TY - JOUR

T1 - The 2k neighborhoods for grid path planning

AU - Rivera, Nicolás

AU - Hernández, Carlos

AU - Hormazábal, Nicolás

AU - Baier, Jorge A.

N1 - Funding Information:
We thank Dietrich Daroch and Alejandro Pimentel for their comments on early drafts of this paper. Nicolás Rivera acknowledges funding from the Becas Chile initiative. Carlos Hernández and Jorge Baier are grateful to Fondecyt which partly funded this work through grants 1150328 and 1161526. Jorge Baier acknowledges funding from Proyecto VRI Puente.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Grid path planning is an important problem in AI. Its understanding has been key for the development of autonomous navigation systems. An interesting and rather surprising fact about the vast literature on this problem is that only a few neighborhoods have been used when evaluating these algorithms. 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 2k-neighborhoods; that is, neighborhoods that admit 2k neighbors per state, where k is a parameter. First, we provide a simple recursive definition of the 2k-neighborhood in terms of the 2k− 1-neighborhood. Second, we derive distance functions, for any k ≥ 2, which allow us to propose admissible heuristics that are perfect for obstacle-free grids, which generalize the well-known Manhattan and Octile distances. Third, we define the notion of canonical path for the 2k-neighborhood; this allows us to incorporate our neighborhoods into two versions of A*, namely Canonical A* and Jump Point Search (JPS), whose performance, we show, scales well when increasing k. Our empirical evaluation shows that, when increasing k, the cost of the solution found improves substantially. Used with the 2k-neighborhood, Canonical A* and JPS, in many configurations, are also superior to the any-angle path planner Theta∗ both in terms of solution quality and runtime. Our planner is competitive with one implementation of the any-angle path planner, ANYA in some configurations. Our main practical conclusion is that standard, well-understood grid path planning technology may provide an effective approach to any-angle grid path planning.

AB - Grid path planning is an important problem in AI. Its understanding has been key for the development of autonomous navigation systems. An interesting and rather surprising fact about the vast literature on this problem is that only a few neighborhoods have been used when evaluating these algorithms. 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 2k-neighborhoods; that is, neighborhoods that admit 2k neighbors per state, where k is a parameter. First, we provide a simple recursive definition of the 2k-neighborhood in terms of the 2k− 1-neighborhood. Second, we derive distance functions, for any k ≥ 2, which allow us to propose admissible heuristics that are perfect for obstacle-free grids, which generalize the well-known Manhattan and Octile distances. Third, we define the notion of canonical path for the 2k-neighborhood; this allows us to incorporate our neighborhoods into two versions of A*, namely Canonical A* and Jump Point Search (JPS), whose performance, we show, scales well when increasing k. Our empirical evaluation shows that, when increasing k, the cost of the solution found improves substantially. Used with the 2k-neighborhood, Canonical A* and JPS, in many configurations, are also superior to the any-angle path planner Theta∗ both in terms of solution quality and runtime. Our planner is competitive with one implementation of the any-angle path planner, ANYA in some configurations. Our main practical conclusion is that standard, well-understood grid path planning technology may provide an effective approach to any-angle grid path planning.

UR - http://www.scopus.com/inward/record.url?scp=85078887058&partnerID=8YFLogxK

U2 - 10.1613/jair.1.11383

DO - 10.1613/jair.1.11383

M3 - Article

AN - SCOPUS:85078887058

VL - 67

SP - 81

EP - 113

JO - Journal of Artificial Intelligence Research

JF - Journal of Artificial Intelligence Research

SN - 1076-9757

ER -