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).

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).

Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short "any-angle" paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

The Model AI Assignments session seeks to gather and disseminate the best assignment designs of the Artificial Intelligence (AI) Education community. Recognizing that assignments form the core of student learning experience, we here present abstracts of eight AI assignments that are easily adoptable, playfully engaging, and flexible for a variety of instructor needs.