Lateral Vehicle Research Articles

RNN-based linear parameter varying adaptive model predictive control for autonomous driving

Autonomous driving is a complex and highly dynamic process that ensures controlling the coupled longitudinal and lateral vehicle dynamics. Model predictive control, distinguished by its predictive feature, optimal performance, and ability to handle constraints, makes it one of the most promising tools for this type of control application. The content of this article handles the problem of autonomous driving by proposing an adaptive linear parameter varying model predictive controller (LPV-MPC), where the controller's prediction model is adaptive by means of a recurrent neural network. The proposed LPV-MPC is further optimised by a hybrid Genetic and Particle Swarm Optimization Algorithm (GA-PSO). The developed controller is tested and evaluated on a challenging track under variable wind disturbance.

A Non‐Iterative Wheel‐Rail Contact Geometry Determination Algorithm and Its Application

AbstractTo ensure a more accurate simulation of the wheel‐rail contact state in vehicle‐track interaction, a non‐iterative contact geometry determination algorithm is proposed. This algorithm decouples lateral movement and roll, independently calculates the minimum wheel‐rail gap on both sides, and overcomes the limitation of simultaneous wheel‐rail contact on both sides. It can be applied to single‐side and two‐side wheel‐rail separation problems. Additionally, by converting track irregularity and rail deformation into the reverse displacement of the wheel, it avoids real‐time calculation of the wheel‐rail spatial position, thereby improving calculation efficiency. The effectiveness of the algorithm is verified through Universal Mechanism software and field measurements. Subsequently, the influence of the measured wheel‐rail profile, rail cant, and rail gauge on the wheel‐rail contact characteristics is analyzed. Finally, vehicle shaking caused by track irregularity and wheel‐rail contact is examined from the perspective of wheel‐rail matching. The study demonstrates that the non‐iterative algorithm is suitable for online simulation by pre‐processing the contact geometry parameters. When the track gauge and rail cant increase, the distribution of wheel‐rail contact points becomes more concentrated. Furthermore, when the excitation frequency of wheel‐rail matching is close to the track irregularity excitation frequency, it causes vibration amplification, resulting in lateral vehicle shaking.

Two-Step Quadratic Programming for Physically Meaningful Smoothing of Longitudinal Vehicle Trajectories

Longitudinal vehicle trajectories suffer from errors and noise because of detection and extraction techniques, challenging their applications. Existing smoothing methods either lack physical meaning or cannot ensure solution existence and uniqueness. To address this, we propose a two-step quadratic programming method that aligns smoothed speeds and higher-order derivatives with physical laws, drivers’ behaviors, and vehicle characteristics. Unlike the well-known smoothing splines method, which minimizes a weighted sum of discrepancy and roughness in a single quadratic programming problem, our method incorporates prior knowledge of position errors into two sequential quadratic programming problems. Step 1 solves half-smoothed positions by minimizing the discrepancy between them and raw positions, subject to physically meaningful bounds on speeds and higher-order derivatives of half-smoothed positions. Step 2 solves smoothed positions by minimizing the roughness while maintaining physically meaningful bounds and allowing the deviations from raw data of smoothed positions by at most those of the half-smoothed positions and prior position errors. The second step’s coefficient matrix is not positive definite, necessitating the matching of the first few smoothed positions with corresponding half-smoothed ones, with equality constraints equaling the highest order of derivatives. We establish the solution existence and uniqueness for both problems, ensuring their well-defined nature. Numerical experiments using Next Generation Simulation (NGSIM) data demonstrate that a third-order derivative constraint yields an efficient method and produces smoothed trajectories comparable with manually re-extracted ones, consistent with the minimum jerk principle for human movements. Comparisons with an existing approach and application to the Highway Drone data set further validate our method’s efficacy. Notably, our method is a postprocessing smoothing technique based on trajectory data and is not intended for systematic errors. Future work will extend this method to lateral vehicle trajectories and trajectory prediction and planning for both human-driven and automated vehicles. This approach also holds potential for broader smoothing problems with known average error in raw data. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: The authors extend their gratitude to the Pacific Southwest Region University Transportation Center and the University of California Institute of Transportation Studies (UC ITS) Statewide Transportation Research Program (STRP) for their valuable financial support.

Utilization of genetic algorithm in tuning the hyper-parameters of hybrid NN-based side-slip angle estimators

This paper proposes a solution to enhance and compare different neural network (NN)-based side-slip angle estimators. The feed-forward neural networks (FFNNs), recurrent neural networks, long short-term memory units (LSTMs), and gated recurrent units are investigated. However, there is a lack in the selection criteria of the architectures’ hyper-parameters. Therefore, the genetic algorithm is integrated with the NN-based estimators to find the optimal hyper-parameters for the studied architectures. The tuned hyper-parameters in this work include the number of neurons, number of layers, activation function, optimizer type, and learning rate. The objective function of the optimization problem is minimizing the root-mean-square error (RMSE) on multiple testing data. The optimal models are further included in the design of a hybrid NN estimator with Kalman filter. In the hybrid estimators, the optimal NN estimators are used as virtual sensors to correct the prediction of the side-slip angle resulting from the mathematical lateral vehicle model. Eventually, the performance of the best selected model is evaluated in terms of different metrics; mean RMSE, mean error variance, mean training time, and mean estimation time. LSTMs are found to achieve the lowest mean RMSE while being tested on highly generalized data yielding the highest training and estimation time. However, FFNNs achieve the lowest RMSE while being tested on low generalized data and the lowest training and estimation time. Meanwhile, it is observed that the hybrid estimators achieved lower RMSE with great enhancement compared to the non-hybridized ones proving the effectiveness of the proposed approach and increasing the side-slip estimation generalization ability in unknown environments with high uncertainties, which are not covered by the training dataset for the NNs estimators.

An NMPC-Based Integrated Longitudinal and Lateral Vehicle Stability Control Based on the Double-Layer Torque Distribution.

With the ongoing promotion and adoption of electric vehicles, intelligent and connected technologies have been continuously advancing. Electrical control systems implemented in electric vehicles have emerged as a critical research direction. Various drive-by-wire chassis systems, including drive-by-wire driving and braking systems and steer-by-wire systems, are extensively employed in vehicles. Concurrently, unavoidable issues such as conflicting control system objectives and execution system interference emerge, positioning integrated chassis control as an effective solution to these challenges. This paper proposes a model predictive control-based longitudinal dynamics integrated chassis control system for pure electric commercial vehicles equipped with electro-mechanical brake (EMB) systems, centralized drive, and distributed braking. This system integrates acceleration slip regulation (ASR), a braking force distribution system, an anti-lock braking system (ABS), and a direct yaw moment control system (DYC). This paper first analyzes and models the key components of the vehicle. Then, based on model predictive control (MPC), it develops a controller model for integrated stability with double-layer torque distribution. The required driving and braking torque for each wheel are calculated according to the actual and desired motion states of the vehicle and applied to the corresponding actuators. Finally, the effectiveness of this strategy is verified through simulation results from Matlab/Simulink. The simulation shows that the braking deceleration of the braking condition is increased by 32% on average, and the braking distance is reduced by 15%. The driving condition can enter the smooth driving faster, and the time is reduced by 1.5 s~5 s. The lateral stability parameters are also very much improved compared with the uncontrolled vehicles.

Space State Model of Lateral Vehicle Motion for Stability

Space State Model of Lateral Vehicle Motion for Stability

Design of steering wheel torque with human-machine interaction for uncoupled shared steering

In the uncoupled shared steering architecture based on the steering-by-wire (SBW) system, direct access to road feel and automation-related information is unavailable to the driver. To address this problem, this paper proposes a steering wheel torque feedback model that considers human-machine interaction information. First, the model predictive control (MPC) is adopted in lateral vehicle control by automation. Then a fuzzy control-based control authority allocation model is applied to assign the control authority weight between the human driver and automation according to the value of the Path Lateral Hazard (PLH) Factor and the Driver’s Intent Evaluation (DIE) Factor. These two factors reflect the probability of lateral vehicle collision and the intensity of the driver’s driving intention, respectively. Next, the road feel feedback torque and the human-machine interface (HMI) feedback torque is incorporated in the steering wheel feedback torque model to enhance the driver’s experience in SBW vehicles and trust in the automation. The HMI feedback torque is designed to provide human drivers with information on control authority weight variation and desired angle deviation between the human driver and automation. Simulation and experiment results suggest that the proposed uncouple shared control method can accelerate driver acceptance of automation and provide the driver with a more intuitive steering experience.

Which partially automated driving function do drivers prefer? Results from two field studies on public highways

Partial driving automation consists of several subsystems that drivers need to trust to an appropriate level and interact with in a secure manner. To investigate whether drivers adapt their trust functional specific, how they experience the subsystems, and what their preferences are, we conducted two field studies with two partially automated (SAE level 2) vehicles and involving a total of 132 drivers. In both studies, participants drove on a public highway with support from partial driving automation systems for longitudinal control (adaptive cruise control, ACC) and lateral control (lane-keeping assistance, LA). Participants in Study 2 were additionally able to use a lane change assistance (LC) system. The drivers' trust generally increased over time and reflected in how much a participant used the automation (Study 1). Hereby, in both studies drivers had functional specific trust: in Study 1 drivers trusted the ACC more than the LA. In Study 2 drivers in addition had lower trust in the LC than in the LA and the ACC. In their thinking-aloud statements, drivers were more positive about ACC and more critical about LA but reported more interaction difficulties with the ACC (Study 1). In Study 2 participants on average preferred the ACC over the LA and the LA over the LC. The interview responses suggest that the lower preference was due to the perceived reliability (LA) and usefulness (LC). In summary, our results indicate that drivers adapt their trust functional specific when using partial driving automation and have an overall preference for ACC that persists despite a higher number of interaction problems.

Vehicle Driving Behavior Analysis and Unified Modeling in Urban Road Scenarios

To improve the simulation accuracy and efficiency of microscopic urban traffic, a unified modeling method considering the behavioral characteristics of vehicle drivers is proposed by considering the lane-changing vehicles on the inlet lanes of signalized intersections and their approach following vehicles on the target lanes as research objects. Based on the driver’s multidirectional, multi-vehicle anticipation ability and introducing lateral vehicle influence coefficients, the full velocity difference car-following model was extended to microscopic traffic models that consider the driver’s capacity for multi-directional, multi-vehicle anticipation. The extended model can describe longitudinal movements of lane changing and car followers using lateral vehicle influential parameters. The influences of traffic control signals and the type of lane change on drivers’ decisions were integrated into the model by reformulating the optimal velocity function of the basic car following the model. Similar modeling methods and components were applied to formulate four groups of experimental models and one group of test models. Vehicle trajectory data and manual observations were collected on urban arteries to calibrate and evaluate the research models, experimental models, and test models. The results show that the car-following behavior is more sensitive to the variation in the status of the lateral moving vehicle and change of lane-changing type compared to lane-changing behavior during the lane-changing process. In addition, when lane changing gradually encroaches on the target lane, the vehicle observes the driving conditions and adjusts its driving behaviors differently. This research helps to analyze travel characteristics and influence mechanisms of vehicles on urban roads, which is a guide for the future development of sustainable transportation and self-driving vehicles and promoting the efficient operation of urban transportation systems.

Metamodeling on uncertainty quantification in the behavior of the tire/road interaction of vehicles

In recent years, the automotive industry has been developing applied research to meet customer’s needs; considering safety, vehicle comfort and energetic efficiency. In particular, automotive tires have a prominent position in this research area, ensuring good vehicle handling, comfort and safety. In the vehicle dynamics performance, excellent gripping and reduced rolling resistance in the tires are crucial to maximize the energetic efficiency in a reliable way. However, to ensure such a level of reliability in vehicle operation, the inherent uncertainties of tires, as well as other factors subject to variability must be taken into account in the vehicle design. In this way, the present paper analyzes in detail the effect of variations in some parameters such as ambient temperature, ground conditions, vertical load, speed and tire inflation on the analysis of vehicle dynamics. A Metamodeling approach associated with the Monte Carlo Simulation was employed to develop the mathematical models to analyze the effect of uncertain parameters on the tire rolling resistance; traction, centripetal and lateral forces, using experimental data from the literature, in the longitudinal and lateral vehicle dynamics. Therefore, the present research brings as an innovation an integrated approach to the input parameters of the system with the rolling resistance through the developed metamodels. There was a substantial variability of up to 15% both up and down in the Maximum Traction Force of a vehicle in response to variations in the vehicle’s weight and the coefficient of tire rolling resistance. In contrast, the Lateral Force exhibited a greater variability, with a 25 downward and 10% upward variation associated with the weight and friction coefficient variability of the vehicle. Further investigations into the sensitivity analysis highlight the significant influence of the friction coefficient and temperature on the Traction Forces of the vehicle.

Online Modeling of Lateral Vehicle Dynamics via Recursive Integrated Physics-Data-Based Method

Online Modeling of Lateral Vehicle Dynamics via Recursive Integrated Physics-Data-Based Method

Data-driven design of model-free control for reference model tracking based on an ultra-local model: Application to vehicle yaw rate control

Lateral vehicle dynamics control is important for autonomous driving. This paper presents a data-driven design of model-referenced model-free control (DD-MR-MFC) based on an ultra-local model for vehicle yaw rate control. The characteristics of lateral vehicle dynamics systems depend on vehicle velocities and weights. For this system, fixed proportional–integral–derivative (PID) controllers cannot provide the desired control performance. Additionally, although model-based control can be applied to lateral vehicle dynamics, the modeling process is time-consuming. To efficiently design controllers that can realize the desired performance, we adopt a model-free approach. In this study, the control law of practical MR-MFC is derived by extending the traditional MFC based on an ultra-local model and using a data-driven design method. The MFC approach can be applied to nonlinear systems with few parameters, and the data-driven method provides optimized parameters from single-experiment time-series data without the need for repeated experiments and system model to be controlled. Additionally, the processing cost is considerably low because the controller parameter can be obtained using least-square methods. The effectiveness of the proposed method is verified using a multibody vehicle simulator. The yaw rate tracking performance is examined under different velocities and loads. Results showed that the root-mean-square error of the proposed method is approximately 1/100th of that when using a fixed PID controller optimized using a data-driven method.

Physics-Informed Data-Based LPV Modeling and Validations of Lateral Vehicle Dynamics

Physics-Informed Data-Based LPV Modeling and Validations of Lateral Vehicle Dynamics

Distributed non‐linear model predictive control with Gaussian process dynamics for two‐dimensional motion of vehicle platoon

AbstractThe platoon control of connected and automated vehicles is an important topic in transportation research. The characteristics of non‐linearities, external disturbances, and strong coupling are non‐negligible in two‐dimensional motion control. An integrated longitudinal and lateral vehicle dynamics is required. A Gaussian Process‐based Distributed Stochastic Model Predictive Control (GP‐DSMPC) for two‐dimensional motion is proposed. It achieves global longitudinal stability and lateral error suppression. Gaussian process (GP) regression is employed to approximate the unknown model error. For the two‐norm chance constraints, over‐approximating the confidence ellipse to an outer polyhedron is an effective way to reduce the conservativeness and coupling effect in longitudinal and lateral motion. A neighbour‐average target trajectory is designed with an upper‐level optimization for adjustable target coefficients. The sum of the local cost functions is used as a Lyapunov candidate to achieve the global stability of the longitudinal motion. Some conditions on penalty weights and target coefficients among subsystems, and terminal outputs are derived. Simulation results reveal that the proposed method is effective for disturbance attenuation and performs better than distributed non‐linear model predictive control without GP estimation under low‐friction road conditions.

Lateral Control Calibration and Testing in a Co-Simulation Framework for Automated Vehicles

Lateral vehicle control is of high importance in automated vehicles as it directly influences the vehicle’s performance and safety during operation. The linear quadratic regulator (LQR) controller stands out due to its high-performance characteristics and is used in the open source for self-driving functions. However, a notable limitation of the current approach is the manual calibration of LQR controllers based on the experience and intuition of the designers, leading to empirical uncertainties. To address this issue and enhance the lateral control performance, this paper concentrates on refining the LQR by employing three optimization algorithms: artificial bee colony optimization (ABC), genetic algorithm (GA), and particle swarm optimization (PSO). These algorithms aim to overcome the reliance on empirical methods and enable a data-driven approach to LQR calibration. By comparing the outcomes of these optimization algorithms to the manual LQR controller within an offline multibody simulation as a testing platform, this study highlights the superiority of the best-performing optimization approach. Following this, the optimal algorithm is implemented on a real-time system for the full vehicle level, revealing the model-in-the-loop and the hardware-in-the-loop gap up to 78.89% with lateral velocity when we use the relative error criterion (REC) method to validate and 2.35 m with lateral displacement when considering the maximum absolute value method.

Adaptive heading control strategy for unmanned ground vehicle with variable wheelbase based on robust-active disturbance rejection control

In order to fully exploit the variable wheelbase characteristics of the unmanned ground vehicle (UGV) with variable configuration, this paper proposes an adaptive heading tracking control strategy based on wheelbase changes. This strategy involves adjusting the wheelbase according to different working conditions to optimize various driving performance aspects. Firstly, the impact of changing wheelbase on the response characteristics of sideslip angle and heading angle relative to the front-wheel steering angle is analyzed by using a lateral vehicle dynamic model. The configurations where the 2nd axle moves forward by 0.5 m, remains unchanged, and moves backward by 0.5 m are defined as the ‘stable configuration’, ‘balanced configuration’, and ‘maneuverable configuration’, respectively. Considering time lag effects of hydraulic systems and external random noise interference, a robust-active disturbance rejection control (r-ADRC) method is developed by incorporating a robust term into active disturbance rejection control (ADRC) in order to achieve desired front-wheel steering angle. Additionally, a torque distribution method based on the tire load rate and the real-time vertical load of each wheel is applied to ensure uniform tire wear and enhance longitudinal driving stability. Finally, simulations under various typical working conditions as well as scaled prototype experiments are conducted, and both the theory behind the changing wheelbases and the effectiveness of proposed control strategy are verified. According to different vehicle configurations and mission requirements, the maneuverability and stability of the ground unmanned vehicle are ensured respectively.

Observer-based safety monitoring of nonlinear dynamical systems with neural networks via quadratic constraint approach

The safety monitoring for nonlinear dynamical systems with embedded neural network components is addressed in this paper. The interval-observer-based safety monitor is developed consisting of two auxiliary neural networks derived from the neural network components of the dynamical system. Due to the presence of nonlinear activation functions in neural networks, we use quadratic constraints on the global sector to abstract the nonlinear activation functions in neural networks. By combining a quadratic constraint approach for the activation function with Lyapunov theory, the interval observer design problem is transformed into a series of quadratic and linear programming feasibility problems to make the interval observer operate with the ability to correctly estimate the system state with estimation errors within acceptable limits. The applicability of the proposed method is verified by simulation of the lateral vehicle control system.

Nonlinear observer-based adaptive control of ground vehicles with uncertainty estimation

In this work, a nonlinear observer-based controller is designed for the attitude control of a ground vehicle with uncertainty estimation. This controller ensures the tracking of desired references in the presence of environmental disturbances and parametric uncertainties, making use of high-order sliding-mode estimators to estimate these perturbations. Furthermore, the controller incorporates a kinematic observer reconstructing the lateral vehicle velocity, based on a novel high-order sliding-mode observer. The proposed controller ensures good performance and better transient behavior with respect to existing controllers when parametric uncertainties and environmental disturbances are present. Its performance is evaluated by numerical simulation in CarSim, considering a challenging double turn maneuver, which is described in the ISO-3888 specifications.

Contribution to the Objective Evaluation of Combined Longitudinal and Lateral Vehicle Dynamics in Nonlinear Driving Range

<div>Since the complexity of modern vehicles is increasing continuously, car manufacturers are forced to improve the efficiency of their development process to remain profitable. A frequently mentioned measure is the consequent integration of virtual methods. In this regard, objective evaluation criteria are essential for the virtual design of driving dynamics. Therefore, this article aims to identify robust objective evaluation criteria for the nonlinear combined longitudinal and lateral dynamics of a vehicle. The article focuses on the acceleration in a turn maneuver since available objective criteria do not consider all relevant characteristics of vehicle dynamics. For the identification of the objective criteria, a generic method is developed and applied. First, an open-loop test procedure and a set of potential robust objective criteria are defined. Subsequently, suitable criteria are selected for different vehicle dynamics characteristics based on an investigation of Pearson correlations between the objective criteria and established subjective rating criteria. For this purpose, a subjective evaluation study with six specifically selected vehicle variants is conducted. Finally, the applicability of the selected objective criteria for vehicles of different segments is assessed through a benchmark of current vehicles. The results are objective criteria for the vehicle characteristics driving stability, oversteer/understeer, and traction. In contrast to existing objective criteria, the identified criteria shows a high robustness to measurement noise. Furthermore, there is a comprehensible correlation to established subjective rating criteria for each objective criterion. Lastly, the benchmark of current vehicles proves the applicability of the identified criteria.</div>

Channel-Level Event-Triggered Communication Scheme for Path Tracking Control of Autonomous Ground Vehicles With Distributed Sensors

In this paper, a channel-level event-triggered communication scheme is investigated for path tracking control of autonomous ground vehicles via an in-vehicle network to ensure path tracking performance while reducing network resource utilization. First, a path tracking system is established considering the effect of norm bounded uncertainty on lateral vehicle dynamics, and a state feedback path tracking controller is designed within the Takagi–Sugeno fuzzy framework. Next, a decentralized event-triggered communication scheme is adopted between the sensors and controller, which makes it possible to save communication resources at the channel level. Finally, the results in the CarSim-Simulink joint-simulation environment show that the proposed controller can ensure a reliable path tracking performance in both lateral offset and heading error. At the same time, compared with the simple time-triggered scheme, the proposed method can effectively reduce the usage of communication resources by more than 80%.