affects the rollover dynamics characteristics of the vehicle. Aiming at this problem, this work analyzes the influence of different driver parameters on vehicle dynamics and establishes a driver model considering the vehicle rollover stability. Based on this, a collaborative control strategy of vehicle anti-rollover considering the driver’s characteristics is designed to assist the driving stability requirements of different types of drivers. It includes the upper layer of supervision decision control and the lower layer of cooperative execution control. The supervisory decision control layer sets different rollover constraint boundaries for different types of drivers, and makes six control decision modes combining driver input and vehicle path tracking error. Aiming at different types of drivers, the lower cooperative execution control layer constrains the front wheel angle by the active steering system to reduce yaw rate and the risk of rollover. Moreover, it reasonably distributes the braking force of four tires by the active braking system to reduce the path tracking error while preventing rollover. The simulation results show that, the proposed cooperative control strategy can provide different control effects for different drivers, and ensure the effective anti-rollover control of the vehicle and achieve good path tracking performance.

3-D Flight Path Tracking Control for Unmanned Aerial Vehicles Under Wind Environments

This paper provides a new design framework for 3D flight path tracking control of unmanned aerial vehicles (UAVs) under wind environments. The new design framework simultaneously achieves the following three points: (i) 3D path tracking error system representation using the Serret-Frenet frame under wind environments, (ii) guaranteed cost control, (iii) simultaneous stabilization by a single controller for different 3D paths with a common interval parameter setting in the Serret-Frenet frame. To realize the three points, a path tracking error system based on the 3D kinematic model of UAVs under wind environments is constructed in the Serret-Frenet frame. The path tracking error system is exactly represented with the Takagi-Sugeno (T-S) fuzzy model in considered operation domains. As an advantage of the T-S fuzzy model construction, this paper considers a guaranteed cost controller design that minimizes the upper bound of a given performance function. The guaranteed cost controller design problem is cast in terms of linear matrix inequalities (LMIs). Thus, the designed controller guarantees not only the path stabilization but also the guaranteed cost control even in path tracking control for a given desired 3D flight path under wind environments. In addition, a simultaneous stabilization problem is also considered in terms of finding a common solution in a set of the LMIs. The simulation results show the utility of the proposed 3D flight path tracking control under wind environments.

Reinforcement Learning-Based End-to-End Parking for Automatic Parking System.

According to the existing mainstream automatic parking system (APS), a parking path is first planned based on the parking slot detected by the sensors. Subsequently, the path tracking module guides the vehicle to track the planned parking path. However, since the vehicle is non-linear dynamic, path tracking error inevitably occurs, leading to inclination and deviation of the parking. Accordingly, in this paper, a reinforcement learning-based end-to-end parking algorithm is proposed to achieve automatic parking. The vehicle can continuously learn and accumulate experience from numerous parking attempts and then learn the command of the optimal steering wheel angle at different parking slots. Based on this end-to-end parking, errors caused by path tracking can be avoided. Moreover, to ensure that the parking slot can be obtained continuously in the process of learning, a parking slot tracking algorithm is proposed based on the combination of vision and vehicle chassis information. Furthermore, given that the learning network output is hard to converge, and it is easy to fall into local optimum during the parking process, several reinforcement learning training methods in terms of parking conditions are developed. Lastly, by the real vehicle test, it is proved that using the proposed method can achieve a better parking attitude than using the path planning and path tracking-based method.

Enhanced Fireworks Algorithm-Auto Disturbance Rejection Control Algorithm for Robot Fish Path Tracking

The robot fish is affected by many unknown internal and external interference factors when it performs path tracking in unknown waters. It was proposed that a path tracking method based on the EFWA-ADRC (enhanced fireworks algorithmauto disturbance rejection control) to obtain high-quality tracking effect. ADRC has strong adaptability and robustness. It is an effective method to solve the control problems of nonlinearity, uncertainty, strong interference, strong coupling and large time lag. For the optimization of parameters in ADRC, the enhanced fireworks algorithm (EFWA) is used for online adjustment. It is to improve the anti-interference of the robot fish in the path tracking process. The multi-joint bionic robot fish was taken as the research object in the paper. It was established a path tracking error model in the Serret-Frenet coordinate system combining the mathematical model of robotic fish. It was focused on the forward speed and steering speed control rate. It was constructed that the EFWA-ADRC based path tracking system. Finally, the simulation and experimental results show that the control method based on EFWAADRC and conventional ADRC makes the robotic fish track the given path at 2:8s and 3:3s respectively, and the tracking error is kept within plus or minus 0:09m and 0:1m respectively. The new control method tracking steady-state error was reduces by 10% compared with the conventional ADRC. It was proved that the proposed EFWA-ADRC controller has better control effect on the controlled system, which is subject to strong interference.

Path control in limit handling and drifting conditions using State Dependent Riccati Equation technique

Tyres operated at or close to their friction limits show a highly nonlinear motion to force response. This state is called limit handling. The objective of this research is to minimize lateral path tracking error while the tyres operate in limit handling. The State Dependent Riccati Equation technique is employed to develop a feedback-feedforward steering controller. It gives a systematic approach to take into account model nonlinearities such as combined slip tyre characteristics. Furthermore, the controller is implemented in a test vehicle and tested on a low friction skid pad. The controller shows robust path tracking performance even when the rear wheels are operated beyond their friction limits, and large body sideslip prevails.

A critical review on automation of steering mechanism of load haul dump machine

This article presents a brief note on the evolution of steering mechanisms and more emphasized on articulated steering system of the load haul dump machine. In this respect, pictorial representation of the evolution of steering mechanisms for on-road and articulated steering mechanisms of the load haul dump machine is made from the available literature. Critical review on basic elements required for the complete automation of the load haul dump vehicle steering system is presented. Different types of controllers for path tracking error minimization of the scale-modeled or simulated model of the load haul dump steering system are tabulated. Few case studies stimulating the complete automation of the load haul dump steering system employed on the field are also discussed. Challenges and some research gaps in making fully automated steering system of the load haul dump machine are identified in this review article. At the end, based on the critical review, some novel methods for making the fully automated steering system of the load haul dump machine is provided, which is the potential future work for the design and development of feasible automatic steering system.

Path-tracking of autonomous vehicles using a novel adaptive robust exponential-like-sliding-mode fuzzy type-2 neural network controller

Abstract Structured and unstructured uncertainties together with external disturbances may pose considerable challenges in realizing desired path-tacking and lane keeping of autonomous vehicles. This paper presents a novel robust adaptive indirect control method based on an exponential-like-sliding-mode fuzzy type-2 neural network approach for enhanced path-tracking performance of road autonomous vehicles subject to parametric uncertainties related to vehicle nominal cornering stiffness, road-tire adhesion coefficient, inertial parameters, and forward speed. A hierarchical controller is designed and the stability of the closed-loop system is ensured along with deriving the adaptation laws by employing the Lyapunov stability theorem. The conventional reaching law related to the sliding mode degrades from the system stability and introduces an inherent chattering of the controller input. The convergence law for the sliding surface is adjusted based on a variable exponential sliding manifold to eliminate possible chattering in the buffeting switch zone near the origin. The proposed exponential-like sliding surface guarantees the swift and smooth global asymptotic convergence of the tracking error toward zero. Furthermore, an adaptive look-ahead path-tracking error term is introduced as an auxiliary error criterion to improve the vehicle path-tracking performance. The effectiveness of the proposed controller is verified through Matlab/Simulink–CarSim co-simulations and comparisons with selected reported control methods for two different road maneuvers. The results suggested substantially improved tracking performance by the proposed controller with robustness to withstand against the perturbed parameters and external disturbances.

A sampling-based optimized algorithm for task-constrained motion planning

We consider a motion planning problem with task space constraints in a complex environment for redundant manipulators. For this problem, we propose a motion planning algorithm that combines kinematics control with rapidly exploring random sampling methods. Meanwhile, we introduce an optimization structure similar to dynamic programming into the algorithm. The proposed algorithm can generate an asymptotically optimized smooth path in joint space, which continuously satisfies task space constraints and avoids obstacles. We have confirmed that the proposed algorithm is probabilistically complete and asymptotically optimized. Finally, we conduct multiple experiments with path length and tracking error as optimization targets and the planning results reflect the optimization effect of the algorithm.

Path planning and tracking for autonomous mining articulated vehicles

This paper presents a path planning and tracking framework for autonomous mining articulated vehicles (AVs). The relation space method is proposed for path planning. In this method, a self-organising, competitive neural network is adopted to identify the space around the vehicle. Then, the vehicle's optimal driving direction is determined by using the spatial geometric relationships of the identified space. A proportional-integral-derivative (PID) controller is used to control the vehicle speed, whereas a model predictive control (MPC) is designed for steering control, where the path tracking error model is used for MPC development. In addition, the AV's dynamics model is built in Adams. The effect and sensitivity of the path-tracking controller are validated through the Matlab-Adams co-simulation. The test results show the satisfactory path-tracking performance.

Design of robust output-feedback-based automatic steering controller for unmanned electric vehicles

This paper presents a robust output-feedback-based automatic steering control scheme for unmanned electric vehicles (UEV). To address the challenging problem, an uncertain dynamic model of the UEV is firstly developed, in which the uncertainties in the tyre cornering stiffness and the actuator faults are included. Then, to deal with the uncertain features and actuator faults of UEV, a robust output-feedback-based control algorithm for automatic steering system of UEV is proposed to achieve the prescribed transient for path tracking errors while keeping all other closed-loop signals bounded. Finally, simulation and experimental results demonstrate that the proposed automatic steering control scheme can effectively improve the tracking performance of UEV.

Path-tracking errors for active trailer steering off-highway: a simulation study

This paper discusses the tracking performance of a path-following steering system when operating off-highway. Simulation studies were conducted on three types of vehicle models: tractor-semitrailer, B-double and A-triple. The vehicles were simulated for a straight-line and a 450 roundabout with various road camber, grade and adhesions. Results indicated that the path-following steering system was unable to provide good tracking performance under those conditions due to longitudinal and lateral wheel slip interfering with its estimation of trailer location and orientation.

Path-tracking errors for active trailer steering off-highway: a simulation study

This paper discusses the tracking performance of a path-following steering system when operating off-highway. Simulation studies were conducted on three types of vehicle models: tractor-semitrailer, B-double and A-triple. The vehicles were simulated for a straight-line and a 450 roundabout with various road camber, grade and adhesions. Results indicated that the path-following steering system was unable to provide good tracking performance under those conditions due to longitudinal and lateral wheel slip interfering with its estimation of trailer location and orientation.

AUV Tunnel Tracking Method Based on Adaptive Model Predictive Control

In this paper, a model predictive path tracking controller is designed for the path tracking of the autonomous underwater vehicle (AUV). Firstly, Serret-Frenet coordinate system is introduced, and the path tracking error system model is established in this coordinate system. Based on Lyapunov theory and Backstepping method, the forward heading of AUV is conversed to the target value. Then, a nonlinear model predictive control design constraint path following control law of the AUV based on rolling to solve constrained optimization problems, satisfy the constraint of extension control input, to hit the target heading control. In the end, AUV-T, an underwater robot developed by Harbin engineering university, was used to test the proposed control law. The results showed that the controller showed good tracking effect.

Tracking-Error Fuzzy-Based Control for Nonholonomic Wheeled Robots

In this paper, the trajectory to be tracked by a differentially driven wheeled mobile robot (DDWMR) is controlled. The considered DDWMR has a chassis with two active wheels and a front idle wheel. After introducing the kinematic model of the robot, the robot trajectory tracking problem using fuzzy and optimal fuzzy logic methods will be analyzed. Also, the same mission will be conducted using model predictive control (MPC) method. Minimizing the path tracking error is the objective of the controllers design. Moreover, the velocity and acceleration constraints are included in the proposed controllers design procedure to prevent the DDWMR from slipping and path curvature deviation. Finally, tracking error results for fuzzy, optimal fuzzy and model predictive controllers are compared. The tracking error analysis of the obtained simulation results, in MATLAB software, reveals the better performance of the designed fuzzy controller (FC) over the MPC, and the better performance of the designed optimal fuzzy controller over the FC.

Adaptive-neural-network-based robust lateral motion control for autonomous vehicle at driving limits

Parametric modeling uncertainties and unknown external disturbance are major concerns in the development of advanced lateral motion controller for autonomous vehicle at the limits of driving conditions. Considering that tyre operating at or close to its physical limits of friction exhibits highly nonlinear force response and that unknown external disturbance can be caused by changing driving conditions, this paper presents a novel lateral motion control method that can maintain the yaw stability of autonomous vehicle while minimizing lateral path tracking error at the limits of driving conditions The proposed control scheme consists of a robust steering controller and an adaptive neural network (ANN) approximator. First, based on reference path model, dynamics model and kinematics model of vehicle, the robust steering controller is developed via backstepping variable structure control (BVSC) to suppress lateral path tracking deviation, to withstand unknown external disturbance and guarantee the yaw stability of autonomous vehicle. Then, by combining adaptive control mechanism based on Lyapunov stability theory and radial basis function neural network (RBFNN), the ANN approximator is designed to estimate uncertainty of tyre cornering stiffness and reduce its adverse effects by learning to approximate arbitrary nonlinear functions, and it ensures the uniform ultimate boundedness of the closed-loop system. Both simulation and experiment results show that the proposed control strategy can robustly track the reference path and at the same time maintains the yaw stability of vehicle at or near the physical limits of tyre friction.

Study on Robust Lateral Controller for Differential GPS-Based Autonomous Vehicles

Recently, technological advancements in autonomous vehicle development have continued to accelerate. In this paper, we propose a lateral controller and navigation algorithm for autonomous vehicles based on the Differential Global Positioning System (DGPS), core technology of autonomous vehicles. In this study, an H-infinity (H∞) controller was designed lateral controller to ensure nominal safety and robustness against noise, external disturbances and structural and non-structural errors in vehicle modeling. Meanwhile, the “pure pursuit” approach which geometrically follows a path was employed as a path-tracking technique for the proposed navigation algorithm. A vehicle modeling simulation was conducted to evaluate the performance of the proposed method using a twodegrees- of-freedom linear model. The lateral H∞ controller and navigation algorithm were applied to an actual vehicle, Their performances were evaluated by comparing the path tracking error at various speeds of autonomous vehicles with that of the proportional-integral-derivative (PID) controller.

A Novel Fuzzy Observer-Based Steering Control Approach for Path Tracking in Autonomous Vehicles

In this paper, the problem of steering control is investigated for vehicle path tracking in the presence of parametric uncertainties and nonlinearities. In practice, the vehicle mass varies due to the number of passengers or amount of payload, while the vehicle velocity also changes during normal cruising, which significantly influences vehicle dynamics. Moreover, the vehicle dynamics are strongly nonlinear caused by the tire/road forces under different road surface conditions. With fuzzy modeling method, the original nonlinear path tracking system with parameter variations is first formulated as a T–S fuzzy model with additive norm-bounded uncertainties, and then an approach to the fuzzy observer-based output feedback steering control for vehicle dynamics is proposed under a fuzzy Lyapunov function framework. By employing matrix inequality convexifying techniques, a sufficient condition is developed in the form of linear matrix inequalities such that the closed-loop path tracking error system is asymptotically stable with a guaranteed $\mathcal {H}_{\infty }$ level. Finally, the effectiveness of the proposed fuzzy observer-based output feedback controller is demonstrated in Carsim/Matlab joint simulation environment, via which the advantage of a T–S fuzzy observer-based output controller over the closed-loop driver model embedded in Carsim is also shown with parametric uncertainties and nonlinearities.

Nonlinear Model Predictive Controller and Feasible Path Planning for Autonomous Robots

Abstract This paper develops the nonlinear model predictive control (NMPC) algorithm to control autonomous robots tracking feasible paths generated directly from the nonlinear dynamic equations.NMPC algorithm can secure the stability of this dynamic system by imposing additional conditions on the open loop NMPC regulator. The NMPC algorithm maintains a terminal constrained region to the origin and thus, guarantees the stability of the nonlinear system. Simulations show that the NMPC algorithm can minimize the path tracking errors and control the autonomous robots tracking exactly on the feasible paths subject to the system’s physical constraints.

Global robust adaptive path-tracking control of underactuated ships under stochastic disturbances

This paper presents a design of new controllers that force underactuated ships under both deterministic and stochastic sea loads to globally track a reference path. First, the loads are decomposed to a deterministic part treated as unknown constants, and a time-varying part considered as stochastic disturbances with unknown time-varying covariances. Second, the path-tracking errors are represented in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov׳s direct methods. Weak and strong nonlinear Lyapunov functions are introduced, and the path-parameter is used as an additional control input to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule. Estimate of the deterministic disturbances and upper covariances of the stochastic disturbances is incorporated in the control design. The effectiveness of the proposed results is illustrated through simulations.

Design of Fractional-Order Controller for Trajectory Tracking Control of a Non-holonomic Autonomous Ground Vehicle

A robust control technique is proposed to address the problem of trajectory tracking of an autonomous ground vehicle (AGV). This technique utilizes a fractional-order proportional integral derivative (FOPID) controller to control a non-holonomic autonomous ground vehicle to track the behaviour of the predefined reference path. Two FOPID controllers are designed to control the AGV’s inputs. These inputs represent the torques that are used in order to manipulate the implemented model of the vehicle to obtain the actual path. The implemented model of the non-holonomic autonomous ground vehicle takes into consideration both of the kinematic and dynamic models. In additional, a particle swarm optimization (PSO) algorithm is used to optimize the FOPID controllers’ parameters. These optimal tuned parameters of FOPID controllers minimize the cost function used in the algorithm. The effectiveness and validation of the proposed method have been verified through different patterns of reference paths using MATLAB–Simulink software package. The stability of fractional-order system is analysed. Also, the robustness of the system is conducted by adding disturbances due to friction of wheels during the vehicle motion. The obtained results of FOPID controller show the advantage and the performance of the technique in terms of minimizing path tracking error and the complement of the path following.