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CartPoleLearningSystem.m
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CartPoleLearningSystem.m
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%**********************************************************************************
% Learning to balance an inverted pendulum system using Reinforcement Learning
% Temporal Difference Algorithm - SARSA is used here to train the Neural Network.
% The code involves the following functions:
% main : controls simulation interations and implements
% the learning system.
%
% cart_pole: the cart and pole dynamics; given action and
% current state, estimates next state
%
% getBox: The cart-pole's state space is divided into 162
% boxes. get_box returns the index of the box into
% which the current state appears.
%
% Learning parameters:
% x: cart position, meters
% xDot: cart velocity
% theta: pole angle, radians
% thetaDot: pole angular velocity
% w: vector of action weights
% v: vector of critic weights
% e: vector of action weight eligibilities
% xBar: vector of critic weight eligibilities
%Code written by: Nikhil Podila , Savinay Nagendra
%email id: [email protected] , [email protected]
%**********************************************************************************
clc;
clear all;
close all;
% System Constants
N_BOXES = 162; % Number of discrete boxes of state space
ALPHA = 1000; % Learning rate for action weights, w
BETA = 0.5; % Learning rate for critic weights, v
GAMMA = 0.95; % Discount factor for critic
LAMDAw = 0.9; % Decay rate for w eligibility trace
LAMDAv = 0.8; % Decay rate for v eligibility trace
MAX_FAILURES = 1000; % Termination criterion
MAX_STEPS = 100000;
% Flags and variables
steps = 0;
failures = 0;
thetaPlot = 0;
xPlot = 0;
%Initialize action and heuristic critic weights and traces
w = zeros(N_BOXES,1);
v = zeros(N_BOXES,1);
xBar = zeros(N_BOXES,1);
e = zeros(N_BOXES,1);
%Starting state
theta = 0;
thetaDot = 0;
x = 0;
xDot = 0;
box = getBox(theta,thetaDot,x,xDot);
while(steps < MAX_STEPS && failures < MAX_FAILURES)
steps = steps + 1;
% Choose action randomly, biased by current weight
y = (rand < probPushRight(w(box)));
% Update traces
e(box) = e(box) + (1 - LAMDAw)*(y - 0.5); % test
xBar(box) = xBar(box) + (1 - LAMDAv);
% Remember prediction of failure for current state
oldp = v(box);
%Apply action to the simulated cart pole
[thetaNext,thetaDotNext,xNext,xDotNext] = cart_pole(y,theta,thetaDot,x,xDot);
thetaPlot(end + 1) = thetaNext;
xPlot(end + 1) = xNext;
%Get box of state space containing the resulting state
box = getBox(thetaNext,thetaDotNext,xNext,xDotNext);
theta = thetaNext;
thetaDot = thetaDotNext;
x = xNext;
xDot = xDotNext;
if (box < 0)
%Failure occurred
failed = 1;
failures = failures + 1;
fprintf('Trial %d was %d steps. \n',failures,steps);
figure(1);
plot(failures,steps,'r*');
hold on;
figure(2);
plot((1:length(thetaPlot)),thetaPlot,'-ob');
figure(3);
plot((1:length(xPlot)),xPlot,'-og');
thetaPlot = 0;
xPlot = 0;
steps = 0;
%Reset state to [0 0 0 0]. Find the box.
theta = 0;
thetaDot = 0;
x = 0;
xDot = 0;
box = getBox(theta,thetaDot,x,xDot);
%Reinforcement upon failure is adaptive. Prediction of failure is 0.
r = -1;
p = 0;
else
%Not a failure
failed = 0;
%Reinforcement is 0. Prediction of failure is given by v weight.
r = 0;
p = v(box);
% figure(failures + 2);
% plot(steps,theta,'*b');
% hold on;
end
% Heuristic reinforcement is:
% current reinforcement + gamma * new failure prediction - previous failure prediction
rhat = r + GAMMA*p - oldp;
for i = 1:N_BOXES,
% Update weights
w(i) = w(i) + ALPHA*rhat*e(i);
v(i) = v(i) + BETA*rhat*xBar(i);
if (failed)
%If failure, zero all traces
e(i) = 0;
xBar(i) = 0;
else
%Otherwise update (decay) the traces
e(i) = e(i)*LAMDAw;
xBar(i) = xBar(i)*LAMDAv;
end
end
end
if(failures == MAX_FAILURES)
fprintf('Pole not balanced. Stopping after %d failures.',failures);
else
fprintf('Pole balanced successfully for at least %d steps\n', steps);
% Failures vs number of steps plot
figure(1);
plot(failures+1,steps,'-or');
title("Number of steps taken to reach each Failure")
hold on;
% Pole angle and Cart position plots for best trial
figure(2);
plot((1:length(thetaPlot)),thetaPlot,'-ob');
title("Pole Angle plot for the best trial")
figure(3);
plot((1:length(xPlot)),xPlot,'-og');
title("Cart Position plot for the best trial")
% Sample plots for pole angle and cart position for best trial (Few steps)
figure(4);
plot((1:301),thetaPlot(1:301),'-ob');
title("Pole Angle plot (few samples) for the best trial")
hold on;
figure(5);
plot((1:301),xPlot(1:301),'-og');
title("Cart Position plot (few samples) for the best trial")
hold on;
end