  Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating
vehicle decision making and motion planning problems, where the prediction
model is a hybrid dynamical system that involves both discrete and continuous
decision variables. However, even the most advanced MIQP solvers can hardly
account for the challenging requirements of automotive embedded platforms.
Thus, we use machine learning to simplify and hence speed up optimization. Our
work builds on recent ideas for solving MIQPs in real-time by training a neural
network to predict the optimal values of integer variables and solving the
remaining problem by online quadratic programming. Specifically, we propose a
recurrent permutation equivariant deep set that is particularly suited for
imitating MIQPs that involve many obstacles, which is often the major source of
computational burden in motion planning problems. Our framework comprises also
a feasibility projector that corrects infeasible predictions of integer
variables and considerably increases the likelihood of computing a
collision-free trajectory. We evaluate the performance, safety and real-time
feasibility of decision-making for autonomous driving using the proposed
approach on realistic multi-lane traffic scenarios with interactive agents in
SUMO simulations.
