  Sampling-based planning algorithm is a powerful tool for solving planning
problems in high-dimensional state spaces. In this article, we present a novel
approach to sampling in the most promising regions, which significantly reduces
planning time-consumption. The RRT# algorithm defines the Relevant Region based
on the cost-to-come provided by the optimal forward-searching tree. However, it
uses the cumulative cost of a direct connection between the current state and
the goal state as the cost-to-go. To improve the path planning efficiency, we
propose a batch sampling method that samples in a refined Relevant Region with
a direct sampling strategy, which is defined according to the optimal
cost-to-come and the adaptive cost-to-go, taking advantage of various sources
of heuristic information. The proposed sampling approach allows the algorithm
to build the search tree in the direction of the most promising area, resulting
in a superior initial solution quality and reducing the overall computation
time compared to related work. To validate the effectiveness of our method, we
conducted several simulations in both $SE(2)$ and $SE(3)$ state spaces. And the
simulation results demonstrate the superiorities of proposed algorithm.
