  Motion-planning problems, such as manipulation in cluttered environments,
often require a collision-free shortest path to be computed quickly given a
roadmap graph. Typically, the computational cost of evaluating whether an edge
of the roadmap graph is collision-free dominates the running time of search
algorithms. Algorithms such as Lazy Weighted A* (LWA*) and LazySP have been
proposed to reduce the number of edge evaluations by employing a lazy lookahead
(one-step lookahead and infinite-step lookahead, respectively). However, this
comes at the expense of additional graph operations: the larger the lookahead,
the more the graph operations that are typically required. We propose Lazy
Receding-Horizon A* (LRA*) to minimize the total planning time by balancing
edge evaluations and graph operations. Endowed with a lazy lookahead, LRA*
represents a family of lazy shortest-path graph-search algorithms that
generalizes LWA* and LazySP. We analyze the theoretic properties of LRA* and
demonstrate empirically that, in many cases, to minimize the total planning
time, the algorithm requires an intermediate lazy lookahead. Namely, using an
intermediate lazy lookahead, our algorithm outperforms both LWA* and LazySP.
These experiments span simulated random worlds in $\mathbb{R}^2$ and
$\mathbb{R}^4$, and manipulation problems using a 7-DOF manipulator.
