  We present a chance-constrained model predictive control (MPC) framework
under Gaussian mixture model (GMM) uncertainty. Specifically, we consider the
uncertainty that arises from predicting future behaviors of moving obstacles,
which may exhibit multiple modes (for example, turning left or right). To
address the multi-modal uncertainty distribution, we propose three MPC
formulations: nominal chance-constrained planning, robust chance-constrained
planning, and contingency planning. We prove that closed-loop trajectories
generated by the three planners are safe. The approaches differ in
conservativeness and performance guarantee. In particular, the robust
chance-constrained planner is recursively feasible under certain assumptions on
the propagation of prediction uncertainty. On the other hand, the contingency
planner generates a less conservative closed-loop trajectory than the nominal
planner. We validate our planners using state-of-the-art trajectory prediction
algorithms in autonomous driving simulators.
