Path generation for articulated steering type vehicle using symmetrical clothoid

Autonomous trajectory following of a wheel loader is closely related to v-shape path planning. Given the desired initial position and orientation of the wheel loader as (x₀, y₀, θ₀) and the desired final position and orientation as (x_truck, y_truck, θ_truck), successful v-shape path planning can be achieved by the derivations of 2 important parameters of the clothoid curve, k (sharpness) and s_m ( total distance of 1 clothoid curve) and determinations of the summit point of v-shape path, (x_e,ye) and direction, θ_e.