A limited class of motion planning problems is known in robotics as “fine motion planning.” Given a set of initial and goal configurations for a robot, the problem is to generate a motion strategy that, when executed, guarantees that the robot will get to a goal configuration despite errors. The errors come from uncertainty in the robot control and in sensing. The basic assumption is that the robot is in a static workplace that is perfectly known in advance and that control and sensing errors stay within predefined uncertainty bounds. To simplify the treatment, the algorithms presented in the paper assume the robot to be a planar rigid object able only to translate in a two-dimensional Euclidean space. After a formal description of the problem, two different methods are presented and a way of combining them is proposed. Experimental results obtained in simulation are presented. A number of improvements are suggested and discussed in detail.

The fine motion planning problem has been studied in robotics for a number of years, and, as with most problems dealing with geometric reasoning, it is complex even with the simplifying assumptions that have been made. The paper provides a remarkably clear description of the problem and of the algorithms and is certainly of great interest to the robotics community. The list of references is quite complete and up to date.