2 research outputs found
Multilevel Motion Planning: A Fiber Bundle Formulation
Motion planning problems involving high-dimensional state spaces can often be
solved significantly faster by using multilevel abstractions. While there are
various ways to formally capture multilevel abstractions, we formulate them in
terms of fiber bundles, which allows us to concisely describe and derive novel
algorithms in terms of bundle restrictions and bundle sections. Fiber bundles
essentially describe lower-dimensional projections of the state space using
local product spaces. Given such a structure and a corresponding admissible
constraint function, we can develop highly efficient and optimal search-based
motion planning methods for high-dimensional state spaces. Our contributions
are the following: We first introduce the terminology of fiber bundles, in
particular the notion of restrictions and sections. Second, we use the notion
of restrictions and sections to develop novel multilevel motion planning
algorithms, which we call QRRT* and QMP*. We show these algorithms to be
probabilistically complete and almost-surely asymptotically optimal. Third, we
develop a novel recursive path section method based on an L1 interpolation over
path restrictions, which we use to quickly find feasible path sections. And
fourth, we evaluate all novel algorithms against all available OMPL algorithms
on benchmarks of eight challenging environments ranging from 21 to 100 degrees
of freedom, including multiple robots and nonholonomic constraints. Our
findings support the efficiency of our novel algorithms and the benefit of
exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR