  This text presents the proofs of the technical facts underlying theoretical
justification of the convergence and performance of the novel algorithm for
reactive navigation of differential drive wheeled robots in dynamic uncertain
environments. The algorithm restricts neither the natures nor the motions of
the obstacles, they need not be rigid but conversely may deform. It does not
consume data about the velocities, shapes, sizes, or orientations of the
obstacles, and does not need a map of the environment or recognition of
individual obstacles. The only information about the scene is the current
distance to the nearest obstacle.

Optimization and Control