# CONVOI

A linear collision avoidance example [5][8][12].

Let *gap, v*_{r}, v_{l} and *a*_{r} respectively represent the distance between the two cars
*(d*_{i-1}-d_{i} in the original paper), the velocity of the rear car (*d*_{i}'), the velocity
of the leading car (*d*_{i-1}') and the acceleration of the rear car (*d*_{i}"). By
using these variables and restricting *v*_{l} by *v*_{1}' >= -2/\v_{l}' <= -0.5 we transformed the
original higher-order differential equation into a four-dimensional differential (in)equation of
order one.

We set the state space to
*[0,4]×[0,2]×[0,2] ×[-2,-0.5]*, and we want to verify that *gap>0* when
starting from *gap=1,v*_{r}=2,v_{l}=2 and *a*_{r}=-0.5.

Input file