Algorithm 2. Obstacle input representation algorithm

Initialize the sectorial and rectangular areas according to the maximum slip angle of the front wheel, the size of the ego vehicle frame, and the speed of the ego vehicle.

Obtain the number $N_{sector}$ and $N_{rec}$ of the sectors and rectangles, and determine the angular interval of the sector $\beta$ and the distance interval of the rectangle $\omega$.

Combine multiple obstacle vehicles and lane boundaries into one obstacle set.

Initialize the sector area representation $S_{sector}=\left[\left[{\beta }_1,r\right],\cdots ,\left[{\beta }_2,r\right]\right]$, and the rectangle area representation within the extended area $S_{rectangle}=\left[\left[{\omega }_1,l\right],\cdots ,\left[{\omega }_j,l\right]\right]$, in which $r$ represents the radius of the sector and $l$ represents the length of the rectangle.

# Calculate sector representation.

For $N_{sector}$ in cycles do:

if The current line segment intersects the set of obstacles:

Confirm the intersection of the current line segment and the obstacle, and calculate the distance from the intersection to the origin, and update the corresponding $S_{sector}$

else:

The current $S_{sector}$ corresponding section is not updated

end for

for $N_{rectangle}$ in cycles do:

if The current line segment intersects the set of obstacles:

Confirm the intersection of the current line segment and the obstacle, and calculate the distance from the intersection to the corresponding horizontal reference line of the vehicle, and update the corresponding $S_{rectangle}$.

else:

The current $S_{rectangle}$ corresponding section is not updated.

end for

Normalize the updated $S_{sector}$ and $S_{rectangle}$.