Completeness in Robot Motion Planning

In robot motion planning, we say that an algorithm is complete for a problem if it is guaranteed, for all instances of the problem, to nd a solution when one exists and to return failure otherwise. Completeness is a desirable property. It provides a guarantee that the algorithm will work as expected for all inputs and thus can be dependably included in a larger system. This is especially important when algorithms are incorporated into industrial applications, where delays and failures can be extremely costly.