├── .gitignore ├── testGroud ├── tracks.mat ├── LevenbergMarquardt.m └── GaussianError2lambda_2viewTest.m ├── functions ├── track2feat3D.m ├── epipolarConstraint.m ├── featureGeneration.m ├── getTrajectory.m ├── trajSettings.m ├── featureConstraint.m ├── slidingWindowManager.m ├── cameraSettings.m ├── trackingStep.m ├── world2pixelNnormal_verFunc.m └── drawFigures.m ├── SIM5_Visual_odometry_demo.m ├── trajectories ├── exampleData1.mat ├── exampleData2.mat └── exampleData3.mat ├── SIM4_WheelOdo_demo.m ├── SIM3_IMU_demo.m ├── SIM1_w2Dfeat_demo.m ├── SIM2_w3Dfeat_demo_verFunc.m ├── README.md ├── SIM6_Visual_inertial_odometry_demo.m └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | dumped/ 2 | trajectories/full* 3 | TODOLIST.md 4 | *.asv 5 | /*/*.asv 6 | -------------------------------------------------------------------------------- /testGroud/tracks.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/testGroud/tracks.mat -------------------------------------------------------------------------------- /functions/track2feat3D.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/functions/track2feat3D.m -------------------------------------------------------------------------------- /SIM5_Visual_odometry_demo.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/SIM5_Visual_odometry_demo.m -------------------------------------------------------------------------------- /testGroud/LevenbergMarquardt.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/testGroud/LevenbergMarquardt.m -------------------------------------------------------------------------------- /trajectories/exampleData1.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/trajectories/exampleData1.mat -------------------------------------------------------------------------------- /trajectories/exampleData2.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/trajectories/exampleData2.mat -------------------------------------------------------------------------------- /trajectories/exampleData3.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robot0321/visual_inertial_odometry_simualtion/HEAD/trajectories/exampleData3.mat -------------------------------------------------------------------------------- /functions/epipolarConstraint.m: -------------------------------------------------------------------------------- 1 | function d_list = epipolarConstraint(featGroup, robotParams, robotParamsPrev, cameraParams) 2 | % epipolar constraint (index k == b1 time / index i == b2 time) 3 | R_b1b2 = robotParamsPrev.Tbw(1:3,1:3) * robotParams.Tbw(1:3,1:3)'; % R_b1w * R_wb2 4 | dp_b1_b1b2 = robotParamsPrev.Tbw(1:3,4) - R_b1b2 * robotParams.Tbw(1:3,4); % Pb1_b1w - Rb1b2 * Pb2_b2w 5 | R = cameraParams.Tcb(1:3,1:3) * R_b1b2 * cameraParams.Tcb(1:3,1:3)'; % Rc1c2 = Rc1b1 * Rb1b2 * Rb2c2 6 | dp = cameraParams.Tcb(1:3,4) + cameraParams.Tcb(1:3,1:3)*dp_b1_b1b2 + (-R*cameraParams.Tcb(1:3,4)); 7 | dp = dp/norm(dp); 8 | d_list = []; 9 | for j=1:length(featGroup.feat_prevTrckNormal) 10 | % epipolar constraint 11 | dpx = [0, -dp(3), dp(2); dp(3), 0, -dp(1); -dp(2), dp(1), 0]; 12 | d_list = [d_list; featGroup.feat_prevTrckNormal(:,j)'* dpx * R * featGroup.feat_currTrckNormal(:,j)]; 13 | % d_list = [d_list; dot(-cross(feat_prevTrckNormal(:,j), R*feat_currTrckNormal(:,j)), dp)]; 14 | end 15 | end -------------------------------------------------------------------------------- /functions/featureGeneration.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Generate random feature near the trajectory 4 | % 2. Select Approximately Uniformly distributed features, and the exact number of features 5 | % 6 | % INPUT : Trajectory described in world frame and feature generation parameters 7 | % OUTPUT : Feature position in world frame 8 | % FUNCTION: Making random feature position near the given trajectory 9 | % 10 | % Tuning Parameter: NONE 11 | % 12 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 13 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 14 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 15 | 16 | 17 | function feat_position = featureGeneration(traj_world_wb, featGenParams) 18 | Nfeatures = featGenParams.Nfeatures; 19 | step = featGenParams.step; 20 | xyRange = featGenParams.xyRange; 21 | zRange = featGenParams.zRange; 22 | 23 | pathL = floor(length(traj_world_wb)/step); 24 | NfeatPerL = ceil(Nfeatures/pathL); 25 | feat_position = []; 26 | for i = 1:pathL 27 | feat_position = [feat_position, traj_world_wb(:,step*(i-1)+1) + [(rand(2,NfeatPerL)-0.5)*xyRange; (rand(1,NfeatPerL)-0.5)*zRange]]; 28 | end 29 | selectIdx = randperm(length(feat_position), Nfeatures); 30 | feat_position = feat_position(:,sort(selectIdx)); 31 | end 32 | -------------------------------------------------------------------------------- /functions/getTrajectory.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Load dataset from mat files 4 | % 2. make T^b_w and t^w_wb with frame tranformation 5 | % 6 | % INPUT : the path of mat file 7 | % OUTPUT : Transformation form world to body (T^b_w) and Translation from world to body in world view (t^w_wb) 8 | % FUNCTION: Load a dataset and make transformation matrix 9 | % 10 | % Tuning Parameter: NONE 11 | % 12 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 13 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 14 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 15 | 16 | function [Tbw, tw_wb] = getTrajectory(dataPath) 17 | load(dataPath, 'dataset'); 18 | tw_wb = dataset.Pw_wb; 19 | if isfield(dataset, 'attitude') 20 | if isfield(dataset.attitude, 'quat'), Rwb = quat2rotm(dataset.attitude.quat); 21 | elseif isfield(dataset.attitude, 'dcm'), Rwb = dataset.attitude.dcm; 22 | elseif isfield(dataset.attitude, 'euler'), Rwb = eul2rotm(dataset.attitude.euler); 23 | else, error('no proper attitude option'); 24 | end 25 | elseif isfield(dataset, 'heading') 26 | heading = pi/180*dataset.heading; % yaw (rad) 27 | pitch = zeros(size(heading)); 28 | roll = pi*ones(size(heading)); 29 | Rwb = angle2dcm(heading, pitch, roll); % dcm rotation matrix 30 | end 31 | tb_bw = zeros(3,1,size(tw_wb,2)); 32 | for i=1:size(tw_wb,2) 33 | tb_bw(:,1,i) = -Rwb(:,:,i)'*tw_wb(:,i); 34 | end 35 | Tbw = [permute(Rwb,[2,1,3]), tb_bw; zeros(1,3,length(tw_wb)),ones(1,1,length(tw_wb))]; % T^b_w 36 | end -------------------------------------------------------------------------------- /functions/trajSettings.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Organizing the parameters for each trajectory 4 | % 2. exampleDataX.mat file is located in ./trajectories 5 | % 3. featGenParams and distRange are set considering 6 | % trajectory scale, body speed, density of features, etc. 7 | % 8 | % INPUT : selected trajectory type (during 'traj1', 'traj2', 'traj3') 9 | % OUTPUT : structure with trajtype, fileName, featGenParams, distRange 10 | % FUNCTION: setting the trajectory options as a function form 11 | 12 | % 13 | % Tuning Parameter: featGenParams, distRange 14 | % 15 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 16 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 17 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 18 | 19 | function pathParams = trajSettings(trajtype) 20 | switch(trajtype) 21 | case 'traj1' 22 | fileName = 'exampleData1.mat'; 23 | featGenParams = struct('Nfeatures',700,'step',5,'xyRange',100,'zRange',30); 24 | distRange = struct('mindist',2, 'maxdist',40); 25 | case 'traj2' 26 | fileName = 'exampleData2.mat'; 27 | featGenParams = struct('Nfeatures',1000,'step',5,'xyRange',150,'zRange',60); 28 | distRange = struct('mindist',3, 'maxdist',150); 29 | case 'traj3' 30 | fileName = 'exampleData3.mat'; 31 | featGenParams = struct('Nfeatures',500,'step',5,'xyRange',50,'zRange',20); 32 | distRange = struct('mindist',1, 'maxdist',60); 33 | otherwise 34 | error('not a proper option!!!') 35 | end 36 | pathParams = struct('pathName',trajtype,'fileName',fileName,'featGenParams',featGenParams,'distRange',distRange); 37 | end -------------------------------------------------------------------------------- /SIM4_WheelOdo_demo.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Wheel Odometry with no slip 4 | % 2. 5 | % 3. 6 | % 7 | % Copyright ? 2011 JaeYoung Chung (robot0321@github) All Rights Reserved 8 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 9 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 10 | clc; clear; close all; 11 | rng(10); 12 | addpath('./functions'); 13 | 14 | %% environment setting 15 | Nfeatures = 500; % the number of features 16 | % x,y: 'Nfeatures' number of features, in range (-50,100) 17 | feat_position = [rand(2,Nfeatures)*100 - 25; rand(1,Nfeatures)*30-15]; 18 | 19 | %% path setting 20 | fwd_speed = 2; % speed along the forward direction 21 | rot_time = 10; % steps needs to be rotated 22 | 23 | % body position and attitude in world view 24 | tw_wb = [0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(0:fwd_speed:50)), 50*ones(1,rot_time), 50:-fwd_speed:0, 0*ones(1,rot_time), zeros(size(50:-fwd_speed:0)); 25 | zeros(size(0:fwd_speed:50)), 0*ones(1,rot_time), 0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(50:-fwd_speed:0)), 50*ones(1,rot_time), 50:-fwd_speed:0; 26 | zeros(1, size(0:fwd_speed:50,2)+size(0:fwd_speed:50,2)+size(50:-fwd_speed:0,2)+size(50:-fwd_speed:0,2)+ rot_time*3)]; 27 | heading = pi/180*[zeros(size(0:fwd_speed:50)), linspace(0,90,rot_time), 90*ones(size(0:fwd_speed:50)), ... 28 | linspace(90,180,rot_time), 180*ones(size(50:-fwd_speed:0)),linspace(180,270,rot_time), 270*ones(size(50:-fwd_speed:0))]; % yaw (rad) 29 | pitch = zeros(size(heading)); 30 | roll = pi*ones(size(heading)); 31 | Rbw = angle2dcm(heading, pitch, roll); % dcm rotation matrix 32 | 33 | % Transformation matrix world to body T^w_b 34 | tb_bw = zeros(3,1,size(tw_wb,2)); 35 | for i=1:size(tw_wb,2) 36 | tb_bw(:,1,i) = -Rbw(:,:,i)*tw_wb(:,i); 37 | end 38 | Tbw = [Rbw, tb_bw; zeros(1,3,size(tw_wb,2)),ones(1,1,size(tw_wb,2))]; % T^b_w 39 | 40 | %% Wheel odometry with error model 41 | 42 | 43 | %% driving robot 44 | 45 | -------------------------------------------------------------------------------- /testGroud/GaussianError2lambda_2viewTest.m: -------------------------------------------------------------------------------- 1 | clear; close all; clc; 2 | addpath('../functions/'); 3 | 4 | %% 5 | NN = 300; 6 | feat_position = [ones(2,NN); [(1:10)*0.1+1,(1:NN-10)+2]]; 7 | Tbw = zeros(4,4,2); 8 | R = eye(3,3); 9 | Tbw(:,:,1) = [R,zeros(3,1);zeros(1,3),1]; 10 | Tbw(:,:,2) = [R,[0;0;-1];zeros(1,3),1]; 11 | 12 | robotParams1 = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,1)); 13 | robotParams2 = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,2)); 14 | cameraParams = cameraSettings(struct('mindist',1, 'maxdist',100), {}); 15 | cameraParams.Tcb(1:3,1:3) = eye(3,3); 16 | 17 | 18 | [feat1_TrckPixel, feat1_TrckNormal] = world2pixelNnormal_verFunc(1:size(feat_position,2), robotParams1, cameraParams); 19 | [feat2_TrckPixel, feat2_TrckNormal] = world2pixelNnormal_verFunc(1:size(feat_position,2), robotParams2, cameraParams); 20 | %% 21 | varlist = []; meanlist = []; 22 | for j=1:size(feat_position,2) 23 | N = 500; 24 | selectFeat = j; %1~10 25 | errorlevel = 1e-3; 26 | w = [1;1]*errorlevel; 27 | 28 | fr3List = []; 29 | for ii=1:N 30 | pts1 = feat1_TrckPixel(:,selectFeat) + w.*randn(2,1); 31 | pts2 = feat2_TrckPixel(:,selectFeat) + w.*randn(2,1); 32 | f_reprod3 = triangulateTwoView(Tbw(:,:,1)/Tbw(:,:,2), cameraParams.K, [pts1, pts2]); 33 | fr3List = [fr3List, f_reprod3]; 34 | end 35 | 36 | % scatter3(fr3List(1,:), fr3List(2,:), fr3List(3,:)); 37 | 38 | pca1 = pca(fr3List'); 39 | pcos = fr3List'*pca1(:,1)./vecnorm(fr3List)'; 40 | projpca = vecnorm(fr3List)'.*pcos; 41 | meanlist = [meanlist, mean(projpca)]; 42 | varlist = [varlist, var(projpca)]; 43 | % figure(2); histogram(projpca,91); hold on; 44 | end 45 | % legend();title(['triangulation2view with Gaussian noise ',num2str(errorlevel)]); 46 | %% 47 | function f_c1 = triangulateTwoView(T12, K, pts) 48 | C12 = T12(1:3,1:3); t12_1 = T12(1:3,4); 49 | obser = K\[pts; ones(1,2)]; % 1st person coordinate 50 | v_1 = obser(:,1); v_1 = v_1/norm(v_1); 51 | v_2 = obser(:,end); v_2 = v_2/norm(v_2); 52 | A = [v_1 -C12*v_2]; b = t12_1; 53 | lambda = A\b; 54 | f_c1 = lambda(1)*v_1; 55 | end -------------------------------------------------------------------------------- /functions/featureConstraint.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Screening the valid index from user-selected constraint 4 | % 5 | % INPUT : User selected constraint-type ('distance', 'heading', 'pixelRange', robotParams, cameraParams) 6 | % OUTPUT : World Index which fits to the constraint 7 | % FUNCTION: Getting the valid (world) index from user-selected contraint 8 | % 9 | % Tuning Parameter: NONE 10 | % 11 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 12 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 13 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 14 | 15 | function world_valid_index = featureConstraint(featConstType, robotParams, cameraParams) 16 | world_valid_index = ones(1, size(robotParams.feat_position,2)); % the number of features 17 | currpos = - robotParams.Tbw(1:3,1:3)'*robotParams.Tbw(1:3,4); 18 | for i=1:length(featConstType) 19 | switch(featConstType{i}) 20 | case('distance') 21 | % Distance Constraint 22 | feat_dist = sqrt(sum((robotParams.feat_position - currpos).^2, 1)); 23 | feat_dist_validx = feat_dist>cameraParams.mindist & feat_dist0; % camera attitude constraint 29 | world_valid_index = world_valid_index & feat_cam_validx; 30 | case('pixelRange') 31 | % Camera Intrinsic Matrix & Pixel Range Constraint 32 | [feat_pixel,~] = world2pixelNnormal_verFunc(1:size(robotParams.feat_position,2), robotParams, cameraParams); 33 | feat_pixel_validx = feat_pixel(1,:)>0 & feat_pixel(1,:)0 & feat_pixel(2,:) 3 | % 1. Managing sliding windows named LiveTracks & DeadTracks 4 | % 2. In real application, world_idx in each tracks are not available 5 | % 3. DeadTrack saves (current) untrakced tracks temporarily 6 | % 7 | % INPUT : previous LiveTracks, currStep (index), RS_valid_index, featGroup, trajParams 8 | % OUTPUT : current LiveTracks & DeadTracks 9 | % FUNCTION: stack the features on the LiveTracks and move some tracks which is untracked from LiveTrack to DeadTrack 10 | % 11 | % Tuning Parameter: NONE 12 | % 13 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 14 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 15 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 16 | 17 | function [LiveTracks, DeadTracks] = slidingWindowManager(LiveTracks, currStep, RS_valid_index, featGroup, trajParams) 18 | tempLiveTracks = cell(1,trajParams.featGenParams.Nfeatures); 19 | misTrackCount = 0; 20 | for trackNumber = 1:numel(RS_valid_index) 21 | tempLiveTracks{featGroup.feat_intrscCurrIdx(RS_valid_index(trackNumber))} = ... 22 | struct('world_idx', [LiveTracks{featGroup.feat_intrscPrevIdx(RS_valid_index(trackNumber))}.world_idx, featGroup.feat_intrscCurrIdx(RS_valid_index(trackNumber))], ... 23 | 'frame', [LiveTracks{featGroup.feat_intrscPrevIdx(RS_valid_index(trackNumber))}.frame, currStep], ... 24 | 'pts', [LiveTracks{featGroup.feat_intrscPrevIdx(RS_valid_index(trackNumber))}.pts, featGroup.feat_currTrckPixel(:,RS_valid_index(trackNumber))]); 25 | if(featGroup.feat_intrscCurrIdx(RS_valid_index(trackNumber)) ~= featGroup.feat_intrscPrevIdx(RS_valid_index(trackNumber))) 26 | misTrackCount = misTrackCount + 1; 27 | end 28 | end 29 | fprintf('misTracking: %d \n', misTrackCount); 30 | 31 | % Stacking newTracks on the LiveTracks 32 | for trackNumber = 1:numel(featGroup.feat_currNewValidx) 33 | tempLiveTracks{featGroup.feat_currNewValidx(trackNumber)} = ... 34 | struct('world_idx', featGroup.feat_currNewValidx(trackNumber), ... 35 | 'frame', currStep, ... 36 | 'pts', featGroup.feat_currNewPixel(:,trackNumber)); 37 | end 38 | 39 | % Moving ended tracks from LiveTracks to DeadTracks 40 | DeadTracks = cell(1,trajParams.featGenParams.Nfeatures); 41 | for trackNumber = 1:numel(featGroup.feat_prevDeadValidx) 42 | DeadTracks{featGroup.feat_prevDeadValidx(trackNumber)} = LiveTracks{featGroup.feat_prevDeadValidx(trackNumber)}; 43 | end 44 | 45 | LiveTracks = tempLiveTracks; 46 | end -------------------------------------------------------------------------------- /SIM3_IMU_demo.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Path generator with checkpoints 4 | % 2. Inverse INS (From world path & att To inertial data with gravity) 5 | % 3. INS (From inertial data To world path & att) with IMU error model 6 | % 7 | % Copyright ? 2011 JaeYoung Chung (robot0321@github) All Rights Reserved 8 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 9 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 10 | clc; clear; close all; 11 | rng(10); 12 | addpath('./functions'); 13 | 14 | %% environment setting 15 | Nfeatures = 500; % the number of features 16 | % x,y: 'Nfeatures' number of features, in range (-50,100) 17 | feat_position = [rand(2,Nfeatures)*100 - 25; rand(1,Nfeatures)*30-15]; 18 | 19 | %% path setting 20 | fwd_speed = 2; % speed along the forward direction 21 | rot_time = 10; % steps needs to be rotated 22 | 23 | % body position and attitude in world view 24 | tw_wb = [0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(0:fwd_speed:50)), 50*ones(1,rot_time), 50:-fwd_speed:0, 0*ones(1,rot_time), zeros(size(50:-fwd_speed:0)); 25 | zeros(size(0:fwd_speed:50)), 0*ones(1,rot_time), 0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(50:-fwd_speed:0)), 50*ones(1,rot_time), 50:-fwd_speed:0; 26 | zeros(1, size(0:fwd_speed:50,2)+size(0:fwd_speed:50,2)+size(50:-fwd_speed:0,2)+size(50:-fwd_speed:0,2)+ rot_time*3)]; 27 | heading = pi/180*[zeros(size(0:fwd_speed:50)), linspace(0,90,rot_time), 90*ones(size(0:fwd_speed:50)), ... 28 | linspace(90,180,rot_time), 180*ones(size(50:-fwd_speed:0)),linspace(180,270,rot_time), 270*ones(size(50:-fwd_speed:0))]; % yaw (rad) 29 | pitch = zeros(size(heading)); 30 | roll = pi*ones(size(heading)); 31 | Rbw = angle2dcm(heading, pitch, roll); % dcm rotation matrix 32 | 33 | % Transformation matrix world to body T^w_b 34 | tb_bw = zeros(3,1,size(tw_wb,2)); 35 | for i=1:size(tw_wb,2) 36 | tb_bw(:,1,i) = -Rbw(:,:,i)*tw_wb(:,i); 37 | end 38 | Tbw = [Rbw, tb_bw; zeros(1,3,size(tw_wb,2)),ones(1,1,size(tw_wb,2))]; % T^b_w 39 | 40 | %% inverse INS (path2imu) in Local frame 41 | 42 | 43 | 44 | 45 | %% INS (imu2path) 46 | % Make IMU data from the checkpoints to the IMU error model 47 | % error model: 1. bias: (1)random constant bias, (2)random 1st-Markov bias 48 | % 2. scale factor : (1)identity (2)random constant diagonal 49 | % (3)random constant with skew (4) (slow)1st-Markov skew 50 | % (5)nonlinear 51 | % 3. hysteresis 52 | % 4. frequency variance with time 53 | % 54 | % function out = IMU(checkpoints, imu_errModel) 55 | % path = path_generator(checkpoints); 56 | % true_6motion = inverseINS(path); % (acc3, gyro3) 57 | % real_6motion = IMUmodel(true_6motion, imu_errModel); 58 | % out = real_6motion; 59 | % end 60 | % 61 | 62 | 63 | %% driving robot 64 | 65 | -------------------------------------------------------------------------------- /SIM1_w2Dfeat_demo.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % In 2-D, Features with angle and distance constraint 4 | % 5 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 6 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 7 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 8 | clc; clear; close all; 9 | rng(10); 10 | addpath('./functions'); 11 | 12 | dual_left_monitor = 1; 13 | if(dual_left_monitor) 14 | figure(1); set(gcf,'Position',[-1700 50 1300 400]); % This is my workspace setting. 15 | else 16 | figure(1); set(gcf,'Position',[100 50 1300 900]); % ... usually this option is proper OR set as you wish 17 | end 18 | 19 | %% environment setting 20 | Nfeatures = 500; % the number of features 21 | % x,y: 'Nfeatures' number of features, in range (-50,100) 22 | feat_position = rand(2,Nfeatures)*100 - 25; 23 | 24 | % Trajectory setting 25 | fwd_speed = 2; % speed along the forward direction 26 | rot_time = 10; % steps needs to be rotated 27 | 28 | % posisiton and heading of robot, heading is the angle from world-x axis 29 | traj = [0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(0:fwd_speed:50)), 50*ones(1,rot_time), 50:-fwd_speed:0, 0*ones(1,rot_time), zeros(size(50:-fwd_speed:0)); 30 | zeros(size(0:fwd_speed:50)), 0*ones(1,rot_time), 0:fwd_speed:50, 50*ones(1,rot_time), 50*ones(size(50:-fwd_speed:0)), 50*ones(1,rot_time), 50:-fwd_speed:0]; 31 | heading = pi/180*[zeros(size(0:fwd_speed:50)), linspace(0,90,rot_time), 90*ones(size(0:fwd_speed:50)), ... 32 | linspace(90,180,rot_time), 180*ones(size(50:-fwd_speed:0)),linspace(180,270,rot_time), 270*ones(size(50:-fwd_speed:0))]; % yaw (rad) 33 | robot = [traj; heading]; 34 | 35 | %% camera setting 36 | theta = 45*pi/180; % angle between principal axis and the edge of the image plane (arbitarilliy selected) 37 | mindist = 2; % minimum distance from a feature to camera principal point 38 | maxdist = 20; % maximum distance " 39 | 40 | %% driving robot 41 | for i=1:length(robot) 42 | % Select constrainted features 43 | currpos = robot(1:2,i); 44 | currhead = robot(3,i); 45 | 46 | % the angle from the principal axis of camera to a line between a feature and camera 47 | feat_angle = atan2(feat_position(2,:)-currpos(2), feat_position(1,:)-currpos(1)) - currhead; 48 | % compensation due to the uncontinuity of angle from atan2 (-pi ~ pi) 49 | feat_angle(feat_angle<-pi) = feat_angle(feat_angle<-pi) + 2*pi; 50 | feat_angle(feat_angle>pi) = feat_angle(feat_angle>pi) - 2*pi; 51 | 52 | % distance constraint 53 | feat_dist = sqrt(sum((feat_position - currpos).^2, 1)); 54 | 55 | % select features with angle and distance constraint 56 | feat_inview_idx = (feat_angle-theta & ... 57 | feat_dist>mindist & feat_dist 3 | % 1. Set the camera parameters (Tcb, focal length, principle point, pixel range, intrinsic matrix) 4 | % 2. Set error parameters (pixel err, distortion, mistracking) including whether use or not 5 | % 6 | % INPUT : distRange(which includes mindist and maxdist) to set in the cameraParams 7 | % OUTPUT : cameraParams including errorParams 8 | % FUNCTION: Set the camera in/extrinsic parameters and error parameters 9 | % 10 | % Tuning Parameter: all the parameters 11 | % 1) camera parameters (Tcb, fx, fy, cx, cy, px, py, K) 12 | % 2) error parameters (isCamPixelError, PixelErr, 13 | % isDistorted, distCoeff, distortOrder, errorFactor 14 | % isMistracked, misTrackingRatio) 15 | % 16 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 17 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 18 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 19 | 20 | function cameraParams = cameraSettings(distRange, errorSetting) 21 | if nargin==1 22 | errorSetting = {}; 23 | end 24 | %% Camera Setting Parameters 25 | Tcb = [angle2dcm(pi/2, 0,pi/2), -[0;0;1e-3]; zeros(1,3), 1]; % T^c_b, extrinsic 26 | % -> the origin of camera frame is at the (x = 1e-3m, y = 0, z = 0) in body frame 27 | fx = 1298.248; fy = 1305.601; % focal_length 28 | cx = 591.385; cy = 417.372; % principle point 29 | px = 1280; py = 800; % 1280 x 800 (option) 30 | K = [fx/2, 0, cx; 31 | 0, fy/2, cy; 32 | 0, 0, 1]; % intrinsic matrix 33 | 34 | %% Camera Image Errors 35 | errorParams = struct(); % Collecting error Parameters 36 | 37 | % noise on camera plane (pixel noise) about 0.1 ~ 2 38 | isCamPixelError = false; 39 | PixelErr = 1; 40 | pixelErrParams = struct('isCamPixelError',isCamPixelError,'PixelErr',PixelErr); 41 | errorParams.pixelErrParams = pixelErrParams; 42 | 43 | % Whether applying undistortion error//distCoeff: 44 | % distortion error is applied at world2pixel() function 45 | isDistorted = false; 46 | distCoeff = [-0.535910, 0.366895, -0.003531, 0.007271, 0]; % example [k1, k2, p1, p2, k3] 47 | distortOrder = [4, 4]; % the order of distortion/undistortion(with error) 48 | errorFactor = [0.1, 0.072, 0.0007, 0.0014]; % at undistortion 49 | distortParams = struct('isDistorted', isDistorted, 'distCoeff', distCoeff, ... 50 | 'distortOrder', distortOrder, 'errorFactor',errorFactor); 51 | errorParams.distortParams = distortParams; 52 | 53 | % Mistracking ratio during tracking (like KLT mistracking) 54 | isMistracked = false; 55 | misTrackingRatio = 0.05; 56 | misTrackParams = struct('isMistracked',isMistracked,'mistrackingRatio',misTrackingRatio); 57 | errorParams.misTrackParams = misTrackParams; 58 | 59 | for idx=1:length(errorSetting) 60 | switch(errorSetting{idx}) 61 | case 'pixelErr' 62 | errorParams.pixelErrParams.isCamPixelError = true; 63 | case 'distortion' 64 | errorParams.distortParams.isDistorted = true; 65 | case 'mistrack' 66 | errorParams.misTrackParams.isMistracked = true; 67 | end 68 | end 69 | 70 | % Organizing total camera parameters 71 | cameraParams = struct('Tcb',Tcb,'fLx',fx,'fLy',fy,'cx',cx, 'cy',cy,'px',px,'py',py, ... 72 | 'mindist',distRange.mindist,'maxdist',distRange.maxdist, 'K',K, 'errorParams', errorParams); 73 | end -------------------------------------------------------------------------------- /SIM2_w3Dfeat_demo_verFunc.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % *** If you use single monitor, set 'dual_left_monitor' to 0 *** 4 | % 1. world, body, camera frame - 3D position, attitude are applied 5 | % 2. Features with Distance, Attitude, Intrinsic Matrix Constraint 6 | % 3. Visualization in 3D dimension and projected camera view 7 | % 4. ideal case - without any distortion, pixel error, etc 8 | % 9 | % world frame (normal x,y,z), body frame (forward-x, right-y, down-z), 10 | % camera frame(forward-z, right-x, down-y) 11 | % intrinsic matrix (K), extrinsic matrix (Tcb) applied 12 | % To make it ideal, check Variable 'isCamPixelError' and 'isDistorted' 13 | % 14 | % External functions: world2pixel.m 15 | % Tuning Parameter: min/maxdist, PixelErr, DistanceThreshold(fundamental matrix), 16 | % distCoeff(& error), misTrackingRatio 17 | % 18 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 19 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 20 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 21 | clc; clear; close all; 22 | rng(10); 23 | addpath('./functions'); 24 | addpath('./trajectories'); 25 | 26 | dual_left_monitor = 1; 27 | if(dual_left_monitor) 28 | figure(1); set(gcf,'Position',[-1700 50 1300 900]); % This is my workspace setting. 29 | else 30 | figure(1); set(gcf,'Position',[100 50 1300 900]); % ... usually this option is proper OR set as you wish 31 | end 32 | 33 | %% environment setting 34 | % Trajectory LIST --> select among 'traj1', 'traj2', 'traj3' 35 | trajtype = 'traj2'; 36 | % Get the trajectory parameters from its type. 37 | trajParams = trajSettings(trajtype); % Set the proper options fitted with the selected trajectory 38 | 39 | % Getting ready-made trajectories from exampleDataX.mat file 40 | [Tbw, traj_world_wb] = getTrajectory(trajParams.fileName); 41 | 42 | % Generating features along the trajectory 43 | feat_position = featureGeneration(traj_world_wb, trajParams.featGenParams); 44 | 45 | %% camera setting 46 | % camera parameter setting, 47 | cameraParams = cameraSettings(trajParams.distRange); 48 | 49 | % Distance Threshold in finding the 8-point RANSAC 50 | estFundaThreshold = 0.2; 51 | 52 | % Feature Tracks 53 | LiveTracks = {}; 54 | DeadTracks = {}; 55 | 56 | %% driving robot 57 | startIdx = 1; featGroup=struct(); 58 | for currStep=startIdx:size(Tbw,3) 59 | % Index saving for optical flow 60 | prevStep=currStep-1; 61 | if(currStep==startIdx), featGroup.feat_prevValidx = []; prevStep=currStep; end 62 | robotParams = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,currStep)); 63 | robotParamsPrev = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,prevStep)); 64 | 65 | %% Feature Tracking & Optical Flow 66 | featGroup = trackingStep(featGroup, robotParamsPrev, robotParams, cameraParams); 67 | 68 | %% data consistency check 69 | % Fundamental Matrix with RANSAC 70 | if (size(featGroup.feat_prevTrckPixel,2) >= 8) 71 | [~, RSvalid_logic] = estimateFundamentalMatrix(featGroup.feat_prevTrckPixel(1:2,:)', featGroup.feat_currTrckPixel(1:2,:)',... 72 | 'Method', 'RANSAC', 'DistanceThreshold', estFundaThreshold); 73 | else, RSvalid_logic = ones(1,size(featGroup.feat_currTrckPixel,2)); 74 | end 75 | 76 | % Testing Inlier Ratio 77 | sum(RSvalid_logic)/size(featGroup.feat_prevTrckPixel,2) 78 | 79 | % update index with the results of RANSAC 80 | featGroup.feat_prevDeadValidx = [featGroup.feat_prevDeadValidx, featGroup.feat_intrscPrevIdx(~RSvalid_logic)]; 81 | 82 | %% Managing feature tracks 83 | % Stacking existed Tracks with new features on the LiveTracks 84 | RS_valid_index = find(RSvalid_logic); 85 | [LiveTracks, DeadTracks] = slidingWindowManager(LiveTracks, currStep, RS_valid_index, featGroup, trajParams); 86 | 87 | TrackParams = struct(); TrackParams.LiveTracks = LiveTracks; TrackParams.DeadTracks = DeadTracks; 88 | %% draw figures 89 | drawFigures(traj_world_wb, feat_position, currStep, RSvalid_logic, TrackParams, featGroup, cameraParams, []) 90 | 91 | %% For next step 92 | featGroup.feat_prevValidx = sort([featGroup.feat_intrscCurrIdx(RS_valid_index), featGroup.feat_currNewValidx]); 93 | end 94 | -------------------------------------------------------------------------------- /functions/trackingStep.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. From previous features, get the (new) current features 4 | % 2. To use in consistency check, slidingWindowManager, etc., save the results in featGroup with various form 5 | % 3. In real application, tracking will be done with other methods like KLT etc. 6 | % 7 | % INPUT : featGroup.feat_prevValidx, (previous/current)robotParams, cameraParams 8 | % OUTPUT : featGroup (including 'feat_intrscPrevIdx','feat_prevTrckPixel','feat_intrscCurrIdx','feat_currTrckPixel' 9 | % 'feat_currNewValidx','feat_currNewPixel','feat_prevDeadValidx','feat_intrsectValidx','feat_world_validx') 10 | % FUNCTION: Getting featGroup from the previous feature and robotParams 11 | % 12 | % Tuning Parameter: NONE 13 | % 14 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 15 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 16 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 17 | 18 | function featGroup = trackingStep(featGroup, robotParamsPrev, robotParams, cameraParams) 19 | % Feature Constraints in Current Step 20 | feat_world_validx = featureConstraint({'distance','heading','pixelRange'}, robotParams, cameraParams); 21 | feat_currValidx = feat_world_validx; 22 | 23 | % build Tracks of tracked (exist on both prev&curr) features 24 | feat_prevDeadValidx = setdiff(featGroup.feat_prevValidx, feat_currValidx); 25 | feat_currNewValidx = setdiff(feat_currValidx, featGroup.feat_prevValidx); % new features 26 | feat_intrsectValidx = intersect(feat_currValidx, featGroup.feat_prevValidx); % features which are tracked 27 | feat_intrscPrevIdx = feat_intrsectValidx; 28 | feat_intrscCurrIdx = feat_intrsectValidx; 29 | 30 | % mistracked (mismatched ?) feature 31 | % for the continuous tracking, mistracking is done on the existed feature, not ramdomly made feature. 32 | if(cameraParams.errorParams.misTrackParams.isMistracked && ~isempty(feat_intrsectValidx)) 33 | numMistrackedFeat = round(length(feat_intrsectValidx) * cameraParams.errorParams.misTrackParams.mistrackingRatio); 34 | mistrackIdx = randperm(length(feat_intrsectValidx), numMistrackedFeat); 35 | newCandidate = [feat_intrsectValidx(mistrackIdx), feat_currNewValidx]; 36 | newCandidIdx = randperm(length(newCandidate), numMistrackedFeat); % select from misTrack + newCurr 37 | feat_intrscCurrIdx(mistrackIdx) = newCandidate(newCandidIdx); 38 | [~, currMistrackIdx,~] = intersect(feat_currNewValidx, newCandidate(newCandidIdx)); 39 | if(~isempty(currMistrackIdx)) 40 | feat_currNewValidx(currMistrackIdx) = []; 41 | end 42 | end 43 | 44 | % Features on Camera Plane 45 | [feat_prevTrckPixel, feat_prevTrckNormal] = world2pixelNnormal_verFunc(feat_intrscPrevIdx, robotParamsPrev, cameraParams); % intersectValidx = featGroup.feat_prevValidx(:, feat_intrscPrevIdx) 46 | [feat_currTrckPixel, feat_currTrckNormal] = world2pixelNnormal_verFunc(feat_intrscCurrIdx, robotParams, cameraParams); % intersectValidx = feat_currValidx(:, feat_intrscCurrIdx) 47 | [feat_currNewPixel,~] = world2pixelNnormal_verFunc(feat_currNewValidx, robotParams, cameraParams); 48 | % caution: not-tracked previous features are not drew (because not interested) 49 | 50 | % Adding Pixel Error if needed 51 | if(cameraParams.errorParams.pixelErrParams.isCamPixelError) 52 | currNewPixelErr = cameraParams.errorParams.pixelErrParams.PixelErr * randn(size(feat_currNewPixel)); 53 | currTrckPixelErr = cameraParams.errorParams.pixelErrParams.PixelErr * randn(size(feat_currTrckPixel)); 54 | feat_currNewPixel = feat_currNewPixel + currNewPixelErr; 55 | feat_currTrckPixel = feat_currTrckPixel + currTrckPixelErr; 56 | end 57 | 58 | featGroup = struct('feat_intrscPrevIdx',feat_intrscPrevIdx, 'feat_prevTrckPixel', feat_prevTrckPixel, ... 59 | 'feat_intrscCurrIdx',feat_intrscCurrIdx, 'feat_currTrckPixel', feat_currTrckPixel, ... 60 | 'feat_currNewValidx',feat_currNewValidx, 'feat_currNewPixel', feat_currNewPixel, ... 61 | 'feat_prevDeadValidx',feat_prevDeadValidx, 'feat_intrsectValidx', feat_intrsectValidx, ... 62 | 'feat_world_validx', feat_world_validx, ... 63 | 'feat_prevTrckNormal',feat_prevTrckNormal, 'feat_currTrckNormal',feat_currTrckNormal); 64 | end -------------------------------------------------------------------------------- /functions/world2pixelNnormal_verFunc.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Calculating the coordinate of the feauture in world frame from the camera parameters and current robot(body) status 4 | % 2. Apply or not camera lens distortion as the setting of the cameraParams.errorParams.distortParams 5 | % 3. undistortion error is represented as the Gaussian form of distortParams.errorFactor 6 | % 4. undistortion is done iteratively 7 | % 8 | % INPUT : feature position in world frame, robotParams, cameraParams 9 | % OUTPUT : the coordiante in image plane [x_pu, y_pu] and the coordinate in the normalized camera frame [x_nu, y_nu, 1] 10 | % FUNCTION: Transfer the features from world frame to image plane and normalized camera frame 11 | % 12 | % Tuning Parameter: NONE 13 | % 14 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 15 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 16 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 17 | 18 | 19 | %% transformation from world frame to pixel frame 20 | % world frame --T^c_w--> camera frame --./Z--> normal camera frame --intrinsic K--> pixel frame 21 | % distortParams: struct('isDistorted', 'distCoeff', 'distortOrder','errorFactor'); 22 | % Assuming there is an error on estimating the distCoeff 23 | 24 | function [pixel2, normal] = world2pixelNnormal_verFunc(feat_world3_valid_idx, robotParams, cameraParams) 25 | % Transformation from world to camera with intrinsic matrix 26 | % features are arraged as 3xN matrix 27 | feat_world3 = robotParams.feat_position(:, feat_world3_valid_idx); 28 | if isempty(feat_world3) 29 | pixel2 = []; normal = []; return; 30 | end 31 | 32 | % Transformation from world frame to camera frame 33 | feat_camera4 = cameraParams.Tcb * robotParams.Tbw * [feat_world3; ones(1,size(feat_world3,2))]; 34 | 35 | % From camera frame to normalized camera frame 36 | % [Xc, Yc, Zc] -- /Zc --> [Xc/Zc, Yc/Zc, 1] = [x_nu, y_nu, 1] 37 | feat_normUndist = feat_camera4(1:3,:)./feat_camera4(3,:); 38 | 39 | 40 | % Error modeling due tothe lens 41 | distortParams = cameraParams.errorParams.distortParams; 42 | distCoeff_Dist = distortParams.distCoeff(1:distortParams.distortOrder(1)); % k1, k2, p1, p2, k3, k4, k5 43 | distCoeff_Undist = distortParams.distCoeff(1:distortParams.distortOrder(2)) ... % k1, k2, p1, p2 44 | + distortParams.errorFactor.*randn(1,distortParams.distortOrder(2)); % adding Gaussian estimation Error 45 | if(distortParams.isDistorted) % Distortion/Undistortion model 46 | % [x_nu, y_nu, 1] -- LensDistortion(5th order) --> [x_nd, y_nd, 1] 47 | feat_normDistort3 = LensDistortion(feat_normUndist, distCoeff_Dist); 48 | 49 | % [x_nd, y_nd, 1] -- undistort(2nd order) --> [x_nu2, y_nu2, 1] 50 | feat_normUndist2 = undistort(feat_normDistort3, distCoeff_Undist, 10); 51 | 52 | % From normalized camera frame to pixel frame 53 | % [x_nu2, y_nu2, 1] -- K* --> [x_pu, y_pu, 1] 54 | normal = feat_normUndist2; 55 | feat_pixel = cameraParams.K * feat_normUndist2; 56 | else 57 | % From normalized camera frame to pixel frame 58 | % [x_nu, y_nu, 1] -- K* --> [x_pu, y_pu, 1] 59 | normal = feat_normUndist; 60 | feat_pixel = cameraParams.K * feat_normUndist; 61 | end 62 | 63 | pixel2 = feat_pixel(1:2,:); 64 | end 65 | 66 | %% Lens distortion model & undistortion 67 | function feat_normDistort3 = LensDistortion(feat_normUndist3, distCoeff5) % 5th order modeling 68 | dc = zeros(1,10); dc(1:length(distCoeff5)) = distCoeff5; % k1~5, p1,2 69 | 70 | x_nu = feat_normUndist3(1,:); y_nu = feat_normUndist3(2,:); 71 | r2 = x_nu.^2 + y_nu.^2; 72 | xy_nd = (1 + ((((dc(7).*r2 + dc(6)).*r2 + dc(5)).*r2 + dc(2)).*r2+ dc(1)).*r2) .* [x_nu;y_nu] ... 73 | + [2*dc(3)*x_nu.*y_nu + dc(4)*(r2+2*x_nu.*x_nu); dc(3)*(r2+2*y_nu.*y_nu) + 2*dc(4)*x_nu.*y_nu]; 74 | feat_normDistort3 = [xy_nd; ones(1,size(xy_nd,2))]; 75 | end 76 | 77 | function feat_normUndistort3 = undistort(feat_normDistorted3, distCoeff, maxIter) %2nd order approximation 78 | Nframe= size(feat_normDistorted3,2); 79 | dc = zeros(1,10); dc(1:length(distCoeff)) = distCoeff; % k1~5, p1,2 80 | 81 | % undistorted points 82 | x= feat_normDistorted3(1,:); y = feat_normDistorted3(2,:); 83 | x0 = x; y0 = y; 84 | for i = 1:maxIter 85 | r2 = x.^2 + y.^2; 86 | icdist = 1./(1 + ((((dc(7).*r2 + dc(6)).*r2 + dc(5)).*r2 + dc(2)).*r2+ dc(1)).*r2); 87 | dx = 2*dc(3)*x.*y + dc(4)*(r2 + 2*x.*x); 88 | dy = dc(3) * (r2 + 2*y.*y) + 2*dc(4)*x.*y; 89 | x = (x0-dx).*icdist; y = (y0-dy).*icdist; 90 | end 91 | feat_normUndistort3 = [x; y; ones(1, Nframe)]; 92 | end -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | * **NOTE:** This README.md provides the guidelines in English and Korean (한국어 설명은 **아래에** 있습니다.) 2 | 3 | # (Mono) Visual { Inertial | Wheel } Odometry Simualtion 4 | MATLAB simulation of (Mono) visual-inertial odometry (VIO) & visual-wheel odometry 5 | 6 | These are MATLAB simulations of (Mono) Visual { Inertial | Wheel } Odometry 7 | These simulations provide the ideal case with **some noises** which can be turned off and on. 8 | 9 | * You can use this simulation as you wish with GNU 3.0 10 | * I checked all the demo files whether it can be runned without any amendation, but the MATLAB version can be critical 11 | * I made this simulations on MATLAB 2019a 12 | 13 | 14 | ## Code Description 15 | 16 | ### Caution: Before Using This Simulation 17 | #### Have to set the 'dual_left_monitor' variable to show figures on your monitor 18 | #### Have to select the simulation trajectory with 'trajtype' variable. 19 | 20 | (Each SIMx-files are in a group) 21 | 1. **SIM1_w2Dfeat_demo.m** 22 | > * SIM1 is a simple 2D simulation of camera. Using features with angle and distance constraint. 23 | 24 | 2. **SIM2_w3Dfeat_demo.m** 25 | > * SIM2 is a 3D simulation of camera with features and optical flow. 26 | > * SIM2 applies 3D position and attitude in world, body, camera frame. 27 | > * SIM2 selects features with distance, camera heading, intrinsic matrix constraint. 28 | > * SIM2 visualizes the **camera-robot in 3D** dimension and **projected camera view** 29 | > * SIM2 describes the **Ideal Case** with on-off camera error model (ex. distortion, pixel error, miss tracking) 30 | > * SIM2 saves the results of feature tracking and tracking failure (Variable: LiveTrack, DeadTrack)\ 31 | 32 | > * **...verSimple.m** is removed. 33 | 34 | 35 | 3. (*not yet*) **SIM3_IMU_demo.m** 36 | > * ~~SIM3 is a simulation of inverse INS(Traj2IMUdata), INS(IMUdata2Traj) and IMU error model~~ 37 | 4. (*not yet*) **SIM4_WheelOdo_demo.m** 38 | > * ~~SIM4 is a simulation of inverse WheelOdometry and WheelOdometry with error model~~ 39 | 5. (*not yet*) **SIM5_Visual_odometry_demo.m** 40 | > * ~~SIM5 is a simulation of visual odometry using the camera in SIM2 ~~ 41 | 42 | 6. (*Editing*) **SIM6_Visual_inertial_odometry_demo.m** 43 | > * SIM6 is a simulation of visual-inertial odometry using the camera in SIM2 and ~~IMU in SIM3~~ 44 | > * SIM6 visualize as same as SIM2 45 | > * SIM6 calculate epipoar constraint cost to with matched features 46 | > * SIM6 reproduce 3D feature position from recorded tracks 47 | 48 | ## To Do List 49 | #### Common 50 | - [ ] Trajectory Generation from waypoint or system dynamics 51 | - [x] Adding some trajectory examples 52 | #### SIM2 53 | - [x] Adding N-straking Tracks 54 | - [x] Adding misTracking Ratio 55 | - [ ] Adding noise transfer process 56 | - [ ] Amending the structure to the real situation. (as like just have camera images -> tracking) 57 | - [ ] Amending the notation of the Translation/Rotation/Transformation vectors/Matrixes in the variables. 58 | #### SIM6 59 | - [ ] SIM6 is a simulation of visual-inertial odometry using the camera in SIM2 and IMU in SIM3 60 | - [x] SIM6 visualize as same as SIM2 61 | - [x] SIM6 calculate epipoar constraint cost to with matched features 62 | - [x] SIM6 reproduce 3D feature position from recorded tracks 63 | 64 | ## Liscence 65 | GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 66 | 67 | ***** 68 | ###(In Korean) 69 | # (모노)비주얼/관성/휠 오도메트리 시뮬레이션 70 | 71 | ## 내용 설명 (Guidelines in Korean) 72 | * (모노) 비주얼 { 관성 | 휠 } 오도메트리에 대한 매트랩 시뮬레이션 입니다. 73 | * 노이즈가 없는 이상적인 케이스가 제공되며, 노이즈는 필요에 따라 사용하거나 사용하지 않도록 설정할 수 있습니다. 74 | * 라이센스는 GNU 버전3를 따릅니다. 이는 자유롭게 사용하되, 같은 라이센스(GNUv3)를 명시하고 그 결과물을 공유해야 한다는 것을 의미합니다. 75 | * 모든 시뮬레이션 파일은 수정없이 바로 동작 가능하도록 체크하고 올립니다만, 문제가 있을 경우 말씀해주세요. 76 | * 혹시 작동이 되지 않는다면, 버전 문제일 수 있습니다. 본 코드는 매트랩2019a에서 작성되었습니다. 77 | 78 | ## 코드 설명 (Code Description in Korean) 79 | 80 | ### 주의: 이 시뮬레이션을 사용하기 전에 81 | #### figure를 보기 위해서는 'dual_left_monitor' 변수를 확인하세요 82 | #### 시뮬레이션을 원하는 실험 경로를 'trajtype'에서 확인하세요 83 | 84 | (각각 같은 숫자를 가지는 SIM파일들은 같은 그룹에 속합니다.) 85 | 1. **SIM1_w2Dfeat_demo.m** 86 | > * SIM1은 간단한 2D환경에서의 카메라 시뮬레이션 입니다. 87 | > * 헤딩과 시야범위의 조건을 통해 간단한 컨셉 코드를 작성하였습니다. 88 | 89 | 2. **SIM2_w3Dfeat_demo.m** 90 | > * SIM2는 3D 환경에서의 특징점과 카메라에 대한 시뮬레이션입니다. 91 | > * SIM2에서는 특징점과의 거리, 카메라 방향, 내부 파라미터 조건을 고려해서 특징점을 고릅니다. 92 | > * SIM2에서는 **카메라로봇이 있는 3D환경**과 특징점들이 **카메라에 잡힌 화면**을 보여줍니다. 93 | > * SIM2는 노이즈를 키고 끌 수 있는 이상적인 상황에서의 시뮬레이션입니다. (왜곡, 픽셀 에러, 추적 실패 등) 94 | > * SIM2에서는 feature들을 추적하고 있는 결과를 LiveTrack에 기록하며, 추적이 끝난 결과를 DeadTrack에 (한 스텝 동안만) 저장합니다. (변수 LiveTrack, DeadTrack) 95 | 96 | > * **...verSimple.m**은 제거되었습니다. 97 | 98 | 3. (*예정*) **SIM3_IMU_demo.m** 99 | > * ~~SIM3는 역 INS와 INS, IMU 에러 모델에 대한 시뮬레이션입니다.~~ 100 | 4. (*예정*) **SIM4_WheelOdo_demo.m** 101 | > * ~~SIM4는 역 휠 오도메트리와 에러 모델이 고려된 휠 오도메트리에 대한 시뮬레이션입니다.~~ 102 | 5. (*예정*) **SIM5_Visual_odometry_demo.m** 103 | > * ~~SIM5는 SIM2의 카메라를 이용한 비주얼 오도메트리에 대한 시뮬레이션입니다.~~ 104 | 105 | 6. (*수정중*) **SIM6_Visual_inertial_odometry_demo.m** 106 | > * SIM6는 SIM2의 카메라와 SIM3의 IMU를 이용한 비주얼-관성 오도메트리에 대한 시뮬레이션입니다. 107 | > * SIM6는 SIM2와 같은 시각화를 합니다. 108 | > * SIM6는 매칭된 특징점에 대해 에피폴라 조건에 따른 비용함수를 계산합니다. 109 | > * SIM6은 기록된 트랙(LiveTrack or DeadTrack)으로 부터 특징점의 3차원 위치를 복구합니다. 110 | 111 | -------------------------------------------------------------------------------- /SIM6_Visual_inertial_odometry_demo.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 0. world, body, camera frame - 3-D position, attitude applied 4 | % 1. visual system from SIM2 + IMU system from SIM3 5 | % 2. Features with Distance, Attitude, Intrinsic Matrix Constraint 6 | % 3. Visualization in 3D dimension and projected camera view 7 | % 4. Feature Tracks on image plane 8 | % 5. Epipoar Constraint cost with matched features 9 | % 10 | % world frame (normal x,y,z), body frame (forward-x, right-y, down-z), 11 | % camera frame(forward-z, right-x, down-y) 12 | % intrinsic matrix (K), extrinsic matrix (Tcb) applied 13 | % 14 | % External functions: world2pixel.m 15 | % Tuning Parameter: min/maxdist, PixelErr, DistanceThreshold(fundamental 16 | % matrix), distCoeff(& error) 17 | % 18 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 19 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 20 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 21 | clc; clear; close all; 22 | rng(10); 23 | addpath('./functions'); 24 | addpath('./trajectories'); 25 | 26 | dual_left_monitor = 1; 27 | if(dual_left_monitor) 28 | figure(1); set(gcf,'Position',[-1900 50 1800 900]); % This is my workspace setting. 29 | else 30 | figure(1); set(gcf,'Position',[100 50 1800 900]); % ... usually this option is proper OR set as you wish 31 | end 32 | 33 | %% environment setting 34 | % Trajectory LIST --> select among 'traj1', 'traj2', 'traj3' 35 | trajtype = 'traj2'; 36 | % Get the trajectory parameters from its type. 37 | trajParams = trajSettings(trajtype); % Set the proper options fitted with the selected trajectory 38 | 39 | % Getting ready-made trajectories from exampleDataX.mat file 40 | [Tbw, traj_world_wb] = getTrajectory(trajParams.fileName); 41 | 42 | % Generating features along the trajectory 43 | feat_position = featureGeneration(traj_world_wb, trajParams.featGenParams); 44 | 45 | %% camera setting 46 | % camera parameter setting, write the error model you need on second parameter 47 | % 'pixelErr', 'distortion', 'mistrack' 48 | cameraParams = cameraSettings(trajParams.distRange, {'pixelErr'}); 49 | 50 | % Distance Threshold in finding the 8-point RANSAC 51 | estFundaThreshold = 0.2; 52 | 53 | % Feature Tracks 54 | LiveTracks = {}; 55 | DeadTracks = {}; 56 | 57 | %% driving robot 58 | startIdx = 1; featGroup=struct(); t=0; 59 | for currStep=startIdx:size(Tbw,3) 60 | % Index saving for optical flow 61 | if(currStep==startIdx) 62 | featGroup.feat_prevValidx = []; 63 | robotParamsPrev = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,currStep)); 64 | end 65 | robotParams = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,currStep)); 66 | 67 | %% Feature Tracking & Optical Flow 68 | featGroup = trackingStep(featGroup, robotParamsPrev, robotParams, cameraParams); 69 | 70 | % Calculating the cost of the epipolar constraint 71 | d_list = epipolarConstraint(featGroup, robotParams, robotParamsPrev, cameraParams); 72 | 73 | %% data consistency check 74 | % consistency_check: 'NONE', 'RANSAC', 'priorSAC' 75 | consistency_check = 'RANSAC'; 76 | switch(consistency_check) 77 | case 'NONE' 78 | RSvalid_logic = true(size(d_list)); 79 | case 'RANSAC' 80 | % Fundamental Matrix with RANSAC 81 | if (size(featGroup.feat_prevTrckPixel,2) >= 8) 82 | [~, RSvalid_logic] = estimateFundamentalMatrix(featGroup.feat_prevTrckPixel(1:2,:)', featGroup.feat_currTrckPixel(1:2,:)',... 83 | 'Method', 'RANSAC', 'DistanceThreshold', estFundaThreshold); 84 | else, RSvalid_logic = ones(1,size(featGroup.feat_currTrckPixel,2)); 85 | end 86 | case 'priorSAC' 87 | RSvalid_logic = d_list < 1e-8 & d_list > -1e-8; 88 | end 89 | 90 | % Testing Inlier Ratio 91 | sum(RSvalid_logic)/size(featGroup.feat_prevTrckPixel,2) 92 | 93 | % update index with the results of RANSAC 94 | featGroup.feat_prevDeadValidx = [featGroup.feat_prevDeadValidx, featGroup.feat_intrscPrevIdx(~RSvalid_logic)]; 95 | 96 | %% Managing feature tracks 97 | % Stacking existed Tracks with new features on the LiveTracks 98 | RS_valid_index = find(RSvalid_logic); 99 | [LiveTracks, DeadTracks] = slidingWindowManager(LiveTracks, currStep, RS_valid_index, featGroup, trajParams); 100 | 101 | % from Tracks, Get the 3D position 102 | reprodFeat = track2feat3D(DeadTracks, Tbw, 1e6, robotParams, cameraParams); 103 | TrackParams = struct(); TrackParams.reprodFeat = reprodFeat; 104 | TrackParams.LiveTracks = LiveTracks; TrackParams.DeadTracks = DeadTracks; 105 | 106 | %% draw figures 107 | drawFigures(traj_world_wb, feat_position, currStep, RSvalid_logic,TrackParams, featGroup, cameraParams, d_list) 108 | 109 | %% For next step 110 | featGroup.feat_prevValidx = sort([featGroup.feat_intrscCurrIdx(RS_valid_index), featGroup.feat_currNewValidx]); 111 | 112 | %% moving features 113 | robotParamsPrev = struct('feat_position', feat_position, 'Tbw',Tbw(:,:,currStep)); 114 | nt = t + pi/10; 115 | delta_sin = 10*[sin(nt)-sin(t); -sin(nt)+sin(t); 0]; 116 | feat_position(:,250:300) = feat_position(:,250:300) + delta_sin; 117 | t = nt; 118 | end 119 | -------------------------------------------------------------------------------- /functions/drawFigures.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % 3 | % 1. Screening the valid index from user-selected constraint 4 | % 5 | % INPUT : User selected constraint-type ('distance', 'heading', 'pixelRange', robotParams, cameraParams) 6 | % OUTPUT : World Index which fits to the constraint 7 | % FUNCTION: Getting the valid (world) index from user-selected contraint 8 | % 9 | % Tuning Parameter: NONE 10 | % 11 | % Copyright (c) 2019 JaeYoung Chung (robot0321@github) All Rights Reserved 12 | % Lisence: GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 13 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 14 | 15 | function drawFigures(traj_world_wb, feat_position, currStep, RSvalid_logic, TrackParams, featGroup, cameraParams, d_list) 16 | subx=2; suby=2; 17 | if(isfield(TrackParams,'reprodFeat')), subx=2; suby=3; end 18 | 19 | figure(1); 20 | %% 3-D features, robot, path and the features in view 21 | subplot(subx,suby,1); 22 | scatter3(feat_position(1,:), feat_position(2,:),feat_position(3,:),'b'); hold on; %features 23 | plot3(traj_world_wb(1,:), traj_world_wb(2,:), traj_world_wb(3,:),'r'); % path 24 | plot3([traj_world_wb(1,currStep)*ones(1,size(featGroup.feat_world_validx,2)); feat_position(1,featGroup.feat_world_validx)], ... 25 | [traj_world_wb(2,currStep)*ones(1,size(featGroup.feat_world_validx,2)); feat_position(2,featGroup.feat_world_validx)], ... 26 | [traj_world_wb(3,currStep)*ones(1,size(featGroup.feat_world_validx,2)); feat_position(3,featGroup.feat_world_validx)],'k'); % view ray 27 | scatter3(traj_world_wb(1,currStep),traj_world_wb(2,currStep),traj_world_wb(3,currStep), 50,'g','filled'); % robot position 28 | % yaw = dcm2angle(Tbw(1:3,1:3,currStep)); 29 | % quiver3(traj_world_wb(1,currStep),traj_world_wb(2,currStep),traj_world_wb(3,currStep), ... 30 | % 3*cos(yaw*pi/180),3*sin(yaw*pi/180),yaw*0); % robot heading 31 | axis equal; grid on; hold off; xlabel('x'); ylabel('y'); 32 | 33 | %% current & previous features on camera image plane 34 | subplot(subx,suby,2); 35 | if ~isempty(featGroup.feat_intrsectValidx) % avoid the error when it is empty 36 | scatter(featGroup.feat_currTrckPixel(1,:), featGroup.feat_currTrckPixel(2,:),50,'r'); hold on; 37 | scatter(featGroup.feat_prevTrckPixel(1,:), featGroup.feat_prevTrckPixel(2,:),'g'); 38 | % draw the valid(yellow) and invalid(black) optical flows 39 | plot([featGroup.feat_prevTrckPixel(1,RSvalid_logic); featGroup.feat_currTrckPixel(1,RSvalid_logic)], [featGroup.feat_prevTrckPixel(2,RSvalid_logic); featGroup.feat_currTrckPixel(2,RSvalid_logic)],'-y'); 40 | plot([featGroup.feat_prevTrckPixel(1,~RSvalid_logic); featGroup.feat_currTrckPixel(1,~RSvalid_logic)], [featGroup.feat_prevTrckPixel(2,~RSvalid_logic); featGroup.feat_currTrckPixel(2,~RSvalid_logic)],'-k'); 41 | end 42 | if ~isempty(featGroup.feat_currNewValidx), scatter(featGroup.feat_currNewPixel(1,:), featGroup.feat_currNewPixel(2,:),50,'r'); end 43 | % optical flow between tracked features 44 | hold off; xlabel('x'); ylabel('y'); 45 | axis([0, cameraParams.px, 0, cameraParams.py]); 46 | set(gca,'XAxisLocation','top','YAxisLocation','left','ydir','reverse'); 47 | 48 | %% LiveTracks & DeadTracks 49 | subplot(subx,suby,4); 50 | for j = 1:length(TrackParams.LiveTracks) 51 | if(~isempty(TrackParams.LiveTracks{j})), LT=plot(TrackParams.LiveTracks{j}.pts(1,:), TrackParams.LiveTracks{j}.pts(2,:),'-og'); hold on; end 52 | end 53 | for j = 1:length(TrackParams.DeadTracks) 54 | if(~isempty(TrackParams.DeadTracks{j})), DT=plot(TrackParams.DeadTracks{j}.pts(1,:), TrackParams.DeadTracks{j}.pts(2,:), '-or'); hold on; end 55 | end 56 | hold off; 57 | title('Tracks'); xlabel('x'); ylabel('y'); 58 | axis([0, cameraParams.px, 0, cameraParams.py]); 59 | set(gca,'XAxisLocation','top','YAxisLocation','left','ydir','reverse') 60 | if exist('LT', 'var')&&~exist('DT', 'var'), legend(LT(1), 'LiveTrack'); end 61 | if exist('LT', 'var')&&exist('DT', 'var'), legend([LT(1),DT(1)], 'LiveTrack','DeadTrack'); end 62 | 63 | %% 3D position reproduce error & projected tracks 64 | if isfield(TrackParams,'reprodFeat') 65 | subplot(subx,suby,3); 66 | normlist = []; idxlist=[]; 67 | for ii=1:length(TrackParams.reprodFeat.feat3D) 68 | if ~isempty(TrackParams.reprodFeat.feat3D{ii}) 69 | normlist = [normlist, norm(TrackParams.reprodFeat.feat3D{ii}-feat_position(:,ii))]; 70 | idxlist = [idxlist, ii]; 71 | end 72 | end 73 | stem(idxlist, normlist); 74 | title(['global 3D position error with mu: ', num2str(TrackParams.reprodFeat.mu)]); 75 | xlabel('index'); ylabel('norm2 err [m]') 76 | xlim([1, 700]); 77 | 78 | % 2D reprojection 79 | subplot(subx,suby,6); 80 | for ii=1:length(TrackParams.reprodFeat.feat2D) 81 | if ~isempty(TrackParams.reprodFeat.feat2D{ii}) 82 | plot(TrackParams.reprodFeat.feat2D{ii}.pts_true(1,:), TrackParams.reprodFeat.feat2D{ii}.pts_true(2,:),'-go','LineWidth',2); hold on 83 | plot(TrackParams.reprodFeat.feat2D{ii}.pts(1,:), TrackParams.reprodFeat.feat2D{ii}.pts(2,:),'-bo'); 84 | end 85 | end 86 | hold off 87 | title(['Live Tracks with mu: ', num2str(TrackParams.reprodFeat.mu)]); xlabel('x'); ylabel('y'); 88 | set(gca,'XAxisLocation','top','YAxisLocation','left','ydir','reverse'); 89 | axis([0, cameraParams.px, 0, cameraParams.py]); 90 | legend('trueTracks', 'reproductTracks'); 91 | end 92 | 93 | %% Epipolar Constraint Parameters 94 | if ~isempty(d_list) 95 | subplot(2,3,5); 96 | % Histogram 97 | h1=histogram(sort(d_list),71); 98 | title('Histogram of Epipolar Constraint Cost'); 99 | % axis([-1e-8, 1e-8, 0, 50]) 100 | 101 | % % Kernel Density Estimation (KDE) 102 | % h=1.06*sqrt(var(d_list))*nthroot(length(d_list), -5); 103 | % syms x 104 | % for ii=1:length(d_list) 105 | % f = 1/sqrt(2*pi)*exp(-((x-d_list(ii))/h).^2); % not /h, since h is too small 106 | % if ii==1, ft = f; 107 | % else, ft = ft + f; 108 | % end 109 | % end 110 | % 111 | % hold on; fplot(ft/2); hold off; 112 | % axis([min(h1.BinEdges), max(h1.BinEdges), 0, max(h1.Values)]); 113 | end 114 | 115 | drawnow(); 116 | end -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------