cellular automata for pathfinding

Cellular Automata for Pathfinding

A Fault tolerant, Parallelizable incremental approach for real time environments

Steve Wilson

Cellular Automata for pathfinding:Over view:

What is a cellular automataHow it is related to other automata

What is path finding Other approaches to pathfindingWhy a new method ?The cellular approachPros and Cons of using cellular automata

Cellular Automata for pathfinding:What is a cellular automata:

Types of “automata”


Types of “automata” or “machines”


Types of automataFinite state machine



One or more states



One or more statesTransition rules



One or more statesTransition rules Input


Types of automataFinite state machinePush down automata



One or more states



One or more statesTransition rules



One or more statesTransition rulesInput



One or more statesTransition rulesInputStack



Turing machine



Turing machineOne or more states



Turing machineOne or more statesTransition rules



Turing machineOne or more statesTransition rulesTape


Types of automataFinite state machinePush down automataTuring machine

Cellular Automata



Cellular AutomataTwo or more states



Cellular AutomataTwo or more statesTransition rules



Cellular AutomataTwo or more statesTransition rulesNeighbor states


Basically


Basically a Cellular automata is a collection of connected finite state machines


Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata



Graph



GraphCells are connected by “edges”



GraphGrid



GraphGrid

Cells are arranged uniformly in a patternand connected spatially



GraphGridSubdivision



GraphGridSubdivision

Used extensively in modeling, cells are connected spatially in a non-uniform manner



GraphGridSubdivisionSynchronized



GraphGridSubdivisionSynchronized

Cells update at the same time based on the previous state



GraphGridSubdivisionSynchronizedConvergent

Does the automata settle down for all starting states


The Most famous cellular is Conway’s Game of Life

epic game of life

https://www.youtube.com/watch?v=C2vgICfQawE

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstacles


Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstaclesUsed in:


Path finding is the simply finding one or more optimal route between two or more points while avoiding obstaclesUsed in:

Design (circuit boards, chips, plumbing)



Design (circuit boards, chips, plumbing) Analysis (critical path)



Design (circuit boards, chips, plumbing) Analysis (critical path)Entertainment (goal seeking)

Cellular Automata for pathfinding:Other approaches to pathfinding:


Backtracking also known as depth first


Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you took


Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different path


Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circles


Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circlesThis can be prevented by remembering everywhere you’ve been


Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circlesPrevented by remembering everywhere you’ve beenEasy to implement recursively


Backtracking also depth known first


Backtracking also known as depth first


Backtracking also known as depth firstBreadth first



Again remembering each branch



Again remembering each branchExcept at each new intersection, go back to the untried path closest to the starting point


Backtracking also known as depth firstBreadth firstA* (A star)

At each intersection select the “best” untried path (based on a heuristic)


A* (A star)

Cellular Automata for pathfinding:Shortcomings of existing methods:


They require both a start and endpoint


They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same time


They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entities


They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions don’t lead to meaningful behavior


They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions partial solutions don’t lead to meaningful behaviorNot easily distributed


They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions partial solutions don’t lead to meaningful behaviorNot easily distributed each entity requires a large amount of information

Cellular Automata for pathfinding:Why a new method?:


Programmers love to reinvent the wheel


Programmers love to reinvent the wheelThe new algorithm might be better


Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methods


Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methodsTo learn something


Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methodsTo learn something (life long learning is important)

Cellular Automata for pathfinding:How does this method work?:


The states of the automata are as follows


The states of the automata are as follows:‘W’ the cell is a wall


The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal (there can be multiple goals)


The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…10,000 the cell is passable



The transitions are:



The transitions are:‘W’ -> ‘W’ Walls don’t change



The transitions are:‘W’ -> ‘W’‘G’ -> ‘G’ Goals don’t change



The transitions are:‘W’ -> ‘W’‘G’ -> ‘G’1…10,000 -> one more than its lowest value neighbor. Where ‘G’ has a value of zero


The passages are initialized to a random passage value (in the demo initialized to 1 for clarity)


The passages are initialized to a random passage value The walls are initialized to ‘W’


The passages are initialized to a random passage value The walls are initialized to ‘W’The goals are initialized to ‘G’


The passages are initialized to a random passage value The walls are initialized to ‘W’The goals are initialized to ‘G’The automata is stepped either synchronously or asynchronously


The passages are initialized to a random passage value The walls are initialized to ‘W’The goals are initialized to ‘G’The automata is stepped either synchronously or asynchronously Each entity can simply move to a neighboring cell with a lower value, going “downhill” to player


A simple example

W W W W W WW G 9 7 1 WW W W W W W


A simple example



A more complicated example

W W W W W WW 1 9 7 1 WW 7 W 5 W WW 8 5 3 G WW W W W W W


Demo Here:

Cellular Automata for pathfinding:Pros and cons:

Cellular Automata for pathfinding:Pros :

The cellular automata can be shared by entities

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributed



Each cell only needs to know about its closest neighbors



Each cell only needs to know about its closest neighborsThe cells don’t need to update synchronously


The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between frames


The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between frames

Entities will naturally move out of dead ends even before the path information fully propagates


The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant



A passage can be blocked to reflect changes in the maze



A passage can be blocked to reflect changes in the mazeGoals can be moved



If a passage is blocked, or the goal movesGoals can be movedContinue to use the existing automata as it updates



If a passage is blocked, or the goal movesContinue to use the existing automata as it updates

Unreachable areas are easily detected

Cellular Automata for pathfinding:Cons:


Requires enough memory to hold the search space


Requires enough memory to hold the search spaceFor a single entity takes more processing than other methods

Cellular Automata for pathfinding:In closing:

This Cellular Automata provides an incremental, fault tolerant, performant pathfinding solution

Cellular Automata for pathfinding:References:

Ascani, E (2011, October 4). Epic Game of Life. Retrieved April 4, 2016, from https://www.youtube.com/watch?v=C2vgICfQawE Codd, E. F. (1968). Cellular automata [Http://dl.acm.org/citation.cfm?id=1098682]. New York: Academic Press. Retrieved April 4, 2016. DeAngelis, M. (2016, February 29). Cat Maze Disguised as Bookshelves. Retrieved April 4, 2016, from http://www.cluttermagazine.com/news/2016/02/cat-maze-disguised-bookshelves Gardner, M. (1983). Wheels, life, and other mathematical amusements (Chp 20-22). New York: W.H. Freeman. Levy, S. (1993). Artificial life: A report from the frontier where computers meet biology. New York: Vintage Books. Pajot, T. (n.d.). Printed Circuit Board. Retrieved April 4, 2016, from http://www.123rf.com/photo_10607345_printed-circuit-board.html

cellular automata for pathfinding

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