Multipath Generalized Adaptive A* (MPGAA*) is an A*- based incremental search algorithm for dynamic terrain that can outperform D* for the (realistic) case of limited visibility ranges. A first contribution of this paper is a brief analysis studying why MPGAA* has poor performance for extended visibility ranges, which concludes that MPGAA* carries out an excessive number of heuristic updates. Our second contribution is a method to reduce the number of heuristic updates that preserves optimality. Finally, a third contribution is a variant of MPGAA*, MPGAA*-back, which we show outperforms MPGAA* and D* on a wide range of dynamic grid pathfinding scenarios, and visibility ranges.

Grid pathfinding, an old AI problem, is central for the development of navigation systems for autonomous agents. A surprising fact about the vast literature on this problem is that very limited neighborhoods have been studied. Indeed, only the 4- and 8-neighborhoods are usually considered, and rarely the 16-neighborhood. This paper describes three contributions that enable the construction of effective grid path planners for extended 2 k -neighborhoods. First, we provide a simple recursive definition of the 2 k -neighborhood in terms of the 2 k –1 -neighborhood. Second, we derive distance functions, for any k >1, which allow us to propose admissible heurisitics which are perfect for obstacle-free grids. Third, we describe a canonical ordering which allows us to implement a version of A* whose performance scales well when increasing k . Our empirical evaluation shows that the heuristics we propose are superior to the Euclidean distance (ED) when regular A* is used. For grids beyond 64 the overhead of computing the heuristic yields decreased time performance compared to the ED. We found also that a configuration of our A*-based implementation, without canonical orders, is competitive with the "any-angle" path planner Theta$^*$ both in terms of solution quality and runtime.