5] v. Lumelsky and A. Stepanov. Path-planning Strategies for a Point Mobile Automaton Moving amidst Unknown Obstacles of Arbitrary Shape. Figure 22: Pushing Plan for the Real-world Experiment

Motion planning for a robot and a movable object amidst polygonal obstacles. A new geometrical approach to planing manipulation tasks. the case of a circular robot and a movable circular object amidst polygonal obstacles. Figure 23: The problem of rotational pushing. (A) describes a square object aligned to the grid. The dots show all possible (discretized) conngurations that the robot can take, and the circles illustrate all the conngurations on the grid that deene some contact mode of the robot and the labeled edge. (B) shows the same object, oriented at some angle. Note that in this case only two conngurations of the robot still deene some contact mode with regard to the same edge.