Tuto5_Motion_Planning/buildPRM.m

function [q1q2_valid, obstacles, connectionMap] = buildPRM(L1, L2, nbPoints)
%%%%%%%%%%%%%%%%%%
%function buildPRM(L1, L2, nbPoints)
% ex. buildPRM(2000, 1000, 10)
%
% Inputs:
%	-L1: length of the first link (in mm)
%	-L2: length of the second link (in mm)
%	-nbPoints: the number of valid points in the roadmap
%
% Outputs:
%	-q1q2_valid: valid joint configurations [q1, q2]
%	-obstacles: array of obstacle structures
%
% author: Guillaume Gibert, guillaume.gibert@ecam.fr
% date: 22/11/2023
%%%%%%%%%%%%%%%%%%

% Initialize variables
q1q2_valid = [];
q1q2_2d = [];
counter = 0;
inner = L1 - L2;

% Define circular obstacles with placeholder values for rectangle fields
circleObstacle1 = struct('type', 'circle', 'center', [1500; 500], 'radius', 400, 'corner', [0; 0], 'width', 0, 'height', 0);
circleObstacle2 = struct('type', 'circle', 'center', [2000; -800], 'radius', 500, 'corner', [0; 0], 'width', 0, 'height', 0);
circleObstacle3 = struct('type', 'circle', 'center', [0; 0], 'radius', inner, 'corner', [0; 0], 'width', 0, 'height', 0);

% Define rectangular obstacles with placeholder values for circle fields
rectObstacle1 = struct('type', 'rectangle', 'corner', [-2000; -2000], 'width', 600, 'height', 1000, 'center', [0; 0], 'radius', 0);
rectObstacle2 = struct('type', 'rectangle', 'corner', [-1000; 1000], 'width', 2000, 'height', 2000, 'center', [0; 0], 'radius', 0);

% Combine all obstacles into an array
obstacles = [circleObstacle1, circleObstacle2, circleObstacle3, rectObstacle1, rectObstacle2];

% creates a figure
figure;

while (size(q1q2_valid, 2) < nbPoints)
    % Sample random points within the workspace boundaries
    q1 = rand() * 360.0;
    q2 = rand() * 360.0;

    % Check if the randomly sampled point is within the workspace and not in obstacles
    if (q1 >= 0 && q1 <= 360) && (q2 >= 0 && q2 <= 360)
        % creates the DH table
        theta = [q1; q2];
        d = [0; 0];
        a = [L1; L2];
        alpha = [0; 0];

        % computes the FK
        wTee = dh2ForwardKinematics(theta, d, a, alpha, 1);

        % determines the position of the end-effector
        position_ee = wTee(1:2, end);

        % Check if the end-effector is not hitting any obstacle
        eeHittingObstacle = 0;

        inAnyObstacle = false;
        for obs = obstacles
            if strcmp(obs.type, 'circle') && isPointInCircle(position_ee, obs.center, obs.radius)
                inAnyObstacle = true;
                break;
            elseif strcmp(obs.type, 'rectangle') && isPointInRectangle(position_ee, obs)
                inAnyObstacle = true;
                break;
            end
        end

        % Store these random values
        if (eeHittingObstacle == 0) && (inAnyObstacle == false)
            % Store and plot valid points
            q1q2_valid = [q1q2_valid theta];
            subplot(1, 2, 1);
            plot(q1, q2, '+g');
            hold on;
            subplot(1, 2, 2);
            plot(position_ee(1), position_ee(2), '+g');
            hold on;
        else
            % Plot invalid points
            subplot(1, 2, 1);
            plot(q1, q2, '*r');
            hold on;
            subplot(1, 2, 2);
            plot(position_ee(1), position_ee(2), '*r');
            hold on;
        end

        counter = counter + 1;
    end
end

% Display stats
fprintf("%d points were sorted to achieve %d valid points\n", counter, nbPoints);

% add limits, labels, and obstacles to the map
subplot(1, 2, 1);
xlim([0 360]);
ylim([0 360]);
xlabel('q1(deg)');
ylabel('q2(deg)');
title('Joint space');

subplot(1, 2, 2);
drawCircle(0, 0, L1 + L2);
drawCircle(0, 0, L1 - L2);
xlim([-(L1 + L2) (L1 + L2)]);
ylim([-(L1 + L2) (L1 + L2)]);
xlabel('x(mm)');
ylabel('y(mm)');
title('Cartesian space');
% creates a connection map
connectionMap = zeros(nbPoints, nbPoints);
% After generating q1q2_valid but before the plotting section
for i = 1:size(q1q2_valid, 2)
    for j = 1:size(q1q2_valid, 2)
        if i ~= j

            pos1 = dh2ForwardKinematics([q1q2_valid(1, i); q1q2_valid(2, i)], [0; 0], [L1; L2], [0; 0], 1)(1:2, end);
            pos2 = dh2ForwardKinematics([q1q2_valid(1, j); q1q2_valid(2, j)], [0; 0], [L1; L2], [0; 0], 1)(1:2, end);
            if ~isLineIntersectingObstacle(pos1, pos2, obstacles)
                connectionMap(i, j) = 1;
            end
        end
    end
end

% Convert q1q2_valid into 2D Cartesian coordinates
for i = 1:size(q1q2_valid, 2)
    pos = dh2ForwardKinematics([q1q2_valid(1, i); q1q2_valid(2, i)], [0; 0], [L1; L2], [0; 0], 1)(1:2, end);
    q1q2_2d = [q1q2_2d, pos]; % Append the 2D position
end

% Plotting connections between valid points
for i = 1:size(q1q2_valid, 2)
    for j = 1:size(q1q2_valid, 2)
        if connectionMap(i, j) == 1

            pos1 = dh2ForwardKinematics([q1q2_valid(1, i); q1q2_valid(2, i)], [0; 0], [L1; L2], [0; 0], 1)(1:2, end);
            pos2 = dh2ForwardKinematics([q1q2_valid(1, j); q1q2_valid(2, j)], [0; 0], [L1; L2], [0; 0], 1)(1:2, end);
            plot([pos1(1), pos2(1)], [pos1(2), pos2(2)], 'g'); % Plot connections
            hold on;
        end
    end
end




% Plotting in Joint Space
subplot(1,2,1);
plot(q1q2_valid(1,:), q1q2_valid(2,:), 'go'); % Plot valid points in green
xlabel('q1 (deg)');
ylabel('q2 (deg)');
title('Joint Space');

% Plotting in Cartesian Space
subplot(1,2,2);

% Plotting obstacles
for i = 1:length(obstacles)
    obstacle = obstacles(i);
    if strcmp(obstacle.type, 'circle')
        % Draw circle obstacle
        drawCircle(obstacle.center(1), obstacle.center(2), obstacle.radius);
    elseif strcmp(obstacle.type, 'rectangle')
        % Draw rectangular obstacle
        % Define the rectangle position using [x, y, width, height]
        rectPosition = [obstacle.corner(1), obstacle.corner(2), obstacle.width, obstacle.height];
        rectangle('Position', rectPosition, 'EdgeColor', 'r', 'LineWidth', 2);
    end
end



xlabel('X (mm)');
ylabel('Y (mm)');
title('Cartesian Space');

% Ensure all plots remain visible
hold off;
return;
end