Nonlinear Tire Research Articles

A Real-Time Nonlinear Model Predictive Control Strategy for Stabilization of an Electric Vehicle at the Limits of Handling

In this paper, we propose a real-time nonlinear model predictive control (NMPC) strategy for stabilization of a vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear four-wheel vehicle model that neglects the wheel dynamics is coupled with a nonlinear tire model to design three MPC strategies of different levels of complexity that are implementable online: one that uses a linearized version of the vehicle model and then solves the resulting quadratic program problem to compute the necessary longitudinal slips on the rear wheels, a second one that employs the real-time iteration scheme on the NMPC problem, and a third one that applies the primal dual interior point method on the NMPC problem instead until convergence. Then, a sliding mode slip controller is used to compute the necessary torques on the rear wheels based on the requested longitudinal slips. After analyzing the relative tradeoffs in performance and computational cost between the three MPC strategies by comparing them against the optimal solution in a series of simulation studies, we test the most promising solution in a high-fidelity environment.

Emergency steering control of autonomous vehicle for collision avoidance and stabilisation

ABSTRACTCollision avoidance and stabilisation are two of the most crucial concerns when an autonomous vehicle finds itself in emergency situations, which usually occur in a short time horizon and require large actuator inputs, together with highly nonlinear tyre cornering response. In order to avoid collision while stabilising autonomous vehicle under dynamic driving situations at handling limits, this paper proposes a novel emergency steering control strategy based on hierarchical control architecture consisting of decision-making layer and motion control layer. In decision-making layer, a dynamic threat assessment model continuously evaluates the risk associated with collision and destabilisation, and a path planner based on kinematics and dynamics of vehicle system determines a collision-free path when it suddenly encounters emergency scenarios. In motion control layer, a lateral motion controller considering nonlinearity of tyre cornering response and unknown external disturbance is designed using tyre lateral force estimation-based backstepping sliding-mode control to track a collision-free path, and to ensure the robustness and stability of the closed-loop system. Both simulation and experiment results show that the proposed control scheme can effectively perform an emergency collision avoidance manoeuvre while maintaining the stability of autonomous vehicle in different running conditions.

Model predictive rollover prevention for steer-by-wire vehicles with a new rollover index

ABSTRACTRecent advances in active safety systems provide new opportunities to handle rollover problems more efficiently. This paper presents a Model Predictive Control (MPC) strategy for rollover prevention through active front steering. A new Rollover Index (RI) and a specified vehicle model are proposed to realise an effective rollover prevention approach. The new RI is represented by vehicle parameters and state variables so that it can be readily incorporated into the MPC objective function. Using a barrier cost function, the proposed MPC controller limits vehicle maneuvers within a safe region of rollover without sacrificing vehicle maneuverability under normal conditions. The roll dynamics, the tire nonlinearity, the lateral load transfer, and the road bank are considered for vehicle modelling to provide appropriate actions at the threshold of a rollover. An affine tire model is used to handle tire nonlinearity in the MPC structure. A high-fidelity CarSim model for an SUV is employed to evaluate the proposed RI and the MPC controller. Simulation results show the reliability of the proposed RI and the effectiveness of the proposed rollover prevention controller for different rollover situations.

A Novel Design of Traction Control Based on a Piecewise-Linear Parameter-Varying Technique for Electric Vehicles With In-Wheel Motors

This paper presents a novel piecewise-linear robust traction controller for electric vehicles with in-wheel motors. Considering the nonlinear tire force and the time-varying wheel and vehicle speeds, a piecewise-linear parameter-varying (PWLPV) slip-ratio model with disturbances is first established. A novel traction controller is then designed. The key of the traction controller proposed in this paper is to separate the traction torque into a feedforward control torque and a PWLPV feedback control torque to track the desired slip ratio. The feedforward controller is calculated through the desired working point of the PWLPV slip-ratio model. The PWLPV controller can guarantee the closed-loop stability and $H_{\infty }$ performance for disturbance rejection. To verify the effectiveness of the proposed traction controller, both simulations and experiments are performed. A high-fidelity vehicle model in veDYNA is employed for simulation studies. Experiments were carried out on an electric vehicle with in-wheel motors. The experimental tests were performed on a brake-measurement track at Nong'an Automotive Proving Ground of the First Automobile Works.

Non-linear tyre model–based non-singular terminal sliding mode observer for vehicle velocity and side-slip angle estimation

Vehicle velocity and side-slip angle are important vehicle states for the electronic stability programme and traction control system in vehicle safety control system and for the control allocation method of electric vehicles with in-wheel motors. This paper proposes an innovative side-slip angle estimator based on the non-linear Dugoff tyre model and non-singular terminal sliding mode observer. The proposed estimation method based on the non-linear tyre model can accurately present the tyre’s non-linear characteristics and can show advantages over estimation methods based on the linear tyre model. The utilised Dugoff tyre model has a relatively simple structure with few parameters, and the proposed non-linear observer can be applied in various vehicle tyres and various road conditions. Precise determination of the Dugoff tyre model parameters is not required and the proposed observer can still perform good estimation results even though tyre parameters and the tyre–road friction coefficient are not accurate. The proposed non-singular terminal sliding mode observer can achieve fast convergence rate and better estimation performance than the traditional sliding mode observer. At the end of this paper, simulations in various conditions are presented to validate the proposed non-linear estimator.

Generating MMM diagram for defining the safety margin of self driving cars

Autonomous driving, is considered as the future of mobility, and research on this topics growing exponentially. On the one hand, these vehicles must be controllable, making rapid maneuvers possible, in case of a sudden accident situation, while on the other hand their motion must be stable, to maintain directional stability under disturbances. It is important to specify the so called “safety margin”, the range of possible motions that the vehicle can produce with keeping its stability. The limits of the possible movement of a vehicle depend on its parameters. The aim of our study is to determine which parameters affect the controllability and stability of a vehicle. To find this, we used the “MRA moment method” to create the “Yaw Moment Diagram” in our simulation environment. This method is usually used to map the possible range of motion and judge the stability and controllability of a possible motion state. Here we will use a two track vehicle model, with nonlinear tire characteristics, and complete model of suspension linkage to create the MMM diagram of a vehicle with given parameters.

Vehicle Dynamics Modeling and Electronic Stability Program/ Active Front Steering Sliding Mode Integrated Control

AbstractChassis integrated control can significantly improve vehicle handling stability and comfort. Because of the complexity of the problem, it has attracted significant research attention. We built a vehicle nonlinear dynamic model with multi‐degree freedom, including body movement, wheel movement, and electronically controlled hydraulic power steering system. We compared the magic formula tire model, Dugoff tire model, brush tire model, and LuGre dynamic friction tire model and steady model. The precision of the model was verified by a comparison between simulation results and the real vehicle test results. Then, based on the vehicle dynamics model, an AFS (active front steering) controller was designed based on sliding mode variable structure control, and an AFS and ESP (electronic stability program) integrated coordination controller was proposed. Finally, based on the nonlinear tire model and multi‐DOF (degree of freedom) vehicle model, sinusoidal and step steering angle input simulation analysis was proposed on different road friction coefficients. The results show that the vehicle has better response characteristics with coordinated control strategy when compared with AFS and ESP only control. The evidence suggests that the proposed integrated control system in this paper can improve vehicle stability and safety.

Coordinated Longitudinal and Lateral Motion Control for Four Wheel Independent Motor-Drive Electric Vehicle

For four wheel independent motor-drive electric vehicle, the vehicle longitudinal and lateral motion can be controlled by distributing the driving and regenerative braking torques of four wheel motors. To meet the driving command of driver and keep the vehicle lateral stability, a hierarchical control system is proposed in this paper. In the upper layer, a nonlinear model predictive control is implemented to solve the nonlinear multiinput multioutput, over-actuated problem. The controller is based on a nonlinear three degree-of-freedom model with nonlinear tire model, considering wheel slips as virtual control input. In the lower layer, the wheel slips are manipulated by a PID controller for generating driving and regenerative braking torques of the independent motors. This proposed controller is tested in a hardware-in-the-loop system with four typical maneuvers, which are constant velocity, accelerating, decelerating, and low road adhesion coefficient situations to show different driver command. The results show that the driver command of longitudinal and lateral motion control are both satisfied.

Nonlinear dynamics modeling and rollover control of an off-road vehicle with mechanical elastic wheel

Nonlinear dynamics modeling and rollover stability control are the indispensable parts of automotive active safety research, especially for the military off-road vehicle with some special demands. The nonlinearity of the vehicle model refers to the nonlinear tire characteristics. By simplifying the structure of non-pneumatic mechanical elastic wheel (ME-Wheel),the change of half long grounding mark, lateral distribution stiffness along with vertical load is studied, and the corresponding fitting model is established. Then, a corrected tire brush model is constructed and a longitudinal and lateral force expression is set up. Finally, a nonlinear 8-DOF vehicle model for an off-road vehicle with ME-Wheel was built up and an active suspension control system based on rollover prediction and Fuzzy proportional-integral-derivative (PID) is designed for rollover prevention, which utilizes a predictive load transfer ratio (PLTR) as the rollover index and the Fuzzy PID controller activates only when the potential for rollover is significant as measured by the PLTR. The effectiveness of proposed tire model and vehicle model are verified by virtual simulations and experiments. Simulation results during single lane-change and fishhook maneuvers show that the PLTR index can provide a time-advanced measure of rollover propensity and Fuzzy PID anti-rollover control algorithm based on PLTR index has better stability of roll than load transfer ratio index.

Straight ahead running of a nonlinear car and driver model – new nonlinear behaviours highlighted

ABSTRACTThe paper deals with the bifurcation analysis of a validated simple model describing a vehicle+driver running straight ahead. The mechanical model of the car has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. The driver is described by a very simple model. Bifurcation analysis is adopted for characterising straight ahead motion at different speeds for different drivers. A nonlinear sensitivity analysis is performed as a function of the driver's parameters and forward vehicle speed. A wealth of unreferenced bifurcations is discovered both for the understeering (UN) and for the oversteering (OV) vehicle. For the UN vehicle, a supercritical Hopf bifurcation may occur as the forward speed is increased. Also tangent (fold) bifurcations (saddle-node bifurcation of limit cycles) occur as the speed (or disturbance) is further increased. For the OV vehicle, a subcritical Hopf bifurcation occurs as the speed reaches a critical value. The preview distance (a driver's control parameter) plays a fundamental role in straight ahead driving. Either too short or too long preview distances are negative for straight ahead running.

A Piecewise Affine Robust Yaw Stability Control Method for In-wheel Motor Electric Vehicle

Considering the nonlinear tire force and suspension K&C characteristic, this paper presents a piecewise affine robust yaw stability control method for the in-wheel motor electric vehicle. Using the piecewise linear to approximate front and rear tire force, and additional steering angle to describe the suspension K&C characteristic, a piecewise affine lateral dynamics model with uncertainty disturbance is firstly established. And then, by means of analysis of the dynamic behavior of front and rear tire force, the unreachable piecewise partition is neglected such that the lateral dynamics model is simplified. By using LMI technique, the yaw stability controller which can guarantee the closed-loop stability and Hinf disturbance rejection is obtained. Simulation results show that the yaw stability control method proposed in this paper is feasible and effective.

Driver Model-Based Fault-Tolerant Control of Independent Driving Electric Vehicle Suffering Steering Failure

This paper presents a fault-tolerant control (FTC) strategy for a four-wheel independent driving electric vehicle suffering steering failure. The method is based on the functional redundancy of driving and braking actuators to recover the vehicle’s steering ability. A dynamic vehicle model is derived with the function of four-wheel driving. A sliding mode controller with a combined sliding surface is employed as a motion controller, allowing the desired vehicle motion to be tracked by the adaptive driver model. An extended Kalman filter-based state estimator is adopted to virtually measure the sideslip angle while considering the nonlinear tire force. A new allocation strategy, involving two distribution modes of coordination, is designed. In addition, a weight coefficient adjustment strategy is implemented in optimal mode based on the lateral load transfer, thus improving the steering performance. Simulations are conducted to verify the proposed FTC algorithm. The results demonstrate that steering failure can be effectively covered by the functional redundancy of the driving/braking actuators.

An Adaptive Vehicle Sideslip Estimator for Reliable Estimation in Low and High Excitation Driving

This work proposes a novel adaptive estimator for reliable vehicle sideslip angle estimation over the full vehicle operating range, using Kalman filtering. It is shown that the vehicle state estimator with adaptive linear tire model proposed in literature only provides reliable estimation for relatively large sideslip angles. This paper proposes a new method that does not suffer this limitation. It relies on the fact that linear tire behavior is mostly a property of the tire/vehicle and to a much lesser extent of the road condition. The proposed estimator therefore contains both a fixed parameter linear tire model, and an adaptive linear tire model. The former allows for reliable and stable estimation for small sideslip angles and linear tire behavior, while the latter allows tracking of nonlinear tire behavior. A smooth transition between the tire models is obtained by adapting the corresponding model covariances in the Kalman filter according to the operating conditions. For this a measure of degree of nonlinearity in tire behavior is defined. Experimental results are provided to demonstrate the robustness and validity of the proposed approach.

Comparison of Adaptive Fuzzy Sliding-Mode Pulse Width Modulation Control With Common Model-Based Nonlinear Controllers for Slip Control in Antilock Braking Systems

A novel application of the adaptive fuzzy sliding-mode control (AFSMC) to the case of an antilock braking system (ABS) is proposed in this paper. ABS is a system in vehicles that allows the wheels to maintain tractive contact with the road and avoid uncontrolled skidding. By using ABS, the stopping distances on dry and slippery surfaces are expected to decrease. The maximum braking force is a nonlinear function of the slip ratios of the wheels, which is sensitive to the vehicle weight and road condition. In this research, a simple low-order model of the braking dynamics is considered and unmodeled dynamics are taken as uncertainties. The robust AFSMC method is used to regulate the wheel slip ratio toward the desired value. The proposed controller employs pulse width modulation (PWM) to generate the braking torque. There is no need to use any reference measured data or experimental knowledge of relevant experts to design the controller. A clear advantage is that the designed controller does not rely on the nonlinear tire–road friction model. The second Lyapunov theorem is employed to prove the closed-loop asymptotic stability. In the simulations, the multibody dynamics method is used for modeling the longitudinal motion of SAIPA X100 and X200 vehicle platforms. Furthermore, the actuation and the switching dynamics of the braking system are taken into account. Resulting performance is compared to the conventional sliding-mode and feedback linearization methods. Analysis of the simulation results reveals the effectiveness of proposed AFSMC method.

Bifurcation of lane change on highway for large bus

In this study, a new method is proposed for analysing the non-linear dynamics and stability in lane changes on highways by large buses. Unlike most of the literature associated with a simulated linear dynamic model for large buses, a verified 4DOF mechanical model with non-linear tire based on vehicle test is used in the lane-change simulation, including sinusoidal steering and steer returning. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering, sinusoidal steering and steer returning with disturbance on highways are investigated using a numerical method. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translates into an oscillatory behaviour leading to instability. Various equilibrium forms of stability are found, as well as saddle and Hopf bifurcations with disturbance ζ variety. The derived knowledge of the bifurcations set is hugely important to fully understand the actual dynamic motions of vehicles when lane changing on an even surface. It is a valuable reference for safety design of large buses to improve the traffic safety of driver–vehicle–road closed-loop system.

Collision Avoidance and Stabilization for Autonomous Vehicles in Emergency Scenarios

Emergency scenarios may necessitate autonomous vehicle maneuvers up to their handling limits in order to avoid collisions. In these scenarios, vehicle stabilization becomes important to ensure that the vehicle does not lose control. However, stabilization actions may conflict with those necessary for collision avoidance, potentially leading to a collision. This paper presents a new control structure that integrates path tracking, vehicle stabilization, and collision avoidance and mediates among these sometimes conflicting objectives by prioritizing collision avoidance. It can even temporarily violate vehicle stabilization criteria if needed to avoid a collision. The framework is implemented using model predictive and feedback controllers. Incorporating tire nonlinearities into the model allows the controller to use all of the vehicle's performance capability to meet the objectives. A prediction horizon comprised of variable length time steps integrates the different time scales associated with stabilization and collision avoidance. Experimental data from an autonomous vehicle demonstrate the controller safely driving at the vehicle's handling limits and avoiding an obstacle suddenly introduced in the middle of a turn.

Vehicle optimal road departure prevention via model predictive control

This article addresses the problem of road departure prevention using integrated brake control. The scenario considered is when a high-speed vehicle leaves the highway on a curve and enters the shoulder or another lane, owing to excessive speed or a reduction in the friction of the road due to adverse weather conditions. In such a scenario, the vehicle speed is too high for the available tyre–road friction and road departure is inevitable; however, its effect can be minimized with an optimal braking strategy. To achieve online implementation, the task is formulated as a receding horizon optimization problem and solved in a linear model predictive control (MPC) framework. In this formulation, a nonlinear tyre model is adopted in order to work properly at the friction limits. The optimization results are close to those obtained previously using a particle model optimization, parabolic path reference (PPR), coupled to a control algorithm, the modified Hamiltonian algorithm (MHA), specifically designed to operate at the vehicle friction limits. This shows that the MPC formulation may be equally effective for vehicle control at the friction limits. The major difference here, compared with the earlier PPR/MHA control formulation, is that the proposed MPC strategy directly generates an optimal brake sequence, while PPR provides an optimal reference first, then MHA responds to the reference to give closed-loop actuator control. The presented MPC approach has the potential for use in future vehicle systems as part of the overall active safety control to improve overall vehicle agility and safety.

Coordinated Chassis Control Based on Vehicle Lateral Acceleration Using Fuzzy Logic Control

This paper presents an advanced coordination of integrated control system which consist of three different controllers namely Electronic Stability Control (ESC), Active Front Steering (AFS), and Active Suspension (AS) using Fuzzy Logic Control (FLC) in order to improve vehicle handling, cornering stability, and rollover prevention with anti-lock brakingsystem (ABS) to avoid wheel locking during generating differential braking by ESC control. Based on a well-developed and validated fourteen degrees of freedom full vehicle model with non-linear tire characteristics, a reference yaw-roll plane vehicle model is introduced to compare and therefore control the yaw rate, side slip angle, and roll angle of the vehicle body. For rollover prevention indices, the dynamic load transfer ratio is defined to check the effectiveness of the proposed controller. The Coordination chassis control is based on the lateral acceleration value as input to FLC, and the outputs are the increment factors to the three controllers varying from zero to one. Three membership functions are chosen to represent the lateral acceleration as input to the supervisor controller, to define the control authority for each actuator. The universe of discourse for each membership function is selected according to the study of the effect of eachcontroller stand alone in vehicle performance. The numerical modelling is carried out through the MATLAB / Simulink environment which suits the control and optimization process. Different standard test maneuvers namely J-turn,fishhook, and double lane change have been carried out by considering standard test maneuvers with different driving speeds. The simulation results are compared during three cases namely, the uncontrolled system, the combined controller, and the proposed coordinated controller. The results show a substantial improvement of the vehicle stability in terms ofvehicle lateral acceleration, side slip angle, yaw rate, roll angle, and the for the developed coordinated controller compared to combined controller or the conventional system without control.

Tire lateral force estimation and grip potential identification using Neural Networks, Extended Kalman Filter, and Recursive Least Squares

This paper presents a novel hybrid observer structure to estimate the lateral tire forces and road grip potential without using any tire–road friction model. The observer consists of an Extended Kalman Filter structure, which incorporates the available prior knowledge about the vehicle dynamics, a feedforward Neural Network structure, which is used to estimate the highly nonlinear tire behavior, and a Recursive Least Squares block, which predicts the road grip potential. The proposed observer was evaluated under a wide range of aggressive maneuvers and different road grip conditions using a validated vehicle model, validated tire model, and sensor models in the simulation environment IPG CarMaker ® . The results confirm its good and robust performance.

Tyre modelling for an autonomous articulated wheel loader conducting a V-shape loading cycle simulation

Virtual product developments (VPDs) tools have a great effect on reducing the cost of development, which explains the considerable amount of attention they received lately from researchers. In this work, two different VPD tyre models, restricted fully non-linear and enhanced non-linear transient models, are tested through modelling and simulation. A detailed multibody mechanical system model of a large wheel loader conducting a V-shape loading cycle was used to test the performance differences between the two transient tyre models. VPD simulations show that both tyre models enable the operator (controller) to drive the machine tracking the desired path; however, the enhanced non-linear tyre model shows larger deviation and less operator comfort when compared with the restricted non-linear transient tyre model. Results also show the ability of the restricted tyre model to produce higher forces and moment to keep the machine on track.