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ComputeTransitionProbabilities.m
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ComputeTransitionProbabilities.m
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function P = ComputeTransitionProbabilities(stateSpace, map)
%COMPUTETRANSITIONPROBABILITIES Compute transition probabilities.
% Compute the transition probabilities between all states in the state
% space for all control inputs.
%
% P = ComputeTransitionProbabilities(stateSpace, map)
% computes the transition probabilities between all states in the state
% space for all control inputs.
%
% Input arguments:
% stateSpace:
% A (K x 3)-matrix, where the i-th row represents the i-th
% element of the state space.
%
% map:
% A (M x N)-matrix describing the world. With
% values: FREE TREE SHOOTER PICK_UP DROP_OFF BASE
%
% Output arguments:
% P:
% A (K x K x L)-matrix containing the transition probabilities
% between all states in the state space for all control inputs.
% The entry P(i, j, l) represents the transition probability
% from state i to state j if control input l is applied.
global GAMMA R P_WIND
global FREE TREE SHOOTER PICK_UP DROP_OFF BASE
global NORTH SOUTH EAST WEST HOVER
global K TERMINAL_STATE_INDEX
P = zeros(K,K,5);
width = size(map,1);
height = size(map,2);
%% ======= INFO ========
% | | | |
% | | 4 | |
% | | | |
% ---------------------------------------
% | | | |
% | 1 | 2 | 3 |
% | | | |
% ---------------------------------------
% | | | |
% 10 | 9 |(m,n,x)| 11 | 12
% | | | |
% ---------------------------------------
% | | | |
% | 5 | 6 | 7 |
% | | | |
% ---------------------------------------
% | | | |
% | | 8 | |
% | | | |
% NORTH 1
% SOUTH 2
% EAST 3
% WEST 4
% HOVER 5
%% ======= FIND INDEXES ==========
shooters = [];
for m = 1 : size(map, 1)
for n = 1 : size(map, 2)
if map(m, n) == SHOOTER
shooters = [shooters;
m, n];
elseif map(m, n) == BASE
base = [m,n];
elseif map(m, n) == PICK_UP
pick_up = [m,n];
elseif map(m, n) == DROP_OFF
drop_off = [m,n];
end
end
end
base_no_packIndex = find(stateSpace(:,1)== base(1) & stateSpace(:,2) == base(2) & stateSpace(:,3) == 0);
base_packIndex = base_no_packIndex + 1;
pick_upIndex = find(stateSpace(:,1)== pick_up(1) & stateSpace(:,2) == pick_up(2) & stateSpace(:,3) == 0);
drop_offIndex = find(stateSpace(:,1)== drop_off(1) & stateSpace(:,2) == drop_off(2) & stateSpace(:,3) == 1);
%Correct_if_equal_5 = map(stateSpace(base_no_packIndex,1),stateSpace(base_no_packIndex,2))
%Correct_if_equal_5 = map(stateSpace(base_packIndex,1),stateSpace(base_packIndex,2))
%Correct_if_equal_3 = map(stateSpace(pick_upIndex,1),stateSpace(pick_upIndex,2))
%Correct_if_equal_4 = map(stateSpace(drop_offIndex,1),stateSpace(drop_offIndex,2))
% for k =1:size(shooters,1)
% shootersIndex = find(stateSpace(:,1) == shooters(k,1) & stateSpace(:,2) == shooters(k,2) & stateSpace(:,3) == 0);
% Correct_if_equal_2 = [map(stateSpace(shootersIndex(1),1),stateSpace(shootersIndex(1),2))]
% end
%% ======= HIT PROBABILITY ==========
prob_hit = zeros(K,1);
prob_no_hit = zeros(K,1);
for i = 1:2:K
distance = zeros(size(shooters,1),1);
prob_hit_vector = ones(size(shooters,1),1);
for n = 1:size(shooters,1)
distance(n) = norm([stateSpace(i,1), stateSpace(i,2)]-[shooters(n,1), shooters(n,2)],1);
if 0<=distance(n) && distance(n)<=R
prob_hit_vector(n) = GAMMA/(distance(n) + 1);
else
prob_hit_vector(n) = 0;
end
prob_hit(i) = prob_hit(i) + (1 - prob_hit(i))*prob_hit_vector(n);
prob_hit(i+1) = prob_hit(i);
end
prob_no_hit(i) = 1 - prob_hit(i);
prob_no_hit(i+1) = 1 - prob_hit(i+1);
end
%% ======= TRANSITION PROBABILITY ==========
for pack = 0:1 % repeat 2 times, for states with and without the pack
for i = pack+1:2:K % i indexes half of the total states (also j)
% -- STATES (m,n,pack) --
%% === NORTH === %%
% input north at (m,n)
if (stateSpace(i,2) ~= height) % input north at (m,n)
if map(stateSpace(i,1),stateSpace(i,2)+1) ~= TREE
crash_prob = 0;
% turn back
P(i,i,1) = P_WIND/4 * prob_no_hit(i); % turn back
crash_prob = crash_prob + P_WIND/4 *prob_hit(i);
for j = pack+1:2:K
if stateSpace(i,2)+1 == stateSpace(j,2) % select the entire row above the cell (m,n)
% cell n.1
if stateSpace(i,1)-1 == stateSpace(j,1) % cell n.1
P(i,j,1) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.2
elseif stateSpace(i,1) == stateSpace(j,1) % cell n.2
P(i,j,1) = (1 - P_WIND) * prob_no_hit(j);
crash_prob = crash_prob + (1 - P_WIND) *prob_hit(j);
% cell n.3
elseif stateSpace(i,1)+1 == stateSpace(j,1) % cell n.3
P(i,j,1) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
% cell n.4
if stateSpace(i,1) == stateSpace(j,1) &&... % cell n.4
stateSpace(i,2)+2 == stateSpace(j,2)
P(i,j,1) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
if stateSpace(i,1)>1
if map(stateSpace(i,1)-1, stateSpace(i,2)+1) == TREE % cell n.1 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)<width
if map(stateSpace(i,1)+1, stateSpace(i,2)+1) == TREE % cell n.3 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,2)<height-1
if map(stateSpace(i,1), stateSpace(i,2)+2) == TREE % cell n.4 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
P(i,base_no_packIndex,1) = P(i,base_no_packIndex,1) + crash_prob;
end
end
%% === SOUTH === %%
% input south at (m,n)
if stateSpace(i,2) ~= 1 % input south at (m,n)
if map(stateSpace(i,1),stateSpace(i,2)-1) ~= TREE
crash_prob = 0;
% turn back
P(i,i,2) = P_WIND/4 * prob_no_hit(i); % turn back
crash_prob = crash_prob + P_WIND/4 *prob_hit(i);
for j = pack+1:2:K
if stateSpace(i,2)-1 == stateSpace(j,2) % select the entire row under the cell (m,n)
% cell n.5
if stateSpace(i,1)-1 == stateSpace(j,1) % cell n.5
P(i,j,2) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.6
elseif stateSpace(i,1) == stateSpace(j,1) % cell n.6
P(i,j,2) = (1 - P_WIND) * prob_no_hit(j);
crash_prob = crash_prob + (1 - P_WIND) *prob_hit(j);
% cell n.7
elseif stateSpace(i,1)+1 == stateSpace(j,1) % cell n.7
P(i,j,2) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
% cell n.8
if stateSpace(i,1) == stateSpace(j,1) &&... % cell n.8
stateSpace(i,2)-2 == stateSpace(j,2)
P(i,j,2) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
if stateSpace(i,1)>1
if map(stateSpace(i,1)-1, stateSpace(i,2)-1) == TREE % cell n.5 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)<width
if map(stateSpace(i,1)+1, stateSpace(i,2)-1) == TREE % cell n.7 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,2)>2
if map(stateSpace(i,1), stateSpace(i,2)-2) == TREE % cell n.8 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
P(i,base_no_packIndex,2) = P(i,base_no_packIndex,2) + crash_prob;
end
end
%% === EAST === %%
% input east at (m,n)
if stateSpace(i,1) ~= width % input east at (m,n)
if map(stateSpace(i,1)+1,stateSpace(i,2)) ~= TREE
crash_prob = 0;
% turn back
P(i,i,3) = P_WIND/4 * prob_no_hit(i); % turn back
crash_prob = crash_prob + P_WIND/4 *prob_hit(i);
for j = pack+1:2:K
if stateSpace(i,1)+1 == stateSpace(j,1) % select the entire right column to the cell (m,n)
% cell n.7
if stateSpace(i,2)-1 == stateSpace(j,2) % cell n.7
P(i,j,3) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.11
elseif stateSpace(i,2) == stateSpace(j,2) % cell n.11
P(i,j,3) = (1 - P_WIND) * prob_no_hit(j);
crash_prob = crash_prob + (1 - P_WIND) *prob_hit(j);
% cell n.3
elseif stateSpace(i,2)+1 == stateSpace(j,2) % cell n.3
P(i,j,3) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
% cell n.12
if stateSpace(i,2) == stateSpace(j,2) &&... % cell n.12
stateSpace(i,1)+2 == stateSpace(j,1)
P(i,j,3) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
if stateSpace(i,2)>1
if map(stateSpace(i,1)+1, stateSpace(i,2)-1) == TREE % cell n.7 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,2)<height
if map(stateSpace(i,1)+1, stateSpace(i,2)+1) == TREE % cell n.3 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)<width-1
if map(stateSpace(i,1)+2, stateSpace(i,2)) == TREE % cell n.12 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
P(i,base_no_packIndex,3) = P(i,base_no_packIndex,3) + crash_prob;
end
end
%% === WEST === %%
% input west at (m,n)
if stateSpace(i,1) ~= 1 % input west at (m,n)
if map(stateSpace(i,1)-1,stateSpace(i,2)) ~= TREE
crash_prob = 0;
% turn back
P(i,i,4) = P_WIND/4 * prob_no_hit(i); % turn back
crash_prob = crash_prob + P_WIND/4 *prob_hit(i);
for j = pack+1:2:K
if stateSpace(i,1)-1 == stateSpace(j,1) % select the entire left column to the cell (m,n)
% cell n.5
if stateSpace(i,2)-1 == stateSpace(j,2) % cell n.5
P(i,j,4) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.9
elseif stateSpace(i,2) == stateSpace(j,2) % cell n.9
P(i,j,4) = (1 - P_WIND) * prob_no_hit(j);
crash_prob = crash_prob + (1 - P_WIND) *prob_hit(j);
% cell n.1
elseif stateSpace(i,2)+1 == stateSpace(j,2) % cell n.1
P(i,j,4) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
% cell n.10
if stateSpace(i,2) == stateSpace(j,2) &&... % cell n.10
stateSpace(i,1)-2 == stateSpace(j,1)
P(i,j,4) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
if stateSpace(i,2)>1
if map(stateSpace(i,1)-1, stateSpace(i,2)-1) == TREE % cell n.5 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,2)<height
if map(stateSpace(i,1)-1, stateSpace(i,2)+1) == TREE % cell n.1 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)>2
if map(stateSpace(i,1)-2, stateSpace(i,2)) == TREE % cell n.10 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
P(i,base_no_packIndex,4) = P(i,base_no_packIndex,4) + crash_prob;
end
end
%% === HOVER === %%
% input hover at (m,n)
crash_prob = 0;
% stay
P(i,i,5) = (1 - P_WIND) * prob_no_hit(i); % stay
crash_prob = crash_prob + (1 - P_WIND) *prob_hit(i);
for j = pack+1:2:K
% cell n.2
if stateSpace(i,2)+1 == stateSpace(j,2) &&... % cell n.2
stateSpace(i,1) == stateSpace(j,1)
P(i,j,5) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.6
elseif stateSpace(i,2)-1 == stateSpace(j,2) &&... % cell n.6
stateSpace(i,1) == stateSpace(j,1)
P(i,j,5) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.9
elseif stateSpace(i,2) == stateSpace(j,2) &&... % cell n.9
stateSpace(i,1)-1 == stateSpace(j,1)
P(i,j,5) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
% cell n.11
elseif stateSpace(i,2) == stateSpace(j,2) &&... % cell n.11
stateSpace(i,1)+1 == stateSpace(j,1)
P(i,j,5) = P_WIND/4 * prob_no_hit(j);
crash_prob = crash_prob + P_WIND/4 *prob_hit(j);
end
end
if stateSpace(i,2)<height
if map(stateSpace(i,1), stateSpace(i,2)+1) == TREE % cell n.2 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,2)>1
if map(stateSpace(i,1), stateSpace(i,2)-1) == TREE % cell n.6 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)>1
if map(stateSpace(i,1)-1, stateSpace(i,2)) == TREE % cell n.9 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
if stateSpace(i,1)<width
if map(stateSpace(i,1)+1, stateSpace(i,2)) == TREE % cell n.11 TREE
crash_prob = crash_prob + P_WIND/4;
end
else
crash_prob = crash_prob + P_WIND/4;
end
P(i,base_no_packIndex,5) = P(i,base_no_packIndex,5) + crash_prob;
%% ===== PICK UP STATE PROBABILITY =====
if pack == 0
P(i,pick_upIndex+1,:) = P(i,pick_upIndex,:);
P(i,pick_upIndex,:) = 0;
end
%% ===== DROP OFF STATE PROBABILITY =====
P(drop_offIndex,:,:) = 0;
P(drop_offIndex,drop_offIndex,:) = 1;
end
end
end