  This work proposes an algorithm to bound the minimum distance between points
on trajectories of a dynamical system and points on an unsafe set. Prior work
on certifying safety of trajectories includes barrier and density methods,
which do not provide a margin of proximity to the unsafe set in terms of
distance. The distance estimation problem is relaxed to a Monge-Kantorovich
type optimal transport problem based on existing occupation-measure methods of
peak estimation. Specialized programs may be developed for polyhedral norm
distances (e.g. L1 and Linfinity) and for scenarios where a shape is traveling
along trajectories (e.g. rigid body motion). The distance estimation problem
will be correlatively sparse when the distance objective is separable.
