A construction vehicle like a wheel loader typically has an articulated steering. The basic idea consists of folding the chassis in the steering direction.

With the track width \(w\) (the lateral wheel separation), the wheel base \(l\) (the longitudinal wheel separation), the steering angle \(\phi\) and \(r\) being the distance between the ICC (instantaneous center of curvature) and the center of the car.

## Forward Kinematic for wheel loader

A kinematic model for a wheel loader can be formulated similarly to the kinematic model of a ackerman vehicle. Considering the state of the vehicle is represented as a quadruple \((x, y, \theta, \phi)\), with \(\theta\) being the heading and \((x,y)\) the position in the world. The most important thing about the steering of a wheel loader is that the rotational center is exactly in the middle of the vehicle where the inflexion point is. Given the speed \(s\) of the vehicle we get

\[ \dot{x} = s\cos\theta\\ \dot{y} = s\sin\theta\\ \dot{\theta} = \frac{s}{l} \tan\phi \approx \frac{s}{l}\phi \]

(Max taylor approximation error of the tangent simplification is about \(3^\circ\) at \(30^\circ\) steering lock)