  Safe motion planning for robotic systems in dynamic environments is
nontrivial in the presence of uncertain obstacles, where estimation of obstacle
uncertainties is crucial in predicting future motions of dynamic obstacles. The
worst-case characterization gives a conservative uncertainty prediction and may
result in infeasible motion planning for the ego robotic system. In this paper,
an efficient, robust, and safe motion-planing algorithm is developed by
learning the obstacle uncertainties online. More specifically, the unknown yet
intended control set of obstacles is efficiently computed by solving a linear
programming problem. The learned control set is used to compute forward
reachable sets of obstacles that are less conservative than the worst-case
prediction. Based on the forward prediction, a robust model predictive
controller is designed to compute a safe reference trajectory for the ego
robotic system that remains outside the reachable sets of obstacles over the
prediction horizon. The method is applied to a car-like mobile robot in both
simulations and hardware experiments to demonstrate its effectiveness.
