  We propose a Stochastic MPC (SMPC) formulation for autonomous driving at
traffic intersections which incorporates multi-modal predictions of surrounding
vehicles for collision avoidance constraints. The multi-modal predictions are
obtained with Gaussian Mixture Models (GMM) and constraints are formulated as
chance-constraints. Our main theoretical contribution is a SMPC formulation
that optimizes over a novel feedback policy class designed to exploit
additional structure in the GMM predictions, and that is amenable to convex
programming. The use of feedback policies for prediction is motivated by the
need for reduced conservatism in handling multi-modal predictions of the
surrounding vehicles, especially prevalent in traffic intersection scenarios.
We evaluate our algorithm along axes of mobility, comfort, conservatism and
computational efficiency at a simulated intersection in CARLA. Our simulations
use a kinematic bicycle model and multimodal predictions trained on a subset of
the Lyft Level 5 prediction dataset. To demonstrate the impact of optimizing
over feedback policies, we compare our algorithm with two SMPC baselines that
handle multi-modal collision avoidance chance constraints by optimizing over
open-loop sequences.
