Old potential function

In the following Figure, we see the potential function as selected in [1]. As discussed in the proposed paper [2], we observe the following weak points:

1.  Since any equilibrium point s* is governed by the condition V'(s*)=0, it is evident that all the inter-vehicle distances will converge at a value greater or equal to λ=20 m.

2.  For inter-vehicle distances smaller than 16 m, the potential function exhibits a strict increase, resulting in large values of the derivative, V'(s).  Due to the nature of our feedback laws, large values of V'(s) can potentially lead to unrealistic accelerations (see section V of [2]).

In order to address these  issues, we introduce a new framework of potential functions. Especially, we propose a family of parameterized potential functions aimed at minimizing the acceleration and inter-vehicle distances of the vehicles.  We approach that by defining an optimization problem where the decision variables are the parameters of the potential function while the objective function incorporates the acceleration and the inter-vehicle distances.