Pathfinding - A* with least turns

Question

Is it possible to modify A* to return the shortest path with the least number of turns?

One complication: Nodes can no longer be distinguished solel

Answer 1

If you really want to minimize the number of turns (as opposed to finding a nice tradeoff between turns and path length), why not transform your problem space by adding an edge for every pair of nodes connected by an unobstructed straight line; these are the pairs you can travel between without a turn. There are O(n) such edges per node, so the new graph is O(n³) in terms of edges. That makes A* solutions as much as O(n³) in terms of time.

Manhattan distance might be a good heuristic for A*.