Today I read a paper titled “Motion Planning via Manifold Samples”
The abstract is:
We present a general and modular algorithmic framework for path planning of robots.
Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions.
In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples.
Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations.
The modular design of the framework enables independent optimization of each modular component.
Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming.
This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles.
We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice.
We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.