Computationally efficient exact remodeling of optimization programs with applications to autonomous driving

Licentiate thesis, 2019

The future of autonomous vehicles is rapidly approaching and the published and available research, both from vehicle manufacturers and universities, is abundant. This new technology promises less pollution, lower accident rates, decreased congestion and the possibility to relax or work while a vehicle takes you where you need to go.

In this thesis we use nonlinear model predictive control to control autonomous vehicles overtaking on highways and driving through intersections. One of the main disadvantages of model predictive control is that the optimal control problems can be computationally expensive to solve. This could certainly be the case for the exact temporal formulation of the intersection and highway problem since the modeling of for both applications include binary decisions; and thus, have mixed integer optimization programs as their optimal control problems. To decrease the computational complexity of these optimal control problems this thesis introduces a novel reformulation technique for optimal control problems which removes the integer decisions present due to the collision constraints; which results in a continuous, nonlinear control problem for both applications. The remodeling technique involves changing the independent variable from travel time to traveled distance, introducing travel time and inverse velocity as states and lastly by introducing new input signals. After the remodeling, the continuous, nonlinear optimal control problems are solved using sequential quadratic programming. Further, it is shown that the introduced remodeling technique guarantees that the subproblems of the sequential quadratic programming scheme provides feasible solutions to the original nonlinear program being solved; for both the intersection and overtaking problem. This makes it possible to stop the sequential quadratic programming scheme prematurely and still have access to a solution that is feasible in the nonlinear program; provided, of course, that the subproblems themselves are feasible.