  Randomized sampling based algorithms are widely used in robot motion planning
due to the problem's intractability, and are experimentally effective on a wide
range of problem instances. Most variants bias their sampling using various
heuristics related to the known underlying structure of the search space. In
this work, we formalize the intuitive notion of guided search by defining the
concept of a guiding space. This new language encapsulates many seemingly
distinct prior methods under the same framework, and allows us to reason about
guidance, a previously obscured core contribution of different algorithms. We
suggest an information theoretic method to evaluate guidance, which
experimentally matches intuition when tested on known algorithms in a variety
of environments. The language and evaluation of guidance suggests improvements
to existing methods, and allows for simple hybrid algorithms that combine
guidance from multiple sources.
