  We propose a Model Predictive Control (MPC) for collision avoidance between
an autonomous agent and dynamic obstacles with uncertain predictions. The
collision avoidance constraints are imposed by enforcing positive distance
between convex sets representing the agent and the obstacles, and tractably
reformulating them using Lagrange duality. This approach allows for smooth
collision avoidance constraints even for polytopes, which otherwise require
mixed-integer or non-smooth constraints. We consider three widely used
descriptions of the uncertain obstacle position: 1) Arbitrary distribution with
polytopic support, 2) Gaussian distributions and 3) Arbitrary distribution with
first two moments known. For each case we obtain deterministic reformulations
of the collision avoidance constraints. The proposed MPC formulation optimizes
over feedback policies to reduce conservatism in satisfying the collision
avoidance constraints. The proposed approach is validated using simulations of
traffic intersections in CARLA.
