# Exploring Active Camber for Path Following and Yaw Stability of Autonomous Vehicles

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

This paper explores active camber for path following and yaw stability control of over-actuated autonomous electric vehicles (AEVs). The camber effect on tyre force is modelled with a modified Dugoff tyre model, where the influence of tyre slip on camber stiffness is considered. Additionally, a nonlinear vehicle model including the longitudinal, lateral and yaw motion of the vehicle and the rotational motion of the wheels is utilised. The control problem of the AEVs is formulated with model predictive control, where both actuator- and safety-related constraints are considered. Comparative studies show that with four-wheel camber control the path following and yaw stability performance of the AEV can be considerably improved.

## Keywords

Active camber Model predictive control Yaw stability Over actuation Autonomous vehicle

## Nomenclature and Notation

$$\mathcal {A}$$

A set in which the elements denote the front left, front right, rear left and rear right wheels, respectively, $$=\{fl,fr,rl,rr\}$$.

$$v_{x}, v_{y}; \omega _{z}$$

Longitudinal, lateral velocity; yaw rate ($$\mathrm {m/s}; \mathrm {rad/s}$$).

$$X, Y; \psi$$

Longitudinal, lateral position; yaw angle ($$\mathrm {m}; \mathrm {rad}$$).

$$a_{x}, a_{y}$$

Longitudinal, lateral acceleration ($$\mathrm {m/s^{2}}$$).

$$\delta _{f}; \gamma _{f}, \gamma _{r}$$

Front steering angle; front, rear camber angle ($$\mathrm {rad}$$).

$$T_{i}$$

Drive/braking torque at the wheel ($$\mathrm {N}\cdot \mathrm {m}$$) ($$i \in \mathcal {A}$$).

$$F_{xi}, F_{yi}, F_{zi}$$

Longitudinal, lateral, vertical tyre force ($$\mathrm {N}$$) ($$i \in \mathcal {A}$$).

$$\alpha _{i}, \kappa _{i}; \omega _{i}$$

Tyre slip angle, slip ratio; angular velocity ($$\mathrm {rad}, -; \mathrm {rad/s}$$) ($$i \in \mathcal {A}$$).

$$C_{\gamma i}, C_{\alpha i}; C_{\kappa i}$$

Tyre camber, cornering; longitudinal stiffness ($$\mathrm {N/rad}; \mathrm {N}$$) ($$i \in \mathcal {A}$$).

$$I_{wi}; r_{e}$$

Tyre rotational inertia; radius ($$\mathrm {kg \cdot m^{2}}; \mathrm {m}$$) ($$i \in \mathcal {A}$$).

$$h_{g}; \mu$$

Height of centre of gravity (CoG); road friction coefficient ($$\mathrm {m}; -$$).

$$m; I_{z}$$

Vehicle mass; yaw inertia ($$\mathrm {kg}; \mathrm {kg \cdot m^{2}}$$).

$$l_{f}, l_{r}; B_{f}, B_{r}$$

Distance from CoG to front, rear axle; front, rear track width ($$\mathrm {m}$$).

## Notes

### Acknowledgment

The authors would like to gratefully acknowledge the support from the Swedish Electromobility Centre, the National Key R&D Programme of China under Grant 2017YFB0103600 and the TRENoP (Transport Research Environment with Novel Perspectives) at KTH Royal Institute of Technology.

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## Authors and Affiliations

1. 1.Department of Aeronautical and Vehicle EngineeringKTH Royal Institute of TechnologyStockholmSweden
2. 2.School of Mechanical EngineeringBeijing Institute of TechnologyBeijingChina