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This is a good basic reference for A* vs Dijkstra. A* has an added heuristic trying to expand the potential field in the direction of the goal. Its not necessarily promised to be faster, but in most cases it is.

http://theory.stanford.edu/~amitp/GameProgramming/AStarComparison.html

RRT and RRT-variants are sampling based and not search based. They will require smoothing after the search. In practice RRTs are nice for higher dimensional spaces like manipulators, but in lower dimensional space (like 2D mobile robots) its not really adventitious over search based. WIth that said, there are RRT implemented global planner plugins if you google for it for you to try out youself if you like.