Tire-road Friction Force Research Articles

A Mathematical Approach Towards Random Road Profile Generation Based on Chaotic Signals of Chua's Circuit

In response to application demands in vehicle dynamics and control, traffic engineering, urban planning, and logistics, the generation of an adequate artificial road profile in terms of the diversity of geometric scenarios has been addressed in the current manuscript. The underlying mathematical principles for generating a geometrically comprehensive, yet logically meaningful, 3D road profile have been taken from high and unbiased sweeping factors of random number sequences over their domain of interest. And to generate such random number sequences, the mathematically manipulated output signal of a well-established chaotic system has been utilized, namely that of the Chua's circuit. Having defined the target road profile mathematically with all its geometrical complexities, a suitable scheme derived from the mentioned chaotic signal has been used to generate the required random number sequences as defining parameters of the road profile. The scheme has been otherwise tested and proven to show the demanded level of randomness in literature. Several attempts have been made to create a diverse range of road profiles, considering the constraints imposed by vehicle dynamics. To generate the road geometries, the limitations imposed by the vehicle's motion, such as the limitations on corresponding curvatures, slopes, and banking angles are negotiated, in terms of vehicle dynamics and available tire-road friction forces, by evaluating how close a vehicle will be to its tire force capacity limits as it travels on sections of the generated road.

An Integrated Tread Beam/LuGre Tire-Road Friction Model

Tire-road interactions modeling is critical for the development of enhanced safety of modern vehicles. This paper presents an integrated tread beam/LuGre tire-road contact friction model and an iterative force computation method to predict frictional forces at any given wheel slips. Steady-state friction force distribution is computed by solving the LuGre dynamic friction model with a power series method. A tread beam model is then used to capture the variation of the normal load on the tire-road contact patch and compute the load-shift impact under vehicle maneuvers. The use of the tread beam model bridges the local friction force estimates by the LuGre model with the global contact behavior under tire dynamics conditions. Numerical results are compared with those obtained by the finite element method and the comparison confirms the integrated modeling approach. This work provides an enabling practical tool for computing tire-road friction forces under dynamic conditions.

Adaptive Unified Monitoring System Design for Tire-Road Information

Knowledge of the tire-road information is not only very crucial in many active safety applications but also significant for self-driving cars. The tire-road information mainly consists of tire-road friction coefficient and road-tire friction forces. However, precise measurement of tire-road friction coefficient and tire forces requires expensive equipment. Therefore, the monitoring of tire-road information utilizing either accurate models or improved estimation algorithms is essential. Considering easy availability and good economy, this paper proposes a novel adaptive unified monitoring system (AUMS) to simultaneously observe the tire-road friction coefficient and tire forces, i.e., vertical, longitudinal, and lateral tire forces. First, the vertical tire forces can be calculated considering vehicle body roll and load transfer. The longitudinal and lateral tire forces are estimated by an adaptive unified sliding mode observer (AUSMO). Then, the road-tire friction coefficient is observed through the designed mode-switch observer (MSO). The designed MSO contains two modes: when the vehicle is under driving or brake, a slip slope method (SSM) is used, and a recursive least-squares (RLS) identification method is utilized in the SSM; when the vehicle is under steering, a comprehensive friction estimation method is adopted. The performance of the proposed AUMS is verified by both the matlab/simulinkCarSim co-simulation and the real car experiment. The results demonstrate the effectiveness of the proposed AUMS to provide accurate monitoring of tire-road information.

Novel electronic braking system design for EVS based on constrained nonlinear hierarchical control

Both environment protection and energy saving have attracted more and more attention in the electric vehicles (EVs) field. In fact, regarding control performance, electric motor has more advantages over conventional internal combustion engine. To decouple the interaction force between vehicle and various coordinating and integrating active control subsystems and estimate the real-time friction force for Advanced Emergency Braking System (AEBS), this paper’s primary intention is uniform distribution of longitudinal tire-road friction force and control strategy for a Novel Anti-lock Braking System (Nov- ABS) which is designed to estimate and track not only any tire-road friction force, but the maximum tire-road friction force, based on the Anti-Lock Braking System (ABS). The longitudinal tire-road friction force is computed through real-time measurement of breaking force and angular acceleration of wheels. The Magic Formula Tire Model can be expressed by the reference model. The evolution of the tire-road friction is described by the constrained active-set SQP algorithm with regard to wheel slip, and as a result, it is feasible to identify the key parameters of the Magic Formula Tire Model. Accordingly, Inverse Quadratic Interpolation method is a proper way to estimate the desired wheel slip in regards to the reference of tireroad friction force from the top layer. Then, this paper adapts the Nonlinear Sliding Mode Control method to construct proposed Nov-ABS. According to the simulation results, the objective control strategy turns out to be feasible and satisfactory.

Corrigendum to “Adaptive Nonlinear Tire-Road Friction Force Estimation for Vehicular Systems Based on a Novel Differentiable Friction Model”

Corrigendum to “Adaptive Nonlinear Tire-Road Friction Force Estimation for Vehicular Systems Based on a Novel Differentiable Friction Model”

Adaptive Nonlinear Tire-Road Friction Force Estimation for Vehicular Systems Based on a Novel Differentiable Friction Model

A novel adaptive nonlinear observer-based parameter estimation scheme using a newly continuously differentiable friction model has been developed to estimate the tire-road friction force. The differentiable friction model is more flexible and suitable for online adaptive identification and control with the advantage of more explicit parameterizable form. Different from conventional estimation methods, the filtered regression estimation parameter is introduced in the novel adaptive laws, which can guarantee that both the observer error and parameter error exponentially converge to zero. Lyapunov theory has been used to prove the stability of the proposed methods. The effectiveness of the estimation algorithm is illustrated via a bus simulation model in the Trucksim software and simulation environment. The relatively accurate tire-road friction force was estimated just by the easily existing sensors signals wheel rotational speed and vehicle speed and the proposed method also displays strong robustness against bounded disturbances.

Adaptive neuro-fuzzy wheel slip control

Due to complex and nonlinear dynamics of a braking process and complexity in the tire–road interaction, the control of automotive braking systems performance simultaneously with the wheel slip represents a challenging problem. The non-optimal wheel slip level during braking, causing inability to achieve the desired tire–road friction force strongly influences the braking distance. In addition, steerability and maneuverability of the vehicle could be disturbed. In this paper, an active neuro-fuzzy approach has been developed for improving the wheel slip control in the longitudinal direction of the commercial vehicle. The dynamic neural network has been used for prediction and an adaptive control of the brake actuation pressure, during each braking cycle, according to the identified maximum adhesion coefficient between the wheel and road surface. The brake actuation pressure was dynamically adjusted on the level that provides the optimal level of the longitudinal wheel slip vs. the brake pressure selected by driver, the current vehicle speed, the brake interface temperature, vehicle load conditions, and the current value of longitudinal wheel slip. Thus the dynamic neural network model operates (learn, generalize and predict) on-line during each braking cycle, fuzzy logic has been integrated with the neural model as a support to the neural controller control actions in the case when prediction error of the dynamic neural model reached the predefined value. The hybrid control approach presented here provided intelligent dynamic model – based control of the brake actuation pressure in order to keep the longitudinal wheel slip on the optimum level during a braking cycle.

Longitudinal wheel slip control using dynamic neural networks

The control of automotive braking systems performance and a wheel slip is a challenging problem due to nonlinear dynamics of a braking process and a tire–road interaction. When the wheel slip is not between the optimal limits during braking, the desired tire–road friction force cannot be achieved, which influences braking distance, the loss in steerability and maneuverability of the vehicle. In this paper, the new approach, based on dynamic neural networks, has been employed for improving of the longitudinal wheel slip control. This approach is based on dynamic adaptation of the brake actuation pressure, during a braking cycle, according to the identified maximum adhesion coefficient between the wheel and road. The brake actuated pressure was adjusted on the level which provides the optimal longitudinal wheel slip versus the brake actuated pressure selected by a driver, the current vehicle speed, load conditions, the brake interface temperature and the current value of the wheel slip. The dynamic neural network has been used for modeling of a nonlinear functional relationship between the brake actuation pressure and the longitudinal wheel slip during a braking cycle. It provided preconditions for control of the brake actuation pressure based on the wheel slip change.

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.

Sliding-mode-based parameter identification with application to tire pressure and tire-road friction

This paper presents a method of simultaneous estimation of tire pressure and tire-road friction. A sliding-mode scheme is designed to identify the system state and the parameter variation of a torsional tire system, which greatly depend on the change in tire pressure. Then, the recursive least-squares method with a forgetting facto is used to estimate the parameter variations of the tire system and the tire-road friction force without a friction model using the information retrieved from the equivalent input for sliding motion. A simulation study is performed to illustrate the effectiveness of the proposed method.