Moving-target search, where a hunter has to catch a moving target, is an important problem for video game developers. In our case, the hunter repeatedly moves towards the target and thus has to solve similar search problems repeatedly. We develop Incremental ARA* (I-ARA*) for this purpose, the first incremental anytime search algorithm for moving-target search in known terrain. We provide an error bound on the lengths of the paths found by I-ARA* and show experimentally in known four-neighbor gridworlds that I-ARA* can be used with smaller time limits between moves of the hunter than competing state-of-the-art moving-target search algorithms, namely repeated A*, G-FRA*, FRA*, and sometimes repeated ARA*. The hunter tends to make more moves with I-ARA* than repeated A*, G-FRA* or FRA*, which find shortest paths for the hunter, but fewer moves with I-ARA* than repeated ARA*, which finds suboptimal paths for the hunter like I-ARA*. Also, the error bounds on the lengths of the paths of the hunter tend to be smaller with I-ARA* than repeated ARA*.

Search-based planning is widely used for mobile robot motion planning because of its guarantees of optimality and completeness. In continuous state-spaces, however, most existing approaches have significant limitations in terms of optimality and completeness because of the underlying grid used. We propose an approach that eliminates the dependency on grids by using more general equivalence classes to quickly find an initial solution and instead of pruning states that fall within an equivalence class and have higher cost, we use an inflated heuristic to lower the priority of these states in the search. In further iterations, we reduce the inflated heuristic in a principled way, thus providing fast solutions with provable suboptimality bounds that can be improved as time allows. The proposed approach produces smooth paths with the resolution dictated by the action set. Finer action sets produce higher resolution paths that are more computationally intensive to calculate and coarser action sets produce lower resolution paths that are faster to compute. To the best of our knowledge, this is the first algorithm that is able to plan in continuous state-spaces with provable guarantees on completeness and bounds on suboptimality for a given action set. Experimental results on 3D (x,y,theta) path planning show that, on average, this approach is able to find paths in less than two seconds that are within 2% of the optimal path cost in worlds of up to 1000x1000 m with a minimum step size of one meter.