Goal-directed path planning is one of the basic and widely studied problems in the field of
mobile robotics. Homotopy classes of trajectories, arising due to the presence of obstacles,
are defined as sets of trajectories that can be transformed into each other by gradual
bending and stretching without colliding with obstacles. The problem of finding least-cost
paths restricted to a specific homotopy class or finding least-cost paths that do not belong to
certain homotopy classes arises frequently in such applications as predicting paths for …

Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as
sets of trajectories that can be transformed into each other by gradual bending and
stretching without colliding with obstacles. The problem of exploring/finding the different
homotopy classes in an environment and the problem of finding least-cost paths restricted to
a specific homotopy class (or not belonging to certain homotopy classes) arises frequently in
such applications as predicting paths for unpredictable entities and deployment of multiple …