Any‐Angle Path Planning

Abstract

In robotics and video games, one often discretizes continuous terrain into a grid with blocked and unblocked grid cells and then uses path-planning algorithms to find a shortest path on the resulting grid graph. This path, however, is typically not a shortest path in the continuous terrain. In this overview article, we discuss a path-planning methodology for quickly finding paths in continuous terrain that are typically shorter than shortest grid paths. Any-angle path-planning algorithms are variants of the heuristic path-planning algorithm A* that find short paths by propagating information along grid edges (like A*, to be fast) without constraining the resulting paths to grid edges (unlike A*, to find short paths).

The Length of Shortest Vertex Paths in Binary Occupancy Grids Compared to Shortest r-Constrained Ones

“…This article generalizes the approach taken by Nash (2012), to handle line segments at a finite number of gradients (Nash, 2012, assumed two gradients only).…”

“…Nash's comprehensive study (2012, also see the overview in Nash & Koenig, 2013) considered grid paths on regular grids in two and three dimensions. His work was subsequently expanded by Bailey et al (2015) in the two-dimensional case to cover both 4-and 8-connected paths, with feasible locations at both cell corners and cell centers (they also studied the lengths of shortest vertex paths versus true shortest paths).…”

Self-reconfiguration of modular underwater robots using an energy heuristic

“…Pal et al [12] used the A* algorithm to generate efficient paths by adding a function of the energy consumption to an Euclidean metric, which is the cost function commonly used for motion planning. Nash et al [7], [8] stated that the A* algorithm generates the shortest path in the discrete environment (grids) but it is not always true in the continuous environment. Brandt [13] investigated the selfreconfiguration properties of the ATRON modular robot by applying A*.…”

“…On random 500 × 500 2D grids with 20% blocked cells, Basic Theta* finds paths shorter than A* with post smoothing techniques 70% of the time [7]. Nash et al [8] state that the paths found by A* on 26-neighbor cubic grids can be ≈ 13% longer than truly shortest paths. Basic Theta* can be easily extended to 3D grids because it is based on the triangle inequality.…”

“…This paper proposes a self-reconfiguration strategy for modular robotic systems that exploiting an energy heuristic determines the transitions of each agent from the start-to the goal configurations with the minimum energy consumption in all intermediate morphologies. The Basic Theta* algorithm proposed by Nash et al [7], [8] is modified to include a cost function that accounts for both the energy spent to move the robots and the energy consumed by the cluster of robots to withstand restoring forces and moments due to morphology changes. The paper evaluates the proposed energy-based self-reconfiguration strategy in simulation and in preliminary model tank experiments.…”