Lateral Dynamic Model Research Articles

Optimization design of unmanned mining truck path tracking controller based on road adhesion coefficient estimation

Abstract In response to the issues of inaccurate tracking precision caused by continuous turning and variable road adhesion coefficients on complex roads in mining areas for unmanned mining trucks, this paper adopts unscented Kalman filter (UKF) to estimate the road adhesion coefficient. Based on this, an adaptive preview feedforward linear quadratic regulator (LQR) control algorithm is designed using genetic algorithm, feedforward control, and linear quadratic optimal path tracking control methods. Firstly, a nine degree of freedom vehicle dynamics model and a two degree of freedom vehicle lateral dynamics model are established, and the Dugoff model to calculate tire forces is introduced; secondly, utilizing UKF to estimate the road adhesion coefficient, and leveraging active disturbance rejection control for rapid tracking of road curvature, an optimized design of the LQR controller is carried out. Then, the effectiveness of the designed controller was verified through Trucksim/Simulink joint simulation testing. Finally, the hardware in the loop test results showed that the designed controller had good tracking accuracy and strong adaptability in complex road and special working conditions in mining areas.

Dynamic modelling and experimental validation of a dynamic track stabiliser vehicle–track spatially coupling dynamics system

A dynamic track stabiliser vehicle is an unconventional vehicle for maintaining the quality of ballasted tracks, and its dynamic performance has a significant impact on its working efficiency. For the first time, this paper proposes a comprehensive dynamic track stabiliser vehicle–track coupled vertical and lateral multi-body dynamics model based on classical vehicle–track coupling dynamics theory. In this model, detailed attention is given to the vertical, lateral, roll, yaw, and pitch motions of the components, including the vehicle body, bogies, wheelsets and stabilisers. The Shen–Hedrick–Elkins theory is employed to describe non-linear wheel–rail contact relationships between the bogie wheelsets and the rails, and three various methodologies are adopted to address complicated wheel–rail interaction problems between the stabiliser wheelsets and the rails. This comprehensive multi-body dynamics model enables a detailed investigation of the dynamic performance of the system under complex excitations, such as the lateral excitation of the stabilisers and vertical downward pressure exerted by hydraulic cylinders, especially the dynamic response of the stabilisers in the vibration environment of the complete vehicle. The dynamics model was fully validated by comparing its results with time- and frequency-domain data obtained from field tests. The results indicate that the model is capable of being used for analysis of the dynamic performance of dynamic track stabiliser vehicles.

An asymmetrically variable wingtip anhedral angles morphing aircraft based on incremental sliding mode control: Improving lateral maneuver capability

This paper presents the design of an asymmetrically variable wingtip anhedral angles morphing aircraft, inspired by biomimetic mechanisms, to enhance lateral maneuver capability. Firstly, we establish a lateral dynamic model considering additional forces and moments resulting during the morphing process, and convert it into a Multiple Input Multiple Output (MIMO) virtual control system by importing virtual inputs. Secondly, a classical dynamics inversion controller is designed for the outer-loop system. A new Global Fast Terminal Incremental Sliding Mode Controller (NDO-GFTISMC) is proposed for the inner-loop system, in which an adaptive law is implemented to weaken control surface chattering, and a Nonlinear Disturbance Observer (NDO) is integrated to compensate for unknown disturbances. The whole control system is proven semi-globally uniformly ultimately bounded based on the multi-Lyapunov function method. Furthermore, we consider tracking errors and self-characteristics of actuators, a quadratic programming-based dynamic control allocation law is designed, which allocates virtual control inputs to the asymmetrically deformed wingtip and rudder. Actuator dynamic models are incorporated to ensure physical realizability of designed allocation law. Finally, comparative experimental results validate the effectiveness of the designed control system and control allocation law. The NDO-GFTISMC features faster convergence, stronger robustness, and 81.25% and 75.0% reduction in maximum state tracking error under uncertainty compared to the Incremental Nonlinear Dynamic Inversion Controller based on NDO (NDO-INDI) and Incremental Sliding Mode Controller based on NDO (NDO-ISMC), respectively. The design of the morphing aircraft significantly enhances lateral maneuver capability, maintaining a substantial control margin during lateral maneuvering, reducing the burden of the rudder surface, and effectively solving the actuator saturation problem of traditional aircraft during lateral maneuvering.

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.

Modal coupling characteristics of primary hunting in metro vehicles: Carbody suspension modes and hunting modes

Due to coupling with carbody suspension modes in railway vehicles, primary hunting can lead to significant low frequency swaying of the carbody, severely deteriorating ride quality. In order to address this issue, this paper conducts a detailed investigation into the coupling effect between suspension modes and hunting modes of metro vehicles. Initially, a simplified lateral dynamics model is established, and a continuous modal tracking method is adopted for track suspension modes and hunting modes. The results indicate that when the modal frequency of one hunting mode approaches that of corresponding suspension mode, the damping ratio of the two modes exhibits abnormal variation, and the modal frequency curve veers or is slightly disturbed. In exploring the coupling characteristics of hunting modes and suspension modes, revealing the variation trends and similarity of modal shapes, polar diagrams of modal shapes are presented, and the correlation distance is calculated. Equivalent conicity exerts a substantial influence on the effect of modal coupling, influencing minimum damping ratio and modal shape similarity within the modal coupling zone. To ensure sufficient stability margin for metro vehicles, it is necessary to avoid excessively low equivalent conicity. Finally, the phenomenon of vibration response deterioration within the modal coupling zone is confirmed through both a simplified model and a full DOF model.

Integration of bio-inspired limb-like structure damping into motor suspension of high-speed trains to enhance bogie hunting stability

Hunting stability is an important performance criterion in railway vehicles. This study proposes an incorporation of a bio-inspired limb-like structure (LLS)-based nonlinear damping into the motor suspension system for traction units to improve the nonlinear critical speed and hunting stability of high-speed trains (HSTs). Initially, a vibration transmission analysis is conducted on a HST vehicle and a metro vehicle that suffered from hunting motion to explore the effect of different motor suspension systems from on-track tests. Subsequently, a simplified lateral dynamics model of an HST bogie is established to investigate the influence of the motor suspension on the bogie hunting behavior. The bifurcation analysis is applied to optimize the motor suspension parameters for high critical speed. Then, the nonlinear damping of the bio-inspired LLS, which has a positive correlation with the relative displacement, can further improve the modal damping of hunting motion and nonlinear critical speed compared with the linear motor suspension system. Furthermore, a comprehensive numerical model of a high-speed train, considering all nonlinearities, is established to investigate the influence of different types of motor suspension. The simulation results are well consistent with the theoretical analysis. The benefits of employing nonlinear damping of the bio-inspired LLS into the motor suspension of HSTs to enhance bogie hunting stability are thoroughly validated.

The Two-Parameter Bifurcation and Evolution of Hunting Motion for a Bogie System

The complex service environment of railway vehicles leads to changes in the wheel–rail adhesion coefficient, and the decrease in critical speed may lead to hunting instability. This paper aims to reveal the diversity of periodic hunting motion patterns and the internal correlation relationship with wheel–rail impact velocities after the hunting instability of a bogie system. A nonlinear, non-smooth lateral dynamic model of a bogie system with 7 degrees of freedom is constructed. The wheel–rail contact relations and the piecewise smooth flange forces are the main nonlinear, non-smooth factors in the system. Based on Poincaré mapping and the two-parameter co-simulation theory, hunting motion modes and existence regions are obtained in the parameter plane consisting of running speed v and the wheel–rail adhesion coefficient μ. Three-dimensional cloud maps of the maximum lateral wheel–rail impact velocity are obtained, and the correlation with the hunting motion pattern is analyzed. The coexistence of periodic hunting motions is further revealed based on combined bifurcation diagrams and multi-initial value phase diagrams. The results show that grazing bifurcation causes the number of wheel–rail impacts to increase at a low-speed range. Periodic hunting motion with period number n = 1 has smaller lateral wheel–rail impact velocities, whereas chaotic motion induces more severe wheel–rail impacts. Subharmonic periodic hunting motion windows within the speed range of chaotic motion, pitchfork bifurcation, and jump bifurcation are the primary forms that induce the coexistence of periodic motion.

Study of the influence of lateral forces and velocity on the lateral dynamics of automobile

Stability of a car's trajectory of motion is the ability of a car to retain its required state of motion, under different conditions of motion. Depending on different states of motion, cars can lose direction of motion instability when there is a lateral force, due to vehicle speed, due to turning or braking the road with different grip coefficients on the sides of the wheel. In such complex moving conditions, cars need to keep a stable trajectory of movement under the driver's control. The paper examines the stability of the car's trajectory in linear motion conditions with the influence of lateral forces and the velocity of the vehicle, these two factors act to change the state of movement of the vehicle, which significantly affects the safety of the vehicle's movement. The authors looked at the effect of vehicle velocity and lateral forces on vehicle transverse dynamics: lateral forces caused by horizontal winds, inclination of the road surface, speed of movement of the vehicle acting on the entire body create centrifugal inertial forces; this force acts to cause the tires to deform. At this point the vehicle is shifted from its original trajectory. In the research content, the authors built a lateral Dynamics Model, in which the influencing factors are set as inputs to the model including vehicle velocity and transverse wind forces, output is the rotation angle of the body, transverse acceleration and horizontal displacement of the vehicle. The simulation results showed that the effect of vehicle speed was relatively large: lateral displacement increased by 228 % at a speed of 120 km/h. Therefore, when driving on the highway, there should always be driver control to ensure that the car does not deviate from the lane

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

A Direct Yaw Moment Control Framework Through Robust T-S Fuzzy Approach Considering Vehicle Stability Margin

The direct yaw moment control system of distributed drive electric vehicles provides a flexible control scheme to enhance the vehicle stability through four independently driven in-wheel motors. However, the vehicle nonlinearities may lead to the invalidation of control. To this end, a Takagi–Sugeno (T-S) fuzzy-based robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H∞</i> control method is proposed to ensure the vehicle performance while addressing the nonlinear challenge. First, thanks to the T-S fuzzy modeling technology, the tire nonlinear characteristics are described by fuzzy rules, based on which the vehicle lateral dynamics model is established. Next, the safety region represented by the tire slip angles phase plane is presented to evaluate the vehicle stability performance. Considering the control priority of vehicle handling performance and stability control with different stability margins, a multiobjective optimization function is transformed into a standard robust performance optimization problem with dynamic weight coefficients. A T-S fuzzy-based robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H∞</i> state feedback controller is then designed to ensure the system stability and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H∞</i> performance. Finally, the hardware-in-the-loop tests are conducted to validate the proposed controller. Comparative results show the effectiveness to improve the vehicle handling performance while ensuring the stability.

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

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

Trajectory Tracking for Autonomous Vehicles Using Robust Model Predictive Control

This paper proposes a novel trajectory tracking control method using a robust model predictive control (RMPC) design technique based on matrix inequality and the theoretical approach of the hybrid & switched system. Firstly, considering bounded model uncertainties and norm-bounded external disturbances, the system states and control matrices are modified. In addition, vehicle time-varying longitudinal speed is considered, and a vehicle lateral dynamic model based on Linear Parameter Varying (LPV) is established by utilizing a polytope with finite vertices. Then the Min-Max robust MPC state feedback control law is obtained at every timestamp by solving a set of matrix inequalities which are derived from Lyapunov stability and the minimization of the worst-case in infinite-horizon quadratic objective function. The numerical simulation results demonstrated that the proposed robust LPV MPC can effectively track vehicle lateral dynamics on both straight and curved roads with varying longitudinal speeds.

Impacts of Tapered Wingtip on Lateral-Directional Stability Coefficients of a Morphing Fixed-wing UAV

Recent developments in unmanned aerial vehicle (UAV) technologies have shown the possibility of morphing applications to provide improvement in various performance metrics in the desired manner. In rotary-wing UAVs, applications mainly focused on propeller blades and rotor arms, while efforts on fixed-wing UAVs mainly concentrated on the main wing and tail geometries. Although every morphing design has its own advantages and disadvantages, all of the applications have similar common purposes to have improved aerodynamics, flight performance, control responses, or a combination of such objectives. In that context, new morphing design attempts require a precise investigation of their pros and cons. Thus, in this study, a new morphing scenario of tapering morphing wingtip is applied to ZANKA-I fixed-wing UAV and investigated in terms of lateral-directional stability considerations. The lateral dynamic model of the aircraft is constituted and necessary aerodynamic, geometric, and inertial assessments are numerically and analytically performed. The lateral-directional stability coefficients are discussed and an improvement in lateral stability is obtained, while directional stability is found to be affected negatively by the morphing application.

Development and performance evaluation of lateral control simulation-based multi-body dynamics model for autonomous agricultural tractor

Development and performance evaluation of lateral control simulation-based multi-body dynamics model for autonomous agricultural tractor

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.

Planning and tracking control of full drive-by-wire electric vehicles in unstructured scenario

Full drive-by-wire electric vehicles (FDWEV) equipped with X-by-wire technology can enable independent driving, braking, and steering of each wheel, making them an ideal platform for developing autonomous driving technology. However, designing a robust control algorithm that comprehensively integrates vehicle path planning in a complex and unstructured scenario is a challenging task for FDWEV. To address this issue, this paper (1) proposes the artificial potential field (APF) method for path planning in the prescribed park with different static obstacles to generate the reference path information, where speed planning is incorporated considering kinematics and dynamic constraints; (2) designs curvature calculation (CC-based) and model predictive control (MPC-based) tracking methods with the lateral dynamics model to track the desired path under different driving conditions, in which a forward-looking behavior model of the driver with variable preview distance is designed based on the fuzzy control theory; (3) conducts CarSim-AMESim-Simulink co-simulation with the existence of obstacles. The simulation results show that the proposed two control approaches are practical for classical driving scenarios. Especially the MPC-based path-tracking controller enhances dynamic tracking performance and ensures good maneuverability under high-dynamic driving conditions.

A road adhesion coefficient-tire cornering stiffness normalization method combining a fractional-order multi-variable gray model with a LSTM network and vehicle direct yaw-moment robust control.

A normalization method of road adhesion coefficient and tire cornering stiffness is proposed to provide the significant information for vehicle direct yaw-moment control (DYC) system design. This method is carried out based on a fractional-order multi-variable gray model (FOMVGM) and a long short-term memory (LSTM) network. A FOMVGM is used to generate training data and testing data for LSTM network, and LSTM network is employed to predict tire cornering stiffness with road adhesion coefficient. In addition to that, tire cornering stiffness represented by road adhesion coefficient can be used to built vehicle lateral dynamic model and participate in DYC robust controller design. Simulations under different driving cycles are carried out to demonstrate the feasibility and effectiveness of the proposed normalization method of road adhesion coefficient and tire cornering stiffness and vehicle DYC robust control system, respectively.

Coordination Control of Active Steering and Direct Yaw Control for the Articulated Steering Vehicle

Lateral stability is vital to vehicle handling stability and traffic safety. It is also a crucial factor for the path-tracking ability of the vehicle in the intelligent transportation system (ITS). Most of the research focuses on vehicles with an Ackerman steering system. The ASV (articulated steering vehicle) has a lower steering radius. Thus, it is widely used in some special vehicles, such as mining and construction vehicles. The ASV has weaker lateral stability than the vehicle with an Ackerman steering system. To improve the stability of an ASV, the nonlinear lateral dynamic model is established and validated by field test. With the lateral dynamic model, the steering characteristic of the ASV is analyzed. Based on the stability criteria analysis, the vehicle sideslip angle and angular velocity phase portrait are chosen as the stability indicator. An integrated AASS (active articulated steering system) DYC (direct yaw control) controller based on the adaptive MPC (model predictive control) method is designed according to the track on the phase plane. The double lane-change and 0.7 Hz sine with dwell maneuver are initiated based on the integrated vehicle dynamic model. The results suggest that the provided controller has a better stability performance than the current antiwindup PID control algorithm. It lays a good foundation for the vehicle safety and path tracking of ASV in the ITS.

Dynamic Model Based Research on Intelligent Vehicle Steering and Obstacle Avoidance

In order to improve road safety, promote the development of autonomous driving, and realize the stability of unmanned vehicles during steering and obstacle avoidance, this paper establishes a lateral dynamic model and a cyclotron curve model based on the 3-degree-freedom vehicle dynamics model. Taking no collision between cars and timely obstacle avoidance as the optimization goal, this paper discretizes the model, a prediction model is established, a soft constraint solver is designed, and a relaxation factor is added to the performance index function. Based on the model prediction and control principle, the obstacle avoidance trajectory planning and tracking of unmanned vehicles is integrated and controlled, and the solution is converted into a quadratic programming problem according to the constraints and rolling optimization characteristics. Finally Matlab/Prescan joint simulation is used to verify the steering and obstacle avoidance quality of the model. The results show that the model has excellent safety, stability and comfort in non-highspeed situations.

Study on the Lateral Dynamic Impedance of Pile Groups in Transversely Isotropic Soil Using Novak’s Plane Model

In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio G h v of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing S / d have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil E p / G v has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.