Temporal vs. spatial formulation of autonomous overtaking algorithms
Johan Karlsson, Nikolce Murgovski, Jonas Sigfrid Sjoberg · 2016
This paper concerns optimally controlling an autonomous vehicle to perform safe and comfortable overtaking of a slower moving leading vehicle using model predictive control. The contribution of this paper is to further analyze the convex relaxation that was introduced in [1] in order to see how it compares with the standard formulation. The main difference between the formulations is that the sampling is done in the temporal domain in the standard formulation, but in the spatial domain for the other. It is shown that it is easy to convert one formulation to the other. Further, it is shown that the formulations are identical under the assumption of constant longitudinal velocity of the controlled vehicle. However, when the longitudinal velocity is not fixed they are not identical, in fact, the temporal formulation becomes a mixed integer problem which is hard to convexify. On the other hand, the spatial formulation can be easily convexified using standard methods. Therefore, in the case of changing velocity, we have to rely on the spatial formulation to achieve good solutions in short computation time.