Path Finding
Simple Grid Path Finding
This has the code for the problem of finding a path through a grid world
The program can be run with the following.
python driver.py data/5.txtCost of path: 178.4680374315354 ############################################################################## #............................................................................# #............................................................................# #.............................OOOOOOOOO......................................# #............................O#########O.....................................# #...........................O.#########O.....................................# #.......................OOOO..#########O.....................................# #......................O......#########O.....................................# #.....OOOOOOOOOOOOOOOOO.......#########O.........................############# ####.O#################################O.........................############# ####.O#################################O.........................############# 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python driver.py data/5.txt --no-diagonalCost of path: 206 ############################################################################## #............................................................................# #............................................................................# #............................OOOOOOOOOOO.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #....OOOOOOOOOOOOOOOOOOOOOOOOO#########O.........................############# ####.O#################################O.........................############# ####.O#################################O.........................############# 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Algorithms
There is also a command line argument (--algorithm) that lets you pick which algorithm to use to find the path. The supported ones are:
- Breath First Search
--algorithm bfs- Dijkstra’s algorithm
--algorithm dijkstra- A* Star
- A-start search that uses a Euclidean Distance heuristic
--algorithm a-star
Movement
The --no-diagonal command line arguments can specify if diagonal movement is allowed in the grid world. Setting this flag means the only valid moves are up, down, left, and right (modulo environmental constraints), while the defaults also allows movements like up one and left one to count as a single move. When diagonal movement is allowed, moving on the diagonal does come at a higher cost (√2 opposed to 1).
Data Format
Data is assumed to be an ASCII grid with the following symbols:
G- is the goal state
.- is walk-able space
#- is an impassable wall
R- is the agent
Grid Path Finding with Fuel Constraints
This has code for finding a path through a grid world where the agent can only move so many steps before refueling.
The program can be run with the following.
python fuel_driver.py fuel_data/3.txtCost of path: 124.76955262170047 ############################################################################## #............................................................................# #............................................................................# #.............................OOOOO+OOO......................................# #............................O#########O.....................................# #............................O#########.O....................................# #............................O#########..O...................................# #............................O#########...O..................................# #............................G#########...O......................############# ####..#################################....O.....................############# ####..#################################....O.....................############# 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python fuel_driver.py fuel_data/3.txt --no-diagonalCost of path: 140 ############################################################################## #............................................................................# #............................................................................# #............................OOOOOO+OOOO.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #............................O#########O.....................................# #............................G#########O.........................############# ####..#################################O.........................############# ####..#################################O.........................############# 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Meta-Algorithm
This uses the same algorithms as above to solve path finding. It does this by first finding all paths between the agent and each station, the path from the agent to the goal state, as well as all paths between stations (and the goal point). Any path that takes too much fuel (is longer than the agents capacity) is removed. This creates a new meta graph represents the distances between each, reachable, point. The path finding algorithm is then re-run to find the best path between these points and the legs in that path are converted back to the actual low level paths.
Data Format
The Data is assumed to be a file where the first row is the agent capacity and the following lines is the grid. There is a new symbol added (+) representing the re-fueling stations.
A Failed Attempt
Originally, I tried to solve this as a joint optimization problem, instead of the meta-graph approach I used a cost function that considered both the minimum distance and the fuel left. This doesn’t work because this cost function isn’t well defined for dynamic programming. When you are solving something via dynamic programming, you need to assume the exact way you go to some point doesn’t matter, the only thing that matters is the value of the cost function at that point. You can’t do this with the join distance and fuel, there are times where you can be at the same point with the same cost value, but different specifics for distance or fuel. This means you can’t forget how you got to here, you would need to track multiple paths. Long story short, this method does not work because the sub-problems we are breaking the pathing problem into aren’t solvable/memorizable on their own.
Implementation
These search algorithms are built on a graph class that exposes 2 main methods:
.get_neighbors(node: Node) -> Sequence[Node]- Get all neightbors of a node. Used to expand the search frontier.
.cost(src: Node, dst: Node) -> Union[float, int]- Get the cost (a.k.a the weight on the edge) between the
srcanddstnodes. This is used to for the meta graph search where the edges are paths with different lengths. It could also be used in encode terrain information, like between two nodes might be swap vs pavement, which would have a higher cost associated with them.
Subclasses
There are two main implementations here, one is a GridGraph which stores vertex information in a grid and the
other is a AdjancenyGraph which stores a collection of nodes, edges with wights. The GridGraph class also
includes a lot of extra methods for outputting ASCII representations of the grid.
Testing
There are very limited tests but they can be executed by running variable libraries as scripts. For example:
python -m path_finding.graph
python -m path_finding.priority_queue
python -m path_finding.path