  Many robotics applications benefit from being able to compute multiple
locally optimal paths in a given configuration space. Examples include path
planning for of tethered robots with cable-length constraints, systems
involving cables, multi-robot topological exploration & coverage, and,
congestion reduction for mobile robots navigation without inter-robot
coordination. Existing paradigm is to use topological path planning methods
that can provide optimal paths from distinct topological classes available in
the underlying configuration space. However, these methods usually require
non-trivial and non-universal geometrical constructions, which are
prohibitively complex or expensive in 3 or higher dimensional configuration
spaces with complex topology. Furthermore, topological methods are unable to
distinguish between locally optimal paths that belong to the same topological
class but are distinct because of genus-zero obstacles in 3D or due to
high-cost or high-curvature regions. In this paper we propose an universal and
generalized approach to multiple, locally-optimal path planning using the
concept of a novel neighborhood-augmented graph, search-based planning in which
can compute paths that are topo-geometrically distinct. This approach can find
desired number of locally optimal paths in a wider variety of configuration
spaces without requiring any complex pre-processing or geometric constructions.
Unlike the existing topological methods, resulting optimal paths are not
restricted to distinct topological classes, thus making the algorithm
applicable to many other problems where locally optimal and geometrically
distinct paths are of interest. We demonstrate the use of our algorithm to
planning for shortest traversible paths for a tethered robot in 3D with
cable-length constraint, and validate the results in simulations and real robot
experimentation.
