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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., Comment: Accepted to CDC'22

We propose a Stochastic MPC (SMPC) approach for autonomous driving which incorporates multi-modal, interaction-aware predictions of surrounding vehicles. For each mode, vehicle motion predictions are obtained by a control model described using a basis of fixed features with unknown weights. The proposed SMPC formulation finds optimal controls which serves two purposes: 1) reducing conservatism of the SMPC by optimizing over parameterized control laws and 2) prediction and estimation of feature weights used in interaction-aware modeling using Kalman filtering. The proposed approach is demonstrated on a longitudinal control example, with uncertainties in predictions of the autonomous and surrounding vehicles., Comment: Accepted to AVEC'22