How do I obtain a cubic relation of the spatial coordinates 'x' and 'y' of a simulated vehicle in the Automated Driving Toolbox using curvature, curvature derivative, heading angle, and lateral offset?

I am using the Automated Driving Toolbox, and I have data on the following four parameters: curvature, curvature derivative, lateral offset, and heading angle. How do I use this data to produce a cubic relationship between the spatial coordinates 'x' and 'y' of the vehicle?

Answer 1

[MathWorks Support Team]

Step 1 

Use the function "clothoidLaneBoundary" in order to get a clothoid curve whose rate of change of curvature varies linearly with distance. The function accepts curvature, curvature derivative, heading angle, and lateral offset. Please refer to the documentation below for more information about the function:

https://www.mathworks.com/help/driving/ref/clothoidlaneboundary.html 

Step 2 

After generating the clothoid curve, obtain the coordinates x and y using the function "computeBoundaryModel". Please refer to the example described in the link below for more details regarding Steps 1 and 2.

https://www.mathworks.com/help/driving/ref/clothoidlaneboundary.computeboundarymodel.html

Step 3 

Feed the obtained x and y to the function "findCubicLaneBoundaries" in order to compute the coefficients of the cubic equation. Please refer to the link below for more details and note that with this function the coefficient "A" refers to the coefficient of the cubic term, not the constant term.

https://www.mathworks.com/help/driving/ref/findcubiclaneboundaries.html