*3.3. Global Path Planner Based on JPS+ (P)*

Figure 3a–c shows the offline work of the path planner, which includes constructing warning areas and identifying subgoals by preprocessing. Without the warning areas computed based on distance maps, the subgoals would be too close to the obstacles for moving robots, which increase the probabilities of colliding with walls.

**Figure 3.** A graphical representation of how Jump Point Search+ (Prune) (JPS+ (P)) preprocesses an initially known grid-based map and what the paths that it plans look like. (**a**) An original map in which the white and black cells are unblocked and blocked locations, respectively. (**b**) Gray cells denote warning areas. (**c**) Jump points are marked as red. (**d**) Green lines denote an optimal path planned by JPS+ (P).

During the process of constructing warning areas, the dynamic brushfire algorithm [31] is used to build the Euclidean distance map (EDM) based on the original map. The minimum distance between robots and obstacles is limited by the physical radius of robots; thus, a user-defined safety distance is required to increase insurance for robots that carry out important tasks. Therefore, the size of warning areas is determined by the above two factors (Figure 3b).

In the JPS family, jump points are the intermediate points that are necessary to travel through for at least one optimal path [14]. To put it simply, JPS and JPS+ call locations where a cardinal search can branch itself to wider areas due to obstacle disappearance in the incoming direction straight jump points. For example, in Figure 3c, an eastern search from A3 wraps around obstacles at C3, and then broadens itself to the southeastern areas. Besides straight nodes, they identify diagonal jump points linking two straight ones where the incoming diagonal search from the first can turn cardinally to reach the second. JPS+ improves JPS through exploiting diagonal-first ordering in the offline phase, and storing for each traversable cell the distance to the nearest jump point or obstacle that can be reached in every cardinal or diagonal direction. More details can be found in [14,32].

This paper applies JPS+ (P), which is an enhanced version of JPS+ with an intermediate pruning trick; thereby, the optimal path in Figure 3d will not generate and expand the diagonal jump point H8. JPS+ (P) requires the same preprocessing overheads to JPS+, but has stronger online efficiency.

To sum up, JPS+ (P)—which we borrow from [32]—has obvious advantages over other high-level planners of hierarchical methods in the literature [24–26], in terms of its low precomputation costs and outstanding online performance. Moreover, it serves as an ideal for the location distribution of jump points, providing a DRL-based controller with meaningful subgoals that can completely throw the problem of local minima out of consideration.
