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, Communicated by V. Loia. B Imen Châari 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.
Path planning is a fundamental optimization problem that is crucial for the navigation of a mobile robot. Among the vast array of optimization approaches, we focus in this paper on Ant Colony Optimization (ACO) and Genetic Algorithms (GA) for solving the global path planning problem in a static environment, considering their effectiveness in solving such a problem. Our objective is to design an efficient hybrid algorithm that takes profit of the advantages of both ACO and GA approaches for the sake of maximizing the chance to find the optimal path even under real-time constraints. In this paper, we present smartPATH, a new hybrid ACO-GA algorithm that relies on the combination of an improved ACO algorithm (IACO) for efficient and fast path selection, and a modified crossover operator to reduce the risk of falling into a local minimum. We demonstrate through extensive simulations that smartPATH outperforms classical ACO (CACO), GA algorithms. It also outperforms the Dijkstra exact method in solving the path planning problem for large graph environments. It improves the solution quality up to 57% in comparison with CACO and reduces the execution time up to 83% as compared to Dijkstra for large and dense graphs. In addition, the experimental results on a real robot shows that smartPATH finds the optimal path with a probability up to 80% with a small gap not exceeding 1m in 98%.
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