How to generate inequality constraints for the slope of the s(t) function?

[IngaVS]

[IngaVS]

In the paper, we see that the safety corridor is a trapezoid，and the slope is about s(t),how to generate the inequality constraint?

[MasterIzumi]

@IngaVS Sorry for the late reply. The driving corridor of the SSC is consecutive axis-aligned cubes, so the inequality constraint is straightforward. For one dimension (speed profile) optimization, the trapezoid corridor is also available, it can be modeled as inequality constraints of the QP problem. Here is a reference for speed optimization "Speed Planning Using Bezier Polynomials with Trapezoidal Corridors". As for spatial-temporal trajectory optimization, I am not sure whether the trapezoid-like cube is available.