Vehicle Dynamic States Research Articles

Hybrid modeling for vehicle lateral dynamics via AGRU with a dual-attention mechanism under limited data

A precise vehicle dynamics model is critical for simulation and algorithm testing. Neural networks have been widely used to build high-fidelity vehicle dynamics models due to the excellent learning ability. However, data starvation is a common phenomenon in neural networks. With limited data, it is difficult for neural networks to achieve precise predictions. To address these problems, a hybrid model combining physics and dual attention neural networks is developed to model vehicle lateral dynamics. First, due to the interpretability of the physical model, linear lateral dynamics model is regarded as a prior model. However, due to the imperfect prior knowledge, there are residuals between the prior and the actual vehicle dynamics. Therefore, neural networks are used to characterize the residuals to achieve recalibration of vehicle dynamics model. Modeling vehicle residual dynamics with neural networks is a time series forecasting problem. The GRU with a dual attention mechanism and adaptive initial hidden states (DA-AGRU) is designed to capture spatial and temporal correlations in the vehicle dynamics data. In particular, considering the unique auto regressive structure of the hybrid model, a spatial attention mechanism with a feature fusion module is designed, so as to globally compute the weights of different channel features. The dataset used to train and validate the model is recorded from a vehicle platform, and the experimental results show that the proposed hybrid model can accurately predict vehicle dynamics states in a data-scarce environment.

Data-Driven Hazard Avoidance Landing of Parafoil: A Deep Reinforcement Learning Approach

This paper examines a couple of realizations of autonomous landing hazard avoidance technology of parafoil: a reinforcement-learning-based approach and a rule-based approach, advocating the former. Furthermore, comparative advantages and behavioral analogies between the two approaches are presented. In the data-driven approach, a decision process observing only a series of nadir-pointing images is designed without explicit augmentation of vehicle dynamics for the homogeneity of observation data. An agent then learns the hazard avoidance steering law in an end-to-end fashion. On the contrary, the rule-based approach is facilitated via explicit notions of guidance-control hierarchy, vehicle dynamic states, and metric details of ground obstacles. The soft actor–critic method is applied to learn a policy that maps the down-looking images to parafoil brakes, whereas a vector field guidance law is employed in the rule-based approach, considering each hazard as a repulsive source. This paper then presents empirical equivalences in designing both approaches and their distinctions. Numerical experiments in multiple test cases validate the reinforcement learning method and present comparisons between the approaches regarding their resultant trajectories. The interesting behaviors of the resultant policy of the data-driven approach are emphasized.

Combined Estimation of Vehicle Dynamic State and Inertial Parameter for Electric Vehicles Based on Dual Central Difference Kalman Filter Method

Distributed drive electric vehicles (DDEVs) possess great advantages in the viewpoint of fuel consumption, environment protection and traffic mobility. Whereas the effects of inertial parameter variation in DDEV control system become much more pronounced due to the drastic reduction of vehicle weights and body size, and inertial parameter has seldom been tackled and systematically estimated. This paper presents a dual central difference Kalman filter (DCDKF) where two Kalman filters run in parallel to simultaneously estimate vehicle different dynamic states and inertial parameters, such as vehicle sideslip angle, vehicle mass, vehicle yaw moment of inertia, the distance from the front axle to centre of gravity. The proposed estimation method only integrates and utilizes real-time measurements of hub torque information and other in-vehicle sensors from standard DDEVs. The four-wheel nonlinear vehicle dynamics estimation model considering payload variations, Pacejka tire model, wheel and motor dynamics model is developed, the observability of the DCDKF observer is analysed and derived via Lie derivative and differential geometry theory. To address system nonlinearities in vehicle dynamics estimation, the DCDKF and dual extended Kalman filter (DEKF) are also investigated and compared. Simulation with various maneuvers are carried out to verify the effectiveness of the proposed method using Matlab/Simulink-Carsim®. The results show that the proposed DCDKF method can effectively estimate vehicle dynamic states and inertial parameters despite the existence of payload variations and variable driving conditions. This research provides a boot-strapping procedure which can performs optimal estimation to estimate simultaneously vehicle system state and inertial parameter with high accuracy and real-time ability.

Vehicle State Estimation Combining Physics-Informed Neural Network and Unscented Kalman Filtering on Manifolds.

This paper proposes a novel vehicle state estimation (VSE) method that combines a physics-informed neural network (PINN) and an unscented Kalman filter on manifolds (UKF-M). This VSE aimed to achieve inertial measurement unit (IMU) calibration and provide comprehensive information on the vehicle's dynamic state. The proposed method leverages a PINN to eliminate IMU drift by constraining the loss function with ordinary differential equations (ODEs). Then, the UKF-M is used to estimate the 3D attitude, velocity, and position of the vehicle more accurately using a six-degrees-of-freedom vehicle model. Experimental results demonstrate that the proposed PINN method can learn from multiple sensors and reduce the impact of sensor biases by constraining the ODEs without affecting the sensor characteristics. Compared to the UKF-M algorithm alone, our VSE can better estimate vehicle states. The proposed method has the potential to automatically reduce the impact of sensor drift during vehicle operation, making it more suitable for real-world applications.

Robust Estimation of Vehicle Dynamic State Using a Novel Second-Order Fault-Tolerant Extended Kalman Filter

<div>The vehicle dynamic state is essential for stability control and decision-making of intelligent vehicles. However, these states cannot usually be measured directly and need to be obtained indirectly using additional estimation algorithms. Unfortunately, most of the existing estimation methods ignore the effect of data loss on estimation accuracy. Furthermore, high-order filters have been proven that can significantly improve estimation performance. Therefore, a second-order fault-tolerant extended Kalman filter (SOFTEKF) is designed to predict the vehicle state in the case of data loss. The loss of sensor data is described by a random discrete distribution. Then, an estimator of minimum estimation error covariance is derived based on the extended Kalman filter (EKF) framework. Finally, experimental tests demonstrate that the SOFTEKF can reduce the effect of data loss and improve estimation accuracy by at least 10.6% compared to the traditional EKF and fault-tolerant EKF.</div>

Path Planning and Obstacle Avoidance Control for Autonomous Multi-Axis Distributed Vehicle Based on Dynamic Constraints

Obstacle avoidance problem for the autonomous vehicle has received more and more attention these years, especially for the autonomous heavy vehicle, which has the high gravity center, large carrying capacity and promising commercial prospect. However, the vehicle dynamic properties have been rarely considered for path planning, which is a crucial factor for driving safety. An integrated collision avoidance framework that consists of a new path planner and a tracking controller considering multiple dynamic constraints is proposed for an autonomous multi-axis distributed vehicle. In the upper level, a new optimal path generator based on the B-splines is designed for safety and stability purposes, and the collision avoidance path is optimized considering multiple dynamic constraints, including the tire nonlinear dynamic, lateral stability limits and the anti-slip constraints. Meanwhile, a safety assessment evaluator according to the time to collision calculation is designed for risk level recognition and path planning weight determination. In the lower level, a path tracking controller based on the nonlinear model predictive control (NMPC) is designed to improve the control accuracy, and a high-fidelity nonlinear dynamic predictive vehicle model with 16 degrees of freedom is established to depict the vehicle dynamic properties comprehensively. To solve the nonlinear optimization problem and get the optimal control steering angle output, an adaptive weight adjustment strategy and a varying predictive duration method are formulated. The optimization constraints related to steering actuator ability, plane stability limits, rollover prevention thresholds and tire adhesion requirements are constructed and converted as the bounds of the vehicle dynamic states. To verify the proposed framework, the simulation and HIL test platform are built and different driving scenarios are validated. The test results show the satisfactory performance of path planning and path tracking considering the dynamic constraints for safety and stability

A Robust Hierarchical Estimation Scheme for Vehicle State Based on Maximum Correntropy Square-Root Cubature Kalman Filter

Accurate acquisition of vehicle dynamics state information is essential for vehicle active safety control systems. However, these states cannot be easily measured, and the measurement is expensive. Conventional Kalman filters perform well for vehicle state estimation in Gaussian environments but exhibit low accuracy and robustness under practical non-Gaussian noise. Vehicle model parameter ingestion, inaccurate tire force calculation, and non-Gaussian noise from on-board sensors cause great challenges to the estimation of vehicle driving states. Therefore, this paper presents a robust hierarchical estimation scheme for vehicle driving state based on the maximum correntropy square-root cubature Kalman filter (MCSCKF) using easily measurable on-board sensor information. First, the vehicle mass is dynamically updated based on the recursive least squares (FRLS) method with a forgetting factor. Then, an adaptive sliding mode observer (ASMO) is designed to estimate the longitudinal and lateral tire forces. Ultimately, the vehicle states are estimated based on the MCSCKF under non-Gaussian noise. Two typical operating situations are carried out to verify the validity of the proposed estimation scheme. The results prove that the proposed estimation scheme can estimate the vehicle's driving state accurately compared to other common methods. And the MCSCKF algorithm has better accuracy and robustness than the traditional Kalman filters for vehicle state estimation in non-Gaussian situations.

Adaptive vehicle dynamics state estimator for onboard automotive applications and performance analysis

This work describes the development of a vehicle state estimator, designed to be employed onboard in real-time, based on the data acquisitions already available within the vehicle CAN bus infrastructure. The proposed estimation algorithm, taking into account the suspension elasto-kinematics, the longitudinal, lateral and combined dynamics of the tyres as well as the aligning interaction torques at the ground, represents at the current stage a significantly complete tool, since it also provides an estimation of road slope and banking angles, generalising the adoption of the presented vehicle model even on highly inclined roads. A further advantage of the presented estimator consists of its capability to identify in real-time and with a good level of accuracy the tyre/road interaction physical characteristics in terms of grip and cornering stiffness.

Tire normal force estimation using artificial neural networks and fuzzy classifiers: Experimental validation

Tire normal forces play a crucial role in vehicle dynamic control systems (VDCs), and an accurate estimation of them could substantially improve vehicle handling and safety. Total normal forces on tires are the combination of the static and dynamic values. These values change by varying the vehicle static parameters (vehicle mass and CG position), the road grade, and vehicle dynamic states. All of the mentioned forces and parameters are used in the design of vehicle dynamics controllers. Therefore, to have an efficient estimation solution to access all different target controllers, the proposed estimation algorithm is divided into two parts. The first part is an ANN-based vehicle mass and CG position estimation algorithm and the second one is a deep-learning-based algorithm and an integrated hardware–software method to estimate dynamic normal forces. The first part includes two neural network (NN) blocks related to vehicle roll and pitch dynamics. The outputs of the NN blocks are load distributions for the axes associated with each dynamics. Based on the measurement unit data, the vehicle’s maneuvers are classified into one of many categories used for downstream tasks. The rules of the fuzzy classification logic determine which of the mentioned blocks to be activated. At the same time, an experimentally validated 9-DOF vehicle model instantaneously observes the estimated values. In the second part, long short-term memory (LSTM), gated recurrent unit (GRU), and an integrated hardware–software method were developed to assess the tire’s dynamic normal forces during maneuvers. The performed simulations and the results of field tests show that the proposed algorithm can accurately estimate the considered parameters in the presence of noise and disturbances. It is shown that the proposed algorithm is more accurate and faster than the extended Kalman filter and recursive least square estimation methods to estimate static values.

Vehicle Dynamics, Lateral Forces, Roll Angle, Tire Wear and Road Profile States Estimation - A Review

Vehicle Dynamics, Lateral Forces, Roll Angle, Tire Wear and Road Profile States Estimation - A Review

Hybrid physics and neural network model for lateral vehicle dynamic state prediction

The physical modeling-based approaches tend to be over-simplistic and cannot forecast the complex dynamical phenomena, thus leading to non-negligible errors. It is not easy to measure some parameters precisely, and they are usually approximated roughly. However, this approximation reduces the modeling accuracy of the physical model, which is a common problem in complex systems research. It is well-known that neural networks are capable of encoding dynamic information. The vehicle can be accurately modeled by collecting data during its motion. However, purely data-driven approaches have low interpretability and cannot be used in commercial applications. In this work, we present a new hybrid modeling architecture. Based on the physical model, the deep learning method is introduced to expand the incomplete dynamics described by differential equations. Compared with the physical modeling-based and purely data-driven approaches, the proposed technique has lower modeling error and higher interpretability. We evaluate the performance of the hybrid model based on the collected data. The test results show that the proposed architecture successfully captures the vehicle dynamics and reduces the error caused by multi-step prediction compared to the data-driven models. The results also show that the proposed method has value for significant research and practical application.

Longitudinal-lateral-cooperative estimation algorithm for vehicle dynamics states based on adaptive-square-root-cubature-Kalman-filter and similarity-principle

It is infeasible to measure vehicle dynamics states (VDS) directly without expensive measurement instruments, especially for the tire-road peak adhesion coefficient (μmax). However, four-wheel-independent-drive-electric-vehicle (4WIDEV) provides convenience for the observation of these dynamic states, because the rotation rate and torque of the in-wheel motor can be acquired directly. Vehicle nonlinear longitudinal-lateral dynamics, the single estimation method for all VDS and the time-varying measurement noise of sensors cause difficulties for the observation. Common the extended-Kalman-filter (EKF) is unsuitable to estimate VDS in strong nonlinear region. This paper propose a longitudinal-lateral cooperative estimation algorithm based on adaptive-square-root-cubature-Kalman-filter (ASRCKF) and partitioned similarity-principle (SP) to estimate the vehicle states and the tire-road peak adhesion coefficient sequentially for 4WIDEV. Firstly, a nonlinear 7-degree-of-freedom (7DOF) vehicle model and magic-formula (MF) tire model are built as the base of the successive estimation scheme. Then, recursive-least-squares (RLS) is adopted to estimate the tire longitudinal force. With the estimated tire longitudinal force, an ASRCKF which can be adjusted adaptively by the feedback dynamics states, is designed for the estimation of vehicle states. Next, the SP algorithm combined with the characteristic of longitudinal-lateral dynamics, which is benefit for μmax estimation when tire dynamics enters the nonlinear region, is proposed. Finally, experiment and simulation results show that excellent performance can be achieved with the proposed estimation method in varying driving conditions.

Comparative simulation study on two estimation methods and two control strategies for semi-active suspension

With regard to the structural characteristics of the McPherson suspension system, when a vehicle is being driven on a rough road surface, the force direction of the suspension varies. This poses challenges to the vehicle’s driving safety and handling stability. Based on Lagrangian equations, this paper proposes a new nonlinear semi-vehicle suspension model and presents comparative studies, conducted through simulation, on the estimated accuracy and computational overhead of the small-computational-overhead extended Kalman filter (EKF) and unscented Kalman estimation (UKF) methods, and on the effectiveness of the skyhook sliding mode control (SHSMC) and nonlinear skyhook-sliding mode control (NSHSMC) semi-active suspension control methods. The response of the vehicle to the state estimation algorithm was evaluated through computer simulations using the Carsim vehicle dynamic software. The simulation results reveal that the vehicle dynamic states were satisfactorily estimated when the vehicle was driven on a rough road surface. Compared with the small-computational-overhead EKF algorithm, the estimated results of these variables based on the UKF algorithm have higher accuracy. However, the UKF algorithm requires longer computation time compared with the EKF algorithm. The SHSMC control algorithm achieved greater improvement for the vehicle’s drive handling stability in the 6–10-Hz vibration region compared with the NSHSMC control algorithm. In a high-frequency region over 10Hz, the semi-active suspension controlled by the SHSMC method had a more adverse effect on the driving comfort.

Comparison and Evaluation of Integrity Algorithms for Vehicle Dynamic State Estimation in Different Scenarios for an Application in Automated Driving.

High-integrity information about the vehicle’s dynamic state, including position and heading (yaw angle), is required in order to implement automated driving functions. In this work, a comparison of three integrity algorithms for the vehicle dynamic state estimation of a research vehicle for an application in automated driving is presented. Requirements for this application are derived from the literature. All implemented integrity algorithms output a protection level for the position and heading solution. In the comparison, four measurement data sets obtained for the vehicle dynamic state estimation, which is based on a Global Navigation Satellite Signal receiver, inertial measurement units and odometry information (wheel speeds and steering angles), are used. The data sets represent four driving scenarios with different environmental conditions, especially regarding the satellite signal reception. All in all, the Kalman Integrated Protection Level demonstrated the best performance out of the three implemented integrity algorithms. Its protection level bounds the position error within the specified integrity risk in all four chosen scenarios. For the heading error, this also holds true, with a slight exception in the very challenging urban scenario.

Model Predictive Control of Soft Constraints for Autonomous Vehicle Major Lane-Changing Behavior With Time Variable Model

Changing lane must not only ensure the safety of the vehicle itself, but also ensure the patency of the traffic flow of the original lane and the target lane. Therefore, successful lane-changing is a key technology for autonomous vehicle control. In order to avoid collisions and ensure the smooth flow of traffic, in this paper a vehicle dynamics state model with time variable is established as plant, and the lateral force of the steering wheel is further optimized through Model Predictive Control(MPC), and then the steering wheel angle is obtained to complete the lane-changing operation. The longitudinal and lateral logic controllers designed through soft constraints can better achieve the results of successful lane-changing and unsuccessful return to the original lane, and the lane-changing characteristics within the safety corridor are analyzed in several ways. The simulation analysis of lane-changing strategy at different vehicle velocities provides helpful guidance for the design of autonomous vehicle controllers.

A hierarchical estimation scheme of tire-force based on random-walk SCKF for vehicle dynamics control

The estimation of vehicle dynamics states is crucial for vehicle stability control and autonomous driving, especially tire-force which governs vehicular motion. However, measuring tire-force directly needs expensive measurement instruments, moreover, vehicle non-linear characteristics, vehicle parameter uncertainties, unknown key variables, and sensor noise could cause great challenges in its observation. Therefore, this paper aims to develop an accurate, affordable tire-force estimator to tackle the above-mentioned issues. A novel hierarchical estimation scheme based on random-walk square-root cubature Kalman filter (SCKF) is proposed and it works without a complex tire model and considers vehicle parameter uncertainties. The estimator scheme contains three blocks. The first block estimates related key variables of tire force observation. The second block estimates both vertical tire-force and longitudinal tire-force. The longitudinal tire-force is observed based on effective tire radius identification, and a proportional integral differential (PID) method is derived based on the Lyapunov principle. Then, a random-walk SCKF algorithm is presented to estimates lateral tire-force. To validate the effectiveness of the proposed estimation scheme, CarSim & Matlab/Simulink joint simulation and real car tests are carried out. Results show that the proposed estimation scheme's accuracy performance and its potential as an affordable solution for the tire-force observation.

Adaptive estimations of tyre–road friction coefficient and body’s sideslip angle based on strong tracking and interactive multiple model theories

Vehicle dynamic states and parameters, such as the tyre–road friction coefficient and body’s sideslip angle especially, are crucial for vehicle dynamics control with close-loop feedback laws. Autonomous vehicles also have strict demands on real-time knowledge of those information to make reliable decisions. With consideration of the cost saving, some estimation methods employing high-resolution vision and position devices are not for the production vehicles. Meanwhile, the bad adaptability of traditional Kalman filters to variable system structure restricts their practical applications. This paper introduces a cost-efficient estimation scheme using on-board sensors. Improved Strong Tracking Unscented Kalman filter is constructed to estimate the friction coefficient with fast convergence rate on time-variant road surfaces. On the basis of previous step, an estimator based on interactive multiple model is built to tolerant biased noise covariance matrices and observe body’s sideslip angle. After the vehicle modelling errors are considered, a Self-Correction Data Fusion algorithm is developed to integrate results of the estimator and direct integral method with error correction theory. Some simulations and experiments are also implemented, and their results verify the high accuracy and good robustness of the cooperative estimation scheme.

Power management optimization in plug-in hybrid electric vehicles subject to uncertain driving cycles

Abstract Optimization of power management in plug-in hybrid electric vehicles (PHEVs) with dual-power-source plays a critical role in achieving higher fuel economy and less pollutant emissions. In this study, power management and optimal control strategies in PHEVs have been investigated subject to uncertain driving cycles of individual drivers for particular trips. First, a stochastic driving cycle is constructed to more accurately model the dynamic characteristics of the uncertain driving cycles, derived from the historic record of individual drivers. Finite-horizon stochastic dynamic programming is adapted to globally optimize the vehicle performance in stochastic sense. Simulation results show that the proposed strategy significantly improves fuel economy, indicating the present optimization approach is very effective in exploring the potential of the hybridization of power train. A higher discretization of (that is, with smaller step sizes in) vehicle dynamics state variables (vehicle velocity, power demand and battery state of charge) has a positive impact on the fuel economy while the limitation of driving operability actually degrades the fuel economy. The commuting time with doubly truncated normal distribution slightly enhances the fuel economy in comparison with uniform distribution. In addition, there exists a tradeoff between the fuel economy and the pollutant emissions. These results could be utilized as a guideline for the design of PHEVs with different objectives.

Real-time estimation and prediction of tire forces using digital map for driving risk assessment

This work aims to develop a driving risk warning system to enhance the road safety. Different from the existing lane departure warning system, speed limit warning system or collision warning system, the warning system proposed in this work focuses on the safety regarding vehicle's dynamics states. Many road accidents are caused by losing control of vehicle dynamics, such as the rollover, car drift and brake failure. First of all, the importance of monitoring vehicle dynamics states, especially the tire forces, is explained. Then the driving risk assessment criteria based on tire forces are developed in this work. The main contribution of this paper is the development of vehicle dynamics models and observers to estimate and predict individual tire forces using only low-cost sensors and ADAS (Advanced Driver Assistance Systems) map. The major new techniques developed in this study can be summarized in three aspects: (1) development of new vehicle dynamics models to estimate vertical, longitudinal, and lateral tire forces, (2) development of new nonlinear observers to minimize the estimation errors caused by sensor noises and model uncertainty, and (3) development of the tire forces prediction algorithm by taking advantage of digital map. The proposed warning system is validated by real vehicle experiments.

Hardware-in-the-loop simulation for estimating dynamics parameters of vehicle

Information about vehicle dynamics states is indispensable for modern dynamics control system on vehicle today. For economic reasons, a technique called “virtual sensor” which bases on dynamical model of vehicle and an observation algorithm are used to estimate real states of vehicle. In this paper, a system based on Hardware-in-the-loop simulation will be used to estimate the vehicle states in real time. CarSim is a professional software for simulating the dynamics of vehicle which is used as a virtual vehicle in this paper. An observer based on Luen-berge method is developed and implemented by Arduino Mega 2560 board. Matlab/Simulink plays the role of acquistion and data transfer center. The simulation results show the good performance of observer in real time condtion when the estimated values are well converged to real values given by CarSim.