Context: I am working on a 20 cm x 20 cm indoor robot on a 2D terrain and I need to decide on its path planning algorithm.
A star advantages: A* is faster than fast marching because it runs linear in path length whereas fast marching runs linear in map size. Also it has variants which works with dynamic changes in maps.
Fast marching advantages: Both algorithms discretize the 2D space. Fast marching approximates the geodesic distances better than A* (which suffers due to discretization) and hence its optimal results is closer reality than A*'s optimal results.
Question: Is there any body of literature which compares these two algorithms conceptually and empirically? Are there any other awesome algorithms for 2D terrains?