Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Trajectory tracking and speed control for intelligent vehicles are put forward higher requirements on accuracy by the high traffic density scenario. A standard Model Predictive Control (MPC) algorithm focuses on the trajectory tracking but ignores the speed control. This paper proposes a simultaneous trajectory tracking and speed control algorithm based on MPC approach to address fine control in both space and time dimensions for intelligent vehicles. A threefold cost function including lateral and longitudinal speed as well as comfort has been proposed to improve the control algorithm. The simulations and comparisons demonstrate that the proposed method has a better tracking and speed control performance than the existing method.

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 Bézier 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.

HighlightsWhat are the main findings?In response to the limited existing research on high-speed autonomous driving under low-adhesion, slippery road conditions, a novel MPC-PID fused trajectory tracking control algorithm is proposed. This approach significantly enhances tracking accuracy and vehicle stability under such complex scenarios.Joint simulation results demonstrate that the proposed method improves trajectory tracking accuracy by at least 22.2%, while comfort, fuel economy, and safety are improved by 9.4%, 19.8%, and 5.3%, respectively.What is the implication of the main finding?This work provides theoretical support and simulation validation for high-speed trajectory tracking control under low-adhesion conditions, offering high engineering applicability and practical significance.The proposed approach facilitates real-time, precise, and robust autonomous driving in dynamically complex environments, promoting the deployment of high-performance control strategies in real-world applications.Autonomous vehicle trajectory tracking control is one of the hot topics in the autonomous driving field. One of the most widely used control methods is MPC (Model Predictive Control). As the control system generally becomes more nonlinear and complex, more nonlinear system factors are added to the MPC method. However, tracking accuracy and the amount of calculation needed are both dependent on a lot of contradictions for NMPC (Nonlinear Model Predictive Control). This research proposes a control algorithm for MPC-fused PID (Proportional-Integral-Derivative) control that ensures tracking accuracy under different high-speed driving conditions on wet and slippery road surfaces. The objective of the algorithm is twofold: first, to enhance trajectory tracking accuracy, and second, to ensure real-time control and optimize the vehicle’s comfort, economy, and safety indexes. The results of the joint simulation in Carsim/MATLAB Simulink show that trajectory tracking accuracy is improved by at least 22.2% under high-speed driving conditions of a vehicle on a wet and slippery road. At the same time, the comfort, economy, and safety of the vehicle are improved by at least 9.4%, 19.8%, and 5.3%, respectively.

Traditional models of vehicle dynamics engineered from physical principles are usually simplified and assumed, resulting in the model cannot accurately reflect the actual dynamic characteristics of the vehicle under some working conditions, affecting the control accuracy and even safety. In view of this, inspired by the single-track model, this paper uses the data-driven methods to establish a new high-performance time-delay feedback neural network vehicle dynamics model. The feedback connection of a network can describe complex dynamics. The multi-time-step input of the state and control can include highly nonlinear and strong coupling characteristics of a vehicle. The test results of modeling accuracy show that the proposed model can achieve higher vehicle dynamics prediction accuracy than nonlinear vehicle model. Different from the traditional vehicle dynamics model, the proposed model has long-term memory cells, which can implicitly predict coefficient of friction and can be applied to different road conditions. Then, the trajectory tracking control algorithm is designed based on the proposed vehicle model. According to the steady-state steering assumption, the feedforward front wheel steering angle is calculated, and the steady-state sideslip angle is integrated into the steering feedback according to the reference path to realize the reference trajectory tracking control. Finally, Simulink/CarSim is used to conduct the simulation analysis under the double lane change conditions to evaluate the proposed control algorithm. The analysis results show that the control algorithm based on the proposed model can achieve an accurate tracking control effect of a vehicle at medium and high speeds, providing high-accuracy track tracking and good lateral stability of intelligent vehicles.

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.

In this paper, the unmanned vehicle trajectory tracking problems were studied. In order to improve the stability of unmanned vehicles, the trajectory tracking control algorithm based on model predictive control (MPC) algorithm was researched by adding the dynamic constraints of centroid, acceleration and tire side angle on the basis of vehicle dynamics model. The trajectory planning layer was established on top of the trajectory tracking control layer, and the Carsim/Simulink simulation platform was built. At different speeds and under different road adhesion conditions, the algorithm was verified and compared. The simulation results showed that the model predictive control algorithm with dynamic constraints was provided with excellent tracking performance under severe conditions and well adaptive to environment interference.

In this thesis, we design and develop controllers for trajectory planning and trajectory tracking to tackle autonomous high-speed overtaking for the next generation of autonomous vehicles. Both the controllers are developed for a JLR Range Rover Sport that is capable of autonomous driving functionalities. To assist with controller development, a high-fidelity vehicle model previously developed in IPG Carmaker is utilised that contains all the multi-body interactions and non-linear tyre characteristics. Trajectory Planning Autonomous high-speed driving is a safety-critical task and it is imperative that the planned trajectory of the vehicle can ensure safety (collision-avoidance) while computing smooth and feasible trajectories. We propose a trajectory planning framework that utilises information of the traffic vehicles to identify safe driving zones on the road using potential field functions and a robust model predictive controller for generating feasible trajectories that ensure the vehicle remains within the safe zones while performing the overtaking manoeuvre. The closed-loop performance of this controller is validated in a high-fidelity co-simulation environment. Trajectory Tracking The trajectory tracking controller is designed to ensure that the vehicle tracks the trajectory as closely as possible and preserves the lateral-yaw stability at all times. In this thesis, an Enhanced Model Reference Adaptive Control algorithm is used to design a generic lateral tracking controller for an autonomous vehicle. The control algorithm is applied to a vehicle path tracking problem and its tracking performance is investigated when subjected to external disturbances such as crosswind, road surface changes, modelling errors, and parameter miss-matches in a high-fidelity co-simulation environment. Combined Planning & Control Finally, the design of a combined motion planning & control scheme is carried out. The lateral tracking controller is augmented to include the dynamics of the steering actuator system and the updated tracking controller is combined with the RMPC based sophisticated path-planning framework to present a hierarchical closed-loop control architecture for autonomous overtaking. This architecture is implemented on the IPG CarMaker/Simulink environment and validated with different overtaking manoeuvring scenarios.

In this paper, a direct yaw moment control algorithm is designed such that the corrective yaw moment is generated through direct control of driving and braking torques of four in-wheel brushless direct current motors located at the empty space of vehicle wheels. The proposed control system consists of a higher-level controller and a lower-level controller. In the upper level of proposed controller, a PID controller is designed to keep longitudinal velocity constant in manoeuvres. In addition, due to probable modelling error and parametric uncertainties as well as adaptation of unknown parameters in control law, an adaptive sliding mode control through adaptation of unknown parameters is presented to yield the corrective yaw moment such that the yaw rate tracks the desired value and the vehicle sideslip angle maintains limited so as to improve vehicle handling stability. The lower-level controller allocates the achieved control efforts (i.e. total longitudinal force and corrective yaw moment) to driving or regenerative braking torques of four in-wheel motors so as to generate the desired tyre longitudinal forces. The additional yaw moment applied by upper-lever controller may saturate the tyre forces. To this end, a novel longitudinal slip ratio controller which is designed based on fuzzy logic is included in the lower-level controller. A tyre dynamic weight transfer-based torque distribution algorithm is employed to distribute the motor driving torque or regenerative braking torque of each in-wheel motor for vehicle stability enhancement. A seven degree-of-freedom non-linear vehicle model with Magic Formula tyre model as well as the proposed control algorithm are simulated in Matlab/Simulink software. Three steering inputs including lane change, double lane change and step-steer manoeuvres in different roads are investigated in simulation environment. The simulation results show that the proposed control algorithm is capable of improving vehicle handling stability and maintaining vehicle yaw stability.

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

Trajectory tracking control algorithm in terms of quasi-velocities for a class of vehicles

This paper describes a unified chassis control (UCC) strategy to improve the lateral stability andmanoeuvrability of vehicles by integrating individual chassis control modules such as electronic stability control (ESC), active front steering (AFS) and continuous damping control (CDC). In order to achieve a target lateral vehicle response, an integrated AFS and four individual wheel braking controls have been used for an optimum distribution of longitudinal and lateral tyre forces the desired yaw moment for lateral stability has been designed by the sliding control method using a planar bicycle model and taking into consideration cornering stiffness uncertainties. The desired yaw moment is generated by the coordinated control of AFS and ESC. Optimal coordination of the control authority for the AFS and the ESC has been determined to minimise longitudinal deceleration. Estimated vertical tyre forces have been used for the optimum distribution of the longitudinal and lateral tyre forces. For the improved performance of the lateral stability control system, the damping forces at the four corners have been controlled to minimise roll angle by the CDC system. The response of the vehicle to the UCC system has been evaluated via computer simulations using vehicle dynamic software CarSim and a UCC controller coded with Matlab/Simulink. Computer simulations of a closed-loop driver–vehicle–controller system subjected to double lane change have been carried out to prove the improved performance of the proposed UCC strategy over a conventional ESC.

This paper is devoted to the formulation of a dynamic model of a serially connected multijoint robotic fish with a pair of wing-like pectoral fins, in which the whole robot is treated as a moving multilink rigid body in fluids. Considering that the thrust of fish mainly results from the force of trailing vortex, added lateral pressure, and leading edge suction force, the dynamic equations of the swimming fish have been derived by summing up the longitudinal force, lateral force, and yaw moment on each propulsive component in the context of Lagrangian mechanics. Along with the bio-inspired central pattern generators (CPGs) as the locomotor controller, the overall dynamic propulsive characteristics of the swimming robot are then estimated in a mathematical environment (i.e. Mathematica). Finally, simulations and experiments are carried out to validate the effectiveness of the built dynamic model. Results demonstrate that the CPG-coupled dynamic model provides a fairly good guide to seeking pragmatic backward swimming patterns for a carangiform robotic fish.

This paper presents a solution method for obtaining the lateral hydrodynamic forces and moments on a submerged body translating at a yaw angle. The method is based on the infinite-fluid formulation of the free-surface random-vortex method (FSRVM), which is reformulated to include the use of slender-body theory. The resulting methodology is given the name: slender-body FSRVM (SB-FSRVM). It utilizes the viscous-flow capabilities of FSRVM with a slender-body theory assumption. The three-dimensional viscous-flow equations are first shown to be reducible to a sequence of two-dimensional viscous-fluid problems in the cross-flow planes with the lowest-order effects from the forward velocity included in the cross-flow plane. The theory enables one to effectively analyze the lateral forces and yaw moments on a body undergoing prescribed forward motion with the possible occurrence of cross-flow separation. Applications are made to several cases of body geometry that are in steady forward motion, but at a yawed orientation. These include the case of a long “cone-tail” body. Comparisons are made with existing data where possible.

Aiming to maximize not only stability limit but also vehicle responsiveness combined yaw moment and lateral force control as a cooperative control is presented. The total lateral force for front and rear wheels as well as direct yaw moment are introduced using the models response of side-slip angle and yaw rate. The side-slip response is the 2DOF vehicle response while the yaw rate response is a suggested first order lag to prevent oscillation in relation to steering input. Three different cases of combining lateral force and direct yaw moment control have been investigated using computer simulations. In order to show the effect of the cooperative control on vehicle stability and responsiveness, a direct yaw moment control to follow the yaw rate response is taken as comparison case. The effect of cooperative control is proved by computer simulations of the vehicle response to a single sine wave steer input with braking.

The paper studies the trajectory tracking control problem of autonomous underwater vehicles (AUV) with practical constraints via economic model predictive control (EMPC) strategy. The cost function in EMPC is designed with two parts. One part is the trajectory tracking cost and the other part is the economic cost which is utilized to keep the AUV tracking within one side of the trajectory. We term this type of trajectory tracking as the unilateral trajectory tracking, which can be applied for hazardous area tracking and obstacle avoidance of AUVs. The effectiveness of the proposed approach is verified via thorough simulation studies.