The sensorless case

If there are no sensors, then better methods can be applied because the formulation reduces from Formulation 10.1 to Formulation 2.3. The simpler value iterations of Section 2.3 or Dijkstra's algorithm can be applied to find a solution. If optimality is not required, then any of the search methods of Section 2.2 can even be applied. For example, one can even imagine performing a bidirectional search on $ {\vec{X}}$ to attempt to connect $ {\vec{x}}_I$ to some $ {\vec{x}}_G$.

Steven M LaValle 2020-08-14