Motion planning is a fundamental problem in autonomous robotics. It
requires finding a path to a specified goal that avoids obstacles and
obeys a robot’s limitations and constraints. It is often desirable for this
path to also optimize a cost function, such as path length.
Formal path-quality guarantees for continuously valued search spaces are
an active area of research interest. Recent results have proven that some
sampling-based planning methods probabilistically converge towards
the optimal solution as computational effort approaches infinity. This
survey summarizes the assumptions behind these popular asymptotically optimal techniques and provides an introduction to the significant
ongoing research on this topic