Theta*
A variant of A* that lets path segments run at any angle instead of forcing the route onto a grid's eight compass directions.
Plain A* on a grid can only step in 45-degree increments, so the shortest route to a target set off at an odd angle comes out as a staircase zigzag that then has to be smoothed afterwards. Theta* fixes this during the search itself: whenever it expands a node it checks whether there is a clear line of sight from that node's grandparent straight to the neighbour, and if so it skips the intermediate step. The paths that fall out are shorter and straighter — the kind of line a person would actually walk.
It was introduced by Kenny Daniel, Alex Nash, Sven Koenig and Ariel Felner (JAIR 2010). The cost is the line-of-sight checks, which are heavier per node than A*'s plain neighbour lookup. Lazy Theta* defers those checks until a node is actually pulled from the open list and cuts out most of them.