  In this work, we propose the Informed Batch Belief Trees (IBBT) algorithm for
motion planning under motion and sensing uncertainties. The original stochastic
motion planning problem is divided into a deterministic motion planning problem
and a graph search problem. We solve the deterministic planning problem using
sampling-based methods such as PRM or RRG to construct a graph of nominal
trajectories. Then, an informed cost-to-go heuristic for the original problem
is computed based on the nominal trajectory graph. Finally, we grow a belief
tree by searching over the graph using the proposed heuristic. IBBT interleaves
between batch state sampling, nominal trajectory graph construction, heuristic
computing, and search over the graph to find belief space motion plans. IBBT is
an anytime, incremental algorithm. With an increasing number of batches of
samples added to the graph, the algorithm finds motion plans that converge to
the optimal one. IBBT is efficient by reusing results between sequential
iterations. The belief tree searching is an ordered search guided by an
informed heuristic. We test IBBT in different planning environments. Our
numerical investigation confirms that IBBT finds non-trivial motion plans and
is faster compared with previous similar methods.
