Vehicle Side Slip and Roll Angle Estimation

We present and compare vehicle maneuver stability under two vehicle dynamics models, one with the rear tire slip angle dynamics and the other with the vehicle side slip angle dynamics. Instead of using vehicle mass center side slip angle, we consider to use rear axial slip angle as one of the state variables for studying vehicle lateral dynamics. Using rear wheel slip angle as a state variable for studying vehicle dynamics has been reported in practices in industry but not rigorously studied. We analyze the new vehicle dynamics and compare the stability results with existing reported results. Both analytical and numerical results have shown that the stability region of the vehicle dynamics by using the rear slip angle is less conservative comparing with using the vehicle side slip angle.

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

This chapter focuses on the estimation of car dynamic variables for the improvement of vehicle safety, handling characteristics and comfort. More specifically, a new estimation process is proposed to estimate longitudinal/lateral tire-road forces, velocity, sideslip angle and wheel cornering stiffness. One main contribution of the process is that it uses measurements from currently available standard sensors (yaw rate, longitudinal/lateral accelerations, steering angle and angular wheel velocities). Another contribution is that the process provides robust sideslip angle estimations with respect to cornering stiffness changes (or tire-road friction variations). Finally, the estimation process is applied and compared to real experimental data, notably sideslip and wheel force measurements. The last few years have seen the emergence in cars of active security systems to reduce dangerous situations for drivers. Among these active security systems, Anti-lock Braking Systems (ABS) and Electronic Stability Programs (ESP) significantly reduce the number of road accidents. However, these systems may be improved if the dynamic potential of a car is well known. For example, information on tire-road friction means a better definition of potential trajectories, and therefore a better management of vehicle controls. Nowadays, certain fundamental data relating to vehicle-dynamics are not measurable in a standard car for both technical and economic reasons. As a consequence, dynamic variables such as tire forces and sideslip angle must be observed or estimated. Vehicle-dynamic estimation has been widely discussed in the literature, e.g. (Kiencke & Nielsen, 2000), (Ungoren et al., 2004), (Lechner, 2002), (Stephant et al., 2006), (Baffet et al, 2006a). The vehicle-road system is usually modeled by combining a vehicle model with a tire-force model in one block. One particularity of this study is that it separates the estimation modeling into two blocks (shown in Figure 1), where the first block concerns the car body dynamic while the second is devoted to the tire-road interface dynamic. The first block contains an Extended Kalman Filter (denoted as

In this paper, we propose a new adaptive side slip observer using a simple combined vehicle dynamics. Though there are many ways to estimate the side slip angle, some problems still exist in the popular estimation techniques based on the kinematic model, the dynamic model, and the combined kinematic-dynamic model. Therefore we propose the adaptive side slip observer. A combined model of linearized roll motion and lateral vehicle dynamics was used to involve the roll motion in the second-order lateral vehicle dynamics. Furthermore, a time delay was also applied to the combined model, reflecting the reaction time between the steering angle and the side slip angle. We designed an H∞ discrete-time slip angle observer using linear matrix inequality to reduce the infinite norm between a set of disturbance inputs and the estimation error. The performance of the proposed method was validated via simulations and experiments.

This paper presents a study on the use of reinforcement learning to control the torque vectoring of a small electric racecar aiming to improve vehicle handling and vehicle stability. The reinforcement-learning algorithm used is Neural Fitted Q Iteration, and the sampling of experiences is based on simulations using the software CarMaker. The cost function is based on the position of the states on the phase-plane of sideslip angle and angular velocity. To investigate the maximum ratio of torque distribution that should be set to guarantee stability as well as the effectiveness of the controller inputs in the learning process, two experiments were done (A and B) with different states and possibilities of torque distribution. The controller A is able to improve the vehicle handling and stability with a significant reduction in vehicle sideslip angle. And it also showed that 70% of torque distribution is enough to keep the vehicle stable.

Embedded unknown input sliding mode observer to estimate the vehicle roll and road bank angles: Experimental evaluation

The vehicle sideslip angle β is one of the most important variables for evaluating vehicle dynamics. In particular, several studies has shown that its knowledge may allow the design of ESC systems having significantly better performances over the standard ones based on yaw rate control, see e.g. [1,2]. However, direct measurement of β requires the use of complex and expensive devices (based on optical or inertial+GPS technologies) which cannot be used in production cars. Therefore, the estimation of the sideslip angle from signals measured from standard ESC sensors (steering angle, longitudinal speed, yaw rate, lateral and longitudinal accelerations) has been intensively studied in the last years, see e.g. [3,4,5,6] and the references therein. All these investigations are based on a Two-Step design procedure: a suitable model of vehicle dynamics is first identified making use of experimental data measured on a testing vehicle; then one of existing observer/filtering method (Kalman Filter, Sliding Mode Observer, Moving Horizon Estimator, …) is used for designing the estimator, here called TSVS/SA (Two-Step Virtual Sensor of Sideslip Angle), see Figure 1A.

An electronic differential for high-performance electric vehicles with independent driving motors is proposed in this paper. This electronic differential endows the electric vehicle with a close-to-zero vehicle side-slip angle. When vehicle side-slip vanishes, the heading direction of the vehicle coincides with the velocity direction of the mass centre. In addition to the side-slip angle, the yaw rate is driven towards an optimal value with the proposed electronic differential on-board. The improvements in vehicle side-slip and yaw rate responses are of great significance to the handling performance of high-performance vehicles. In this paper, the mathematical relationships between the vehicle dynamic states and the independent motor torques are revealed, based on which the proposed electronic differential controller is designed. Simulation results manifest that in various challenging steering scenarios, the proposed control method outperforms two common electronic differential control schemes in terms of vehicle side-slip and yaw rate responses.

It is interesting and worth while to study on method of measuring rail/wheel contact point and contact force of running railway vehicles, since many things in real rail/wheel contact phenomenon are still unknown, In this paper, the Japanese conventional method of measuring vertical load and lateral force is introduced. The strain of the disk surface is used for measuring forces. A new method, which detects the contact point as well as vertical load and lateral force, is proposed also in this paper. Firstly, the surface strain on disk type wheel is analyzed by an FEM program, NASTRAN, under the condition that vertical, lateral or longitudinal force separately acts on various points along the wheel profile. By the calculated result, it shows the possibility of detecting the rail/wheel contact point by means of measuring lateral distribution of compress strain which changes according to the load position, i.e. rail/wheel contact point. Secondly, the idea above is verified by static load experiments using an actual disk type wheelset. The location of an area where lateral force affects little on surface strain is investigated, since the lateral distribution of strain should be measured in such an area to avoid the interference of bending by lateral force. And finally, theory for the measurement is modified for on-track testing and the best position and direction for strain gauges is proposed in accordance with the calculated and experimental results.

Estimation of lateral tire–road forces and sideslip angle for electric vehicles using interacting multiple model filter approach

A lateral acceleration is considered to be a significant sensor signal for an estimation of a side slip angle. Due to the fact that a characteristic of a lateral G sensor, the sensor has a technical issue when a road bank angle has presented. In order to resolve the issue, this paper describes a novel method for the real time estimation of a vehicle side slip angle and a road bank angle simultaneously. A Bayesian tracking approach is used to estimate the road bank angle by comparing a measured lateral acceleration with the calculated one in the case of various angle. A Kalman Filter has been implemented through bicycle model using vehicle roll angle, road bank angle and angular velocity of side slip angle. The performance of the proposed estimation method has been evaluated via vehicle tests on a real road.

The knowledge of key vehicle states is crucial to guarantee adequate safety levels for modern passenger cars, for which active safety control systems are lifesavers. In this regard, vehicle sideslip angle is a pivotal state for the characterization of lateral vehicle behavior. However, measuring sideslip angle is expensive and unpractical, which has led to many years of research on techniques to estimate it instead. This paper presents a novel method to estimate vehicle sideslip angle, with an innovative combination of a kinematic-based approach and a dynamic-based approach: part of the output of the kinematic-based approach is fed as input to the dynamic-based approach, and vice-versa. The dynamic-based approach exploits an Unscented Kalman Filter (UKF) with a double-track vehicle model and a modified Dugoff tire model, that is simple yet ensures accuracy similar to the well-known Magic Formula. The proposed method is successfully assessed on a large amount of experimental data obtained on different race tracks, and compared with a traditional approach presented in the literature. Results show that the sideslip angle is estimated with an average error of 0.5 deg, and that the implemented cross-combination allows to further improve the estimation of the vehicle longitudinal velocity compared to current state-of-the-art techniques, with interesting perspectives for future onboard implementation.

In this paper, the feedback linearization scheme is applied to the control of vehicle's lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in Liaw and Chung (2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. Feedback linearization control laws are proposed in this paper to stabilize the vehicle's dynamics at bifurcation points. Numerical simulations for an example model demonstrate the effectiveness of the analytical results

The vehicle state is of significant to examine and control vehicle performance. But some vehicle states such as vehicle velocity and side slip angle which are vital to active safety application of vehicle can not be measured directly and must be estimated instead. In this paper, a Cubature Kalman Filter (CKF) based algorithm for estimation vehicle velocity, yaw rate and side slip angle using steering wheel angle, longitudinal acceleration and lateral sensors is proposed. The estimator is designed based on a three-degree-of-freedom (3DOF) vehicle model. Effectiveness of the estimation is examined by comparing the outputs of the estimator with the responses of the vehicle model in Car Sim under double lane change and slalom conditions.

issues of controllability and stabilization design for vehicle's lateral dynamics are presented. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is obtained. It is observed that saddle node bifurcation will appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. In order to possibly prevent the occurrence of such an instability, the controllability of vehicle dynamics at the saddle node bifurcation point is discussed. This leads to the design of a direct state feedback control law for system stabilization. Two-Parameter bifurcation analysis of system behavior is also obtained to classify the regime of the effective control gains for system stabilization. Numerical simulations for an example model demonstrate the effectiveness of analytical results.