Monthly Archives: May 2016

Evolving Neural Networks through Augmenting Topologies – Part 3 of 4

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This part of the NEAT tutorial will show how to use the RNeat package (not yet on CRAN) to solve the classic pole balance problem.

The simulation requires the implementation of 5 functions:

  • processInitialStateFunc – This specifies the initial state of the system, for the pole balance problem the state is the cart location, cart velocity, cart acceleration, force being applied to the cart, pole angle, pole angular velocity and pole angular acceleration.
  • processUpdateStateFunc – This specifies how to take the current state and update it using the outputs of the neural network. In this example this function simulates the equations of motion and takes the neural net output as the force that is being applied to the cart.
  • processStateToNeuralInputFunc – Allows for modifying the state / normalisation of the state before it is passed as an input to the neural network
  • fitnessUpdateFunc – Takes the old fitness, the old state and the new updated state and determines what the new system fitness is. For the pole balance problem this function wants to reward the pendulum being up right, and reward the cart being close to the middle of the track.
  • terminationCheckFunc – Takes the state and checks to see if the termination should be terminated. Can chose to terminate if the pole falls over, the simulation has ran too long or the cart has driven off of the end of the track.
  • plotStateFunc – Plots the state, for the pole balance this draws the cart and pendulum.

Onto the code:

?View Code RSPLUS
install.packages("devtools")
library("devtools")
install_github("RNeat","ahunteruk") #Install from github as not yet on CRAN
library("RNeat")
drawPoleFunc <- function(fixedEnd.x,fixedEnd.y,poleLength, theta,fillColour=NA, borderColour="black"){
  floatingEnd.x <- fixedEnd.x-poleLength * sin(theta)
  floatingEnd.y <- fixedEnd.y+poleLength * cos(theta)
 
  polygon(c(fixedEnd.x,floatingEnd.x,floatingEnd.x,fixedEnd.x),
             c(fixedEnd.y,floatingEnd.y,floatingEnd.y,fixedEnd.y),
              col = fillColour, border=borderColour)
}
 
drawPendulum <- function(fixedEnd.x,fixedEnd.y,poleLength, theta,radius,fillColour=NA, borderColour="black"){
  floatingEnd.x <- fixedEnd.x-poleLength * sin(theta)
  floatingEnd.y <- fixedEnd.y+poleLength * cos(theta)
  createCircleFunc(floatingEnd.x,floatingEnd.y,radius,fillColour,borderColour)
}
 
#Parameters to control the simulation
simulation.timestep = 0.005
simulation.gravity = 9.8 #meters per second^2
simulation.numoftimesteps = 2000
 
pole.length = 1 #meters, total pole length
pole.width = 0.2
pole.theta = pi/4
pole.thetaDot = 0
pole.thetaDotDot = 0
pole.colour = "purple"
 
 
pendulum.centerX = NA
pendulum.centerY = NA
pendulum.radius = 0.1
pendulum.mass = 0.1
pendulum.colour = "purple"
 
cart.width=0.5
cart.centerX = 0
cart.centerY = 0
cart.height=0.2
cart.colour="red"
cart.centerXDot = 0
cart.centerXDotDot = 0
cart.mass = 0.4
cart.force = 0
cart.mu=2
 
 
track.limit= 10 #meters from center
track.x = -track.limit
track.height=0.01
track.y = 0.5*track.height
track.colour = "blue"
 
leftBuffer.width=0.1
leftBuffer.height=0.2
leftBuffer.x=-track.limit-0.5*cart.width-leftBuffer.width
leftBuffer.y=0.5*leftBuffer.height
leftBuffer.colour = "blue"
 
rightBuffer.width=0.1
rightBuffer.height=0.2
rightBuffer.x=track.limit+0.5*cart.width
rightBuffer.y=0.5*rightBuffer.height
rightBuffer.colour = "blue"
 
#Define the size of the scene (used to visualise what is happening in the simulation)
scene.width = 2*max(rightBuffer.x+rightBuffer.width,track.limit+pole.length+pendulum.radius)
scene.bottomLeftX = -0.5*scene.width
scene.height=max(pole.length+pendulum.radius,scene.width)
scene.bottomLeftY = -0.5*scene.height
 
poleBalance.InitialState <- function(){
   state <- list()
   state[1] <- cart.centerX
   state[2] <- cart.centerXDot
   state[3] <- cart.centerXDotDot
   state[4] <- cart.force
   state[5] <- pole.theta
   state[6] <- pole.thetaDot
   state[7] <- pole.thetaDotDot
   return(state)
}
 
poleBalance.ConvertStateToNeuralNetInputs <- function(currentState){
    return (currentState)
}
 
poleBalance.UpdatePoleState <- function(currentState,neuralNetOutputs){
   #print("Updating pole state")
   #print(neuralNetOutputs)
   cart.centerX <- currentState[[1]]
   cart.centerXDot <- currentState[[2]]
   cart.centerXDotDot <- currentState[[3]]
   cart.force <- currentState[[4]]+neuralNetOutputs[[1]]
   pole.theta <- currentState[[5]]
   pole.thetaDot <- currentState[[6]]
   pole.thetaDotDot <- currentState[[7]]
 
   costheta = cos(pole.theta)
   sintheta = sin(pole.theta)
   totalmass = cart.mass+pendulum.mass
   masslength = pendulum.mass*pole.length
 
   pole.thetaDotDot = (simulation.gravity*totalmass*sintheta+costheta*(cart.force-masslength*pole.thetaDot^2*sintheta-cart.mu*cart.centerXDot))/(pole.length*(totalmass-pendulum.mass*costheta^2))
 
   cart.centerXDotDot = (cart.force+masslength*(pole.thetaDotDot*costheta-pole.thetaDot^2*sintheta)-cart.mu*cart.centerXDot)/totalmass
 
   cart.centerX = cart.centerX+simulation.timestep*cart.centerXDot
   cart.centerXDot = cart.centerXDot+simulation.timestep*cart.centerXDotDot
   pole.theta = (pole.theta +simulation.timestep*pole.thetaDot )
   pole.thetaDot = pole.thetaDot+simulation.timestep*pole.thetaDotDot
 
   currentState[1] <- cart.centerX
   currentState[2] <- cart.centerXDot
   currentState[3] <- cart.centerXDotDot
   currentState[4] <- cart.force
   currentState[5] <- pole.theta
   currentState[6] <- pole.thetaDot
   currentState[7] <- pole.thetaDotDot
   return (currentState)
}
 
 
 
poleBalance.UpdateFitness <- function(oldState,updatedState,oldFitness){
   #return (oldFitness+1) #fitness is just how long we've ran for
   #return (oldFitness+((track.limit-abs(updatedState[[1]]))/track.limit)^2) #More reward for staying near middle of track
 
   height <- cos(updatedState[[5]]) #is -ve if below track
   heightFitness <- max(height,0)
   centerFitness <- (track.limit-abs(updatedState[[1]]))/track.limit
   return (oldFitness+(heightFitness + heightFitness*centerFitness))
}
 
poleBalance.CheckForTermination <- function(frameNum,oldState,updatedState,oldFitness,newFitness){
   cart.centerX <- updatedState[[1]]
   cart.centerXDot <- updatedState[[2]]
   cart.centerXDotDot <- updatedState[[3]]
   cart.force <- updatedState[[4]]
   pole.theta <- updatedState[[5]]
   pole.thetaDot <- updatedState[[6]]
   pole.thetaDotDot <- updatedState[[7]]
 
   oldpole.theta <- oldState[[5]]
   if(frameNum > 20000){
     print("Max Frame Num Exceeded , stopping simulation")
     return (T)
   }
 
   height <- cos(pole.theta)
   oldHeight <- cos(oldpole.theta)
   if(height==-1 & cart.force==0){
     return(T)
   }
 
    if(oldHeight >= 0 & height < 0){
      #print("Pole fell over")
      return (T)
    }
    if(cart.centerX < track.x | cart.centerX > (track.x+2*track.limit)){
      #print("Exceeded track length")
       return (T)
    } else {
      return (F)
    }
}
 
poleBalance.PlotState <-function(updatedState){
   cart.centerX <- updatedState[[1]]
   cart.centerXDot <- updatedState[[2]]
   cart.centerXDotDot <- updatedState[[3]]
   cart.force <- updatedState[[4]]
   pole.theta <- updatedState[[5]]
   pole.thetaDot <- updatedState[[6]]
   pole.thetaDotDot <- updatedState[[7]]
 
     createSceneFunc(scene.bottomLeftX,scene.bottomLeftY,scene.width,scene.height,
                 main="Simulation of Inverted Pendulum - www.gekkoquant.com",xlab="",
                 ylab="",xlim=c(-0.5*scene.width,0.5*scene.width),ylim=c(-0.5*scene.height,0.5*scene.height))
 
    createBoxFunc(track.x,track.y,track.limit*2,track.height,track.colour)
    createBoxFunc(leftBuffer.x,leftBuffer.y,leftBuffer.width,leftBuffer.height,leftBuffer.colour)
    createBoxFunc(rightBuffer.x,rightBuffer.y,rightBuffer.width,rightBuffer.height,rightBuffer.colour)
    createBoxFunc(cart.centerX-0.5*cart.width,cart.centerY+0.5*cart.height,cart.width,cart.height,cart.colour)
    drawPoleFunc(cart.centerX,cart.centerY,2*pole.length,pole.theta,pole.colour)
    drawPendulum(cart.centerX,cart.centerY,2*pole.length,pole.theta,pendulum.radius,pendulum.colour)
 
}
 
config <- newConfigNEAT(7,1,500,50)
poleSimulation <- newNEATSimulation(config, poleBalance.InitialState,
                                poleBalance.UpdatePoleState,
                                poleBalance.ConvertStateToNeuralNetInputs,
                                poleBalance.UpdateFitness,
                                poleBalance.CheckForTermination,
                                poleBalance.PlotState)
 
for(i in seq(1,1000)){ 
      poleSimulation <- NEATSimulation.RunSingleGeneration(poleSimulation,T,"videos","poleBalance",1/simulation.timestep) 
}
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