  We provide a systematic analysis of levels of integration between discrete
high-level reasoning and continuous low-level reasoning to address hybrid
planning problems in robotics. We identify four distinct strategies for such an
integration: (i) low-level checks are done for all possible cases in advance
and then this information is used during plan generation, (ii) low-level checks
are done exactly when they are needed during the search for a plan, (iii) first
all plans are computed and then infeasible ones are filtered, and (iv) by means
of replanning, after finding a plan, low-level checks identify whether it is
infeasible or not; if it is infeasible, a new plan is computed considering the
results of previous low- level checks. We perform experiments on hybrid
planning problems in robotic manipulation and legged locomotion domains
considering these four methods of integration, as well as some of their
combinations. We analyze the usefulness of levels of integration in these
domains, both from the point of view of computational efficiency (in time and
space) and from the point of view of plan quality relative to its feasibility.
We discuss advantages and disadvantages of each strategy in the light of
experimental results and provide some guidelines on choosing proper strategies
for a given domain.
