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Research Papers

Estimating Road Angles With the Knowledge of the Vehicle Yaw Angle

[+] Author and Article Information
Ling-Yuan Hsu

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, R.O.C.lance1214@gmail.com

Tsung-Lin Chen1

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, R.O.C.tsunglin@mail.nctu.edu.tw

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(3), 031004 (Apr 14, 2010) (9 pages) doi:10.1115/1.4001330 History: Received October 29, 2008; Revised December 10, 2009; Published April 14, 2010; Online April 14, 2010

This paper presents a method of estimating road angles using state observers and three types of sensors (lateral acceleration sensors, longitudinal velocity sensors, and suspension displacement sensors). The proposed method differs from those in most existing literature in three aspects. First, a “full-state” vehicle model is used to describe nonlinear vehicle dynamics on a sloped road. Second, “switching observer” techniques are used to suggest suitable sensors and to construct state observers. Lastly, the road angles are described by three Euler angles, and two of them are estimated simultaneously. The analysis indicates that (1) road angles affect vehicle dynamics through components of the gravitational force acting on the vehicle body. These gravitational forces can be correctly estimated with an estimation accuracy less than 7.5%, even when road angles vary with time. (2) Those road angles can be correctly estimated only when the vehicle yaw angle is known.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

A vehicle on a sloped road: (a) the road curve angle ψr, (b) the road bank angle ϕr, and (c) the road grade angle θr

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Figure 2

Four coordinate systems for the vehicle modeling. {g}: global frame, {b}: body frame, {r}: road frame, and {a}: aux-frame.

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Figure 3

A diagram of the switching observer scheme. One observer estimates state values within a switching cycle while the other is held static. They switch their roles of estimating state values in the next cycle.

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Figure 4

Vehicle maneuvering: steering angle versus time

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Figure 10

Estimating road angles and their effects for Case IV. The estimation system can estimate three gravitational forces accurately when the road angles vary as sinusoidal waves.

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Figure 11

Estimating road angles and their effects for Case V: With the additional sensor measurements of vehicle yaw rate, road bank rate, and road grade rate, three angle estimations still fail.

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Figure 5

Estimating vehicle dynamics for Case I. The estimation system can estimate most vehicle dynamics correctly, except for longitudinal displacement xa and lateral displacement ya.

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Figure 6

Estimating road angles and their effects for Case I. The estimation system can estimate three gravitational forces accurately but fails to estimate three angles.

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Figure 7

Singular values of the observability matrices for gravitational force estimations and for angle estimations. None of the singular value of the gravitational force estimation is zero. One of the singular values of the angle estimation is zero along the entire trajectory.

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Figure 8

Estimating road angles and their effects for Case II. The estimation system can estimate three gravitational forces and three angles accurately with the additional information of vehicle yaw angle.

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Figure 9

Estimating road angle and their effects for Case III. The suspension displacement plots (the third column) indicate that the front-left and rear-left tires are off the ground. The estimation system can still estimate three gravitational forces accurately.

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