## 1 Introduction  
Path-planning for mobile robots involves identifying an efficient path from a start position to a goal position on a given environmental map using online sensor data. The path-planning algorithms are divided into those facilitating local and global planning. Local path-planning (\"obstacle avoidance\") prevents collisions, even when unexpected (unregistered) obstacles are encountered [1, 2]. Global path-planning generates waypoints that connect the start to the goal using the given map [3, 4]. In practice, local and global plannings are integrated as the robot proceeds via various waypoints to a goal, while the local planner calculates the actions to arrive at each waypoint using current sensor data. Therefore, the efficient waypoints in safe regions that can constitute the shortest path are essential for higher level applications. Most global planners initially extract safe/navigable regions from a global map and then find an appropriate path between the safe regions. Safe regions can be represented as empty/unoccupied cells of a grid map or as the nodes of a graph. Grid map-based planning is applicable in two-dimensional (2D) environments because it is possible to directly recognize safe regions and their relationships when planning possible paths between them via regularly decomposed grid cell representation [5, 6]. However, to solve scalability issues in high-dimensional applications with limited computational power and time, the grid-based planners require additional effort like the cost approximation [7]. Graph-based methods were developed to handle path-planning in large environments. The computational burdens are lower than those of grid-based methods. The two most widely used approaches are the probabilistic roadmap (PRM) [8] and the rapidly exploring random tree (RRT) [9; 10]. These are termed sampling-based methods, because they sample/generate nodes stochastically in empty regions [11; 12]. PRM planners first construct a graph (a roadmap) that covers the entire environment and includes collision-free paths. Then, they compute the shortest path from a start position to a goal along the roadmap. Although the multiple-query approach of a PRM planner aids path-planning in complex or high-dimensional spaces [13], many practical path-planning problems can be solved using a single-query approach such as that of an RRT. RRT planners basically expand a tree via random sampling of empty regions from the start position and stop when the tree attains the goal. The RRT variants differ in terms of how they optimize the initial feasible solution or how they modify the tree structure. RRT-Connect simultaneously grows two RRTs rooted at the start and the goal toward each other until they meet, reducing the computational time required for a converged solution [14]. RRT* asymptotically converges to an optimal solution by additionally rewiring the tree [15; 16]. RRT*-Connect combines RRT-Connect and RRT*, yielding asymptotically optimal solutions faster than either algorithm alone [17]. Although various RRT algorithms deal with high-dimensional and complex state spaces by ensuring probabilistic completeness and delivering optimal asymptotic solutions, convergence to the optimal solution is slow for environments with narrow passages and when non-solution areas in the entire configuration space are (unnecessarily) subjected to dense sampling [18; 19]. The informed RRT* (IRRT*) was developed to improve the convergence rate and the final solution quality by restricting the sampling region to an ellipsoid defined by the solution of the previous optimization step [20]. It obtains a final optimal solution in less time than the basic RRT*. However, as the IRRT* employs a vanilla RRT* sampling method (the sampling target is the entire space) to achieve an initial solution, the IRRT* suffers from problems similar to those of the RRT*.