Algorithmic motion planning in robotics

A survey is presented of an approach to motion planning that emphasizes object-oriented, exact, and discrete (or combinatorial) algorithmic techniques in which worst-case asymptotically efficient solutions are being sought. Following a statement of the problem, motion planning in static and known environments is treated. The discussion covers general solutions, lower bounds, the projection method, the retraction method, the expanded obstacles, the single-component approach, and a mobile convex object moving in a 2D polygonal space. Variants of the motion-planning problem are then considered, namely, optimal motion planning, adaptive and exploratory motion planning, motion planning in the presence of moving obstacles, constrained motion planning, motion planning with uncertainty, and general task planning.<>