Computationally Efficient Autonomous Overtaking on Highways

This paper studies the problem of optimal overtaking of a slow-moving leading vehicle in the presence of oncoming and/or adjacent vehicles with varying but known longitudinal speeds. A computationally efficient modeling approach is introduced, in which the overtaking problem is formulated by sampling in relative distance to the leading vehicle, replacing velocity state with its inverse and utilizing a nonlinear change of control variables. These three steps achieve a computationally efficient nonlinear control problem that can be solved using the sequential quadratic programming. Measures have been taken to ensure the feasibility of the nonlinear problem, even when the sequential quadratic programming iterates are stopped prematurely. A case study is presented, where this new formulation is compared with the previously published formulations in terms of solution quality and computation time.