  Motion planning problems often have many local minima. Those minima are
important to visualize to let a user guide, prevent or predict motions. Towards
this goal, we develop the motion planning explorer, an algorithm to let users
interactively explore a tree of local-minima. Following ideas from Morse
theory, we define local minima as paths invariant under minimization of a cost
functional. The local-minima are grouped into a local-minima tree using
lower-dimensional projections specified by a user. The user can then
interactively explore the local-minima tree, thereby visualizing the problem
structure and guide or prevent motions. We show the motion planning explorer to
faithfully capture local minima in four realistic scenarios, both for holonomic
and certain non-holonomic robots.
