Relaxed Dijkstra and A* with linear complexity for robot path planning problems in large-scale grid environments

Although there exist efficient methods to determine an optimal path in a graph, such as Dijkstra and A* algorithms, large instances of the path planning problem need more adequate and efficient techniques to obtain solutions in reasonable time. We propose two new time-linear relaxed versions of Dijkstra (RD) and A* (RA*) algorithms to solve the global path planning problem in large grid environments. The core idea consists in exploiting the grid-map structure to establish an accurate approximation of the optimal path, without visiting any cell more than once. We conducted extensive simulations (1290 runs on 43 maps of various types) for the proposed algorithms, both in four-neighbor and eight-neighbor grid environments, and compared them against original Dijkstra and A* algorithms with different heuristics. We demonstrate that our relaxed versions exhibit a substantial gain in terms of computational time (more than 3 times faster in average), and in most of tested problems an optimal solution (in at least 97 % of cases for RD and 82 % for RA*) or a very close one is reached (at most 9 % of extra length, and less than 2 % in average). Besides, the simulations also show that RA* provides a better trade-off between solution quality and execution time than previous bounded relaxations of A* that exist in the literature.