Motion planning in dynamic and partially unknown environments is a difficult problem requiring both perception and control components. We propose a solution to the control component while cleanly abstracting perception. We show that this clean abstraction can be used to synthesize verifiably safe reference trajectories using a combination of reachability analysis and Mixed Integer Linear Programming. Experiments with prototype implementation of this algorithm show promise as it has subsecond synthesis performance for nonlinear vehicle models in scenarios with hundred plus obstacles on standard hardware.
