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This paper demonstrates the implementation of a model-based vehicle estimator, which can be used for lateral tire force estimation without using any highly nonlinear tire-road friction models. The lateral tire force estimation scheme has been designed, and it consists of the following three steps: the yaw moment estimation based on a disturbance observer, the sum of the lateral tire force of two front tires and two rear tires estimation based on a least-square method, and individual lateral tire force estimation based on a heuristic method. The proposed estimator is evaluated under two typical driving conditions and the estimation values are compared with simulator data from CarSim and experimental data provided by GM. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

To improve the handling performance and the safety of vehicles, a considerable number of active control systems for the vehicle lateral dynamics have commercially been developed and utilized over the last two decades. Lateral tire-road friction force is a vital signal that affects the stability of a vehicle under cornering. The accurate information of this force signal can greatly enhance the performance of some steering systems and active safety systems, such as electronic stability program (ESP). However, no commercial vehicles are equipped with sensors which can directly measure this force signal, which is due to either cost pressure or technical difficulty. This provides a room for an appropriate estimation algorithm. In fact, the ever-increasing demand for safety and driving comfortability makes it a very active research field in both academic society and auto industry. A vast variety of research results can be found in the literature [

A dynamic automobile model with 3 degree-of-freedom (DOF) is considered (shown in Figure

A 3 DOF vehicle model.

In the estimation algorithm presented in this paper, we assume that the location of the center of gravity (CG) of the vehicle is known. In what follows, we will discuss the yaw dynamic model with respect to the five different points listed here: CG (

Yaw Dynamic w.r.t. CG: according to the rotation dynamic equation of the CG, we have

Yaw Dynamic w.r.t. center of the left rear wheel:

Yaw Dynamic w.r.t. center of the left front wheel:

Yaw Dynamic w.r.t. center of the right front wheel:

Yaw Dynamic w.r.t. center of the right rear wheel:

In this section, we will discuss how to combine the yaw dynamic model of the vehicle body, yaw rate, and acceleration in longitudinal and lateral directions to estimate the moment of the lateral tire forces w.r.t. different points in the vehicle body. Here, we will assume that the information of location of the center of gravity of the vehicle and the longitudinal force of each tire are both available. The general structure of the disturbance observer is shown in Figure

General structure of the disturbance observer based torque estimation.

As shown in Figure

For illustrating the proposed estimator clearly, we will take the yaw dynamic model w.r.t. CG as an example to analyze it. From (

The low pass weighted filter

In Section

As shown in (

Unfortunately, the matrix

To overcome the rank deficiency problem discussed above, the kinematic model in (

For reference point

For reference point

For reference point

For reference point

For reference point

To verify the estimation algorithm for the lateral tire forces discussed in this paper, CarSim data and experimental data provided by GM are utilized. Then, two typical experiments are selected for CarSim simulation: first of which is the standard double lane change shown in Figure

Double lane change: motion profile.

Fish hook: profile of steering angle.

A big pickup with the gross vehicle weight of 2024 kg and the yaw inertia of 3200 kg·m^{2} has been used for the simulation studies. Meanwhile,

CarSim data for double lane change with

Lateral force for front-left tire

Lateral force for front-right tire

Lateral force for rear-left tire

Lateral force for rear-right tire

CarSim data for double lane change with

Lateral force for front-left tire

Lateral force for front-right tire

Lateral force for rear-left tire

Lateral force for rear-right tire

CarSim data for fish hook with

Lateral force for front-left tire

Lateral force for front-right tire

Lateral force for rear-left tire

Lateral force for rear-right tire

Figure

For fish hook condition, Figure

In this section, experimental evaluations are carried out to verify the effectiveness of the proposed estimated method. The experimental data is provided by GM. The vehicle parameters used in this experimental test are shown in Table

Vehicle parameters.

Parameters | Values |
---|---|

Vehicle total mass m/kg | 2083 |

Vehicle yaw moment of inertia ^{2}) |
3100 |

Distance from vehicle COG to front axle |
1.325, 1.637 |

Front and rear track width |
0.78 |

With maximum

Experimental results provided by GM for four lateral tire forces.

Lateral force for front-left tire

Lateral force for front-right tire

Lateral force for rear-left tire

Lateral force for rear-right tire

In this paper, we proposed a model-based algorithm to estimate the lateral tire force without resorting to complex tire-road friction model. A significant advantage of this approach is that no complex tire models are involved in the estimation algorithm which not only relieves the computation effort but also increases the robustness with respect to the large variation of the road conditions. Another strong point of this estimation method is that it can incorporate the longitudinal tire forces explicitly, which are often ignored in those bicycle model based estimation algorithm. The CarSim simulation and experimental results demonstrate the ability of this approach to provide accurate estimations and show its practical potential as a low-cost solution for calculating lateral tire forces.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This project is supported by National Natural Science Foundation of China (Grant nos. 51075112 and 51175135), the GPS and Vehicle Dynamics Laboratory at Auburn University in Alabama, USA, and GM (General Motors).