  Motion path planning is an intrinsically geometric problem which is central
for design of robot systems. Since the early years of AI, robotics together
with computer vision have been the areas of computer science that drove its
development. Many questions that arise, such as existence, optimality, and
diversity of motion paths in the configuration space that describes feasible
robot configurations, are of topological nature. The recent advances in
topological data analysis and related metric geometry, topology and
combinatorics have provided new tools to address these engineering tasks. We
will survey some questions, issues, recent work and promising directions in
data-driven geometric and topological methods with some emphasis on the use of
discrete Morse theory.
