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dvm_GPSINS_meas _CorrectedEq.m
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dvm_GPSINS_meas _CorrectedEq.m
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%%
mex -setup;
%% demonstrates mono visual odometry on an image sequence
disp('===========================');
clear; close all; dbstop error; clc;
img_dir = 'D:\VO\data_odometry_gray\dataset\sequences\03\image_0';
param.f = 721.5;
param.cu = 609.5;
param.cv = 172.8;
param.height = 1.6;
param.pitch = -0.08;
first_frame = 0;
last_frame = 200;
% init visual odometry
visualOdometryMonoMex('init',param);
% init transformation matrix array
Tr_total{1} = eye(4);
Tr_ekf_total{1} = eye(4);
Tr_ekf{1} = eye(4);
% create figure
figure('Color',[1 1 1]);
ha1 = axes('Position',[0.05,0.7,0.9,0.25]);
axis off;
ha2 = axes('Position',[0.05,0.05,0.9,0.6]);
set(gca,'XTick',-500:10:500);
set(gca,'ZTick',-500:10:500);
axis equal, grid on, hold on;
% for all frames do
replace = 0;
% >>>>>>>>START: EKF PARAMETERS<<<<<<<<<<<<<
NN = last_frame - first_frame + 1;
n_states=61;
n_meas_states = 9;
% n_meas_states_dash = 3;
q_proc=0.1; %std of process
r_meas= 0.1; %std of measurement
Q_proc=q_proc^2*eye(n_states); % covariance of process
Q_proc(5,5) = 0.01^2;
Q_proc(6,6) = 0.01^2;
Q_proc(7,7) = 0.01^2;
Q_proc(8,8) = 0.01^2;
Q_proc(9,9) = 0.01^2;
Q_proc(10,10) = 0.01^2;
[Q_proc_E, Q_proc_e] = eig(Q_proc);
R_meas=r_meas^2*eye(n_meas_states); % covariance of measurement
% R_meas_dash=r_meas^2*eye(n_meas_states_dash);
[R_meas_E, R_meas_e] = eig(R_meas);
% [R_meas_E_dash, R_meas_e_dash] = eig(R_meas_dash);
dt = 0.1;
m = 1030; % Mass of vehicle in kg
ms = 810; % Kg
h = 0.505; % m
tf = 1.28; % m
tr = tf;
d = tf/2;
a = 0.968; % m
b = 1.392; % m
ks_FL = 20600; % Spring Constant N/m
ks_FR = 20600;
ks_RL = 15200;
ks_RR = 15200;
c_FL = 1570; % Damping Constant N.s/m
c_FR = 1570;
c_RL = 1760;
c_RR = 1760;
m_b = 1; % Mass of the vehicle sans frong and rear wheels
m_wFL = 25; % Mass of wheel
m_wFR = 25;
m_wRL = 25;
m_wRR = 25;
kaf = 6695;
g = 9.81;
dof = 14;
Ix = 300;
Iy = 1058.4;
Iz = 1087.8;
Ca_FL = 200520;
Ca_FR = 200520;
Ca_RL = 76426;
Ca_RR = 76426;
Ck_FL = 30;
Ck_FR = 30;
Ck_RL = 24;
Ck_RR = 24;
wheelr = (0.4/2)+0.11;
% >>>>>>>>>>>>>NOISE START<<<<<<<<<<<<<<<<<<<<<
mu = zeros(3,1);
QR = [0.1^2 0 0; 0 0.1^2 0; 0 0 (0.01*0.01)^2]; % Covariance
n = length(QR(:,1)); % Size
[QRE, QRe] = eig(QR); % Eigenvectors and eigenvalues of Sigma
% Create sample sets to represent the Gaussian distributions
S = NN;
for i = 1:S
ra(:,i) = randn(n,1); % Generate normal samples
q(:,i) = mu + QRE*sqrt(QRe)*ra(:,i); % Convert to samples with mean mu and covariance Q
end
% >>>>>>>>>>>>>NOISE END<<<<<<<<<<<<<<<<<<<<<<<
load('D:\VO\data_odometry_gray\dataset\sequences\03\03.txt');
gtdata = X03';
for i=1:NN
gtEulAng(:,i) = rotm2eul([X03(i,1:3); X03(i,5:7); X03(i,9:11)]);
end
gt = [gtdata(4,1:NN);gtdata(12,1:NN); gtEulAng(2,1:NN); gtEulAng(3,1:NN); gtEulAng(1,1:NN); gtdata(8,1:NN)];
for i = 2:NN
delta(i-1) = gtEulAng(2,i)-gtEulAng(2,i-1);
end
delta(201) = 0;
velX(1) = 0;
velY(1) = 0;
for i=2:NN
velX(i) = (gt(1,i)-gt(1,i-1))/dt;
velY(i) = (gt(2,i)-gt(2,i-1))/dt;
end
% gt = [x z yaw roll pitch y]
% Trans roll == pitch
% Trans pitch == yaw
% Trans yaw == roll
% gt_meas = [gt(1,:)+0.1*randn(NN,1)'; gt(2,:)+0.1*randn(NN,1)'; gt(3,:)+0.01*randn(NN,1)'];
gt_m = [gt(1,:); gt(2,:); gt(3,:)];
gt_meas = gt_m + q;
% x_handle = [x vx z vz yaw yawR roll rollR pitch pitchR y vy Vxz ax az ay Axz fxFL fxFR fxRL fxRR fyFL fyFR fyRL fyRR]
s_state=[...
gt(1,1);... % 1. x
velX(2);... % 2. vx
gt(1,2);... % 3. z
10;... % 4. vz
gt(1,3);... % 5. yaw
1;... % 6. yawR
gt(1,4);... % 7. roll
1;... % 8. rollR
gt(1,5);... % 9. pitch
1;... % 10. pitchR
gt(1,6);... % 11. y
1;... % 12. vy
1;... % 13. Vxz
1;... % 14. ax
1;... % 15. az
1;... % 16. ay
1;... % 17. Axz
1;... % 18. fxFL
1;... % 19. fxFR
1;... % 20. fxRL
1;... % 21. fxRR
1;... % 22. fyFL
1;... % 23. fyFR
1;... % 24. fyRL
1;... % 25. fyRR
1;... % 26. fzFL
1;... % 27. fzFR
1;... % 28. fzRL
1;... % 29. fzRR
1;... % 30. sFL
1;... % 31. sFR
1;... % 32. sRL
1;... % 33. sRR
1;... % 34. wFL
1;... % 35. wFR
1;... % 36. wRL
1;... % 37. wRR
1;... % 38. vFL
1;... % 39. vFR
1;... % 40. vRL
1;... % 41. vRR
1;... % 42. beta
1;... % 43. alphaFL
1;... % 44. alphaFR
1;... % 45. alphaRL
1;... % 46. alphaRR
1;... % 47. yawA
1;... % 48. pitchA
1;... % 49. rollA
1;... % 50. delta
1;... % 51. zs sprung mass displacement
1;... % 52. zsR sprung mass velocity
1;... % 53. zsA sprung mass acceleration
1;... % 54. zs_FL
1;... % 55. zs_FR
1;... % 56. zs_RL
1;... % 57. zs_RR
1;... % 58. zsR_FL
1;... % 59. zsR_FR
1;... % 60. zsR_RL
1;... % 61. zsR_RR
]; % initial state
x=s_state+q_proc*randn(n_states,1); % initial state with noise
% x_dash = x;
P = 0.1*eye(n_states); % initial state covraiance
% P_dash = P;
x_store = zeros(n_states,NN); %estmate
meas_store = zeros(n_meas_states,NN); %actual
% meas_store_dash = zeros(n_meas_states_dash,NN);
% >>>>>>>>>>>>>END: EKF PARAMTERS<<<<<<<<<<<<<<
for frame=first_frame:last_frame
% 1-based index
k = frame-first_frame+1;
% read current images
% I = imread([img_dir '/I1_' num2str(frame,'%06d') '.png']);
I = imread([img_dir '/' num2str(frame,'%06d') '.png']);
% compute egomotion
Tr = visualOdometryMonoMex('process',I,replace);
% accumulate egomotion, starting with second frame
if k>1
% if motion estimate failed: set replace "current frame" to "yes"
% this will cause the "last frame" in the ring buffer unchanged
if isempty(Tr)
replace = 1;
Tr_total{k} = Tr_total{k-1};
Tr_ekf_total{k} = Tr_ekf_total{k-1};
eulAng(:,k) = rotm2eul(Tr_total{k}(1:3,1:3));
eulAngEkf(:,k) = rotm2eul(Tr_ekf_total{k}(1:3,1:3));
% on success: update total motion (=pose)
else
replace = 0;
Tr_total{k} = Tr_total{k-1}*inv(Tr);
Tr_ekf_total{k} = Tr_ekf_total{k-1}*inv(Tr);
eulAng(:,k) = rotm2eul(Tr_total{k}(1:3,1:3));
eulAngEkf(:,k) = rotm2eul(Tr_ekf_total{k}(1:3,1:3));
end
end
% update image
axes(ha1); cla;
imagesc(I); colormap(gray);
axis off;
% update trajectory
axes(ha2);
if k>1
plot([Tr_total{k-1}(1,4) Tr_total{k}(1,4)], ...
[Tr_total{k-1}(3,4) Tr_total{k}(3,4)],'-xb','LineWidth',1);
hold on;
plot([Tr_ekf_total{k-1}(1,4) Tr_ekf_total{k}(1,4)], ...
[Tr_ekf_total{k-1}(3,4) Tr_ekf_total{k}(3,4)],'-+r','LineWidth',1);
% meas = [Tr_total{k}(1,4); Tr_total{k}(3,4);eulAng(2,k)];%; gt_meas(1,k);gt_meas(2,k);gt_meas(3,k)];
meas = [Tr_ekf_total{k}(1,4); Tr_ekf_total{k}(3,4);eulAngEkf(2,k);eulAngEkf(3,k);eulAngEkf(1,k);Tr_ekf_total{k}(2,4); gt_meas(1,k);gt_meas(2,k);gt_meas(3,k)];
meas_store(:,k)= meas; % save actual state
% meas_dash = [gt_meas(1,k);gt_meas(2,k);gt_meas(3,k)];
% meas_store_dash(:,k)= meas_dash;
e = Q_proc_E*sqrt(Q_proc_e)*randn(n_states,1);
d = R_meas_E*sqrt(R_meas_e)*randn(n_meas_states,1);
% cam_z = IMU_x = car front direction
% cam_x = -IMU_y = car right direction
% cam_y = -IMU_z = car down direction
% x_handle = [x vx z vz yaw yawR roll rollR pitch pitchR y vy Vxz ax az ay Axz fxFL fxFR fxRL fxRR fyFL fyFR fyRL fyRR]
% x_handle=@(x)[x(1)+(x(2)*dt)+e(1);(x(13)*sin(x(5)))+e(2);x(3)+(x(4)*dt)+e(3);(x(13)*cos(x(5)))+e(4);x(5)+(x(6)*dt)+e(5);x(6)+e(6); x(7)+(x(8)*dt)+e(7); x(8)+e(8); x(9)+(x(10)*dt)+e(9); x(10)+e(10);x(11)+(x(12)*dt)+e(11);x(12)+e(12); x(13)+e(13)];
x_handle=@(x)[...
x(1) + x(2) * dt + 0.5 * x(14) * (dt ^ 2); % x
x(2) + x(14) * dt; % x vel
x(3) + x(4) * dt + 0.5 * x(15) * (dt ^ 2); % z
x(4) + x(15) * dt; % z vel
x(5) + x(6) * dt + 0.5 * x(47) * (dt ^ 2); % yaw
x(6) + x(47) * dt; % yaw rate
x(7) + x(8) * dt + 0.5 * x(49) * (dt ^ 2); % roll
x(8) + x(49) * dt; % roll rate
x(9) + x(10) * dt + 0.5 * x(48) * (dt ^ 2); % pitch
x(10) + x(48) * dt; % pitch rate
x(11) + x(12) * dt + 0.5 * x(16) * (dt ^ 2); % y
x(12) + x(16) * dt; % y vel
x(13) + x(17)*dt; % Vxy
x(14); % (1/m)*((x(18)+x(19))*cos(x(50)) - (x(22)+x(23))*sin(x(50)) + x(20) + x(21) + ms*h*x(47)*x(7)) + x(12)*x(5); %ax
x(15); % az
x(16); % (1/m)*((x(22)+x(23))*cos(x(50)) + (x(18)+x(19))*sin(x(50)) + x(24) + x(25) - ms*h*x(49)) - x(2)*x(5); % ay
x(17); % Axy
x(18); %-Ck_FL * x(30); % fxFL
x(19); %-Ck_FR * x(31); % fxFR
x(20); %-Ck_RL * x(32); % fxRL
x(21); %-Ck_RR * x(33); % fxRR
x(22); %-Ca_FL * x(43); % fyFL
x(23); %-Ca_FR * x(44); % fyFR
-Ca_RL * x(45); % fyRL
-Ca_RR * x(46); % fyRR
ks_FL*(-x(54)) + c_FL*(-x(58)) + m_wFL*g + (0.5*m*g + ((m*h*x(16))/tf))*(b/(a+b)) - 0.5*m*x(14)*(h/(a+b)); % fzFL
ks_FR*(-x(55)) + c_FR*(-x(59)) + m_wFR*g + (0.5*m*g - ((m*h*x(16))/tf))*(b/(a+b)) - 0.5*m*x(14)*(h/(a+b)); % fzFR
ks_RL*(-x(56)) + c_RL*(-x(60)) + m_wRL*g + (0.5*m*g + ((m*h*x(16))/tr))*(a/(a+b)) + 0.5*m*x(14)*(h/(a+b)); % fzRL
ks_RR*(-x(57)) + c_RR*(-x(61)) + m_wRR*g + (0.5*m*g - ((m*h*x(16))/tr))*(a/(a+b)) + 0.5*m*x(14)*(h/(a+b)); % fzRR
x(30); %x(34)*wheelr/x(38) - 1; % slip ratio FL
x(31); %x(35)*wheelr/x(39) - 1; % slip ratio FR
x(32); %x(36)*wheelr/x(40) - 1; % slip ratio RL
x(33); %x(37)*wheelr/x(41) - 1; % slip ratio RR
x(34); % wheel angular velocity FL
x(35); % FR
x(36); % RL
x(37); % RR
sqrt(x(2)^2 + x(12)^2) + x(6)*((tf/2)-a*x(42)); % FL acutal wheel velocity
sqrt(x(2)^2 + x(12)^2) + x(6)*((-tf/2)-a*x(42)); % FR
sqrt(x(2)^2 + x(12)^2) + x(6)*((tf/2)+b*x(42)); % RL
sqrt(x(2)^2 + x(12)^2) + x(6)*((-tf/2)+b*x(42)); % RR
atan(x(12)/x(2)); % Beta
x(43); %x(50) - atan((x(12) + b*x(6))/(x(2) + tf*x(6)*0.5)); % alpha FL
x(44); %x(50) - atan((x(12) + b*x(6))/(x(2) - tf*x(6)*0.5)); % alpha FR
atan((-x(12) + b*x(6))/(x(2) + tr*x(6)*0.5)); % alpha RL
atan((-x(12) + b*x(6))/(x(2) - tr*x(6)*0.5)); % alpha RR
x(47); %(1/Iz)*(tf*0.5*(x(18)*cos(x(50)) - x(22)*sin(x(50)) - x(19)*cos(x(50)) + x(23)*sin(x(50))) + tr*0.5*(x(20)-x(21)) + a*(x(22)*cos(x(50))+x(18)*sin(x(50))+x(23)*cos(x(50))+x(19)*sin(x(50))) - b*(x(24)-x(25))); % yawA
(1/Iy)*(b*(x(29)+x(28)) - a*(x(27)+x(26))); % pitchA
ms*g*h*x(7) - ms*(x(16) + x(14)*x(8))*h + (x(26)+x(29)-x(28)-x(27))*d; %rollA
x(50); % delta
x(51) + x(52)*dt + 0.5*x(53)*(dt^2); % zs sprung mass displacement
x(52) + x(52)*dt; % zsR sprung mass velocity
(1/ms)*(x(26) + x(27) + x(28) + x(29)); % zsA sprung mass accelration
x(51) - a*x(9) + tf*x(7)*0.5; % zs_FL
x(51) - a*x(9) - tf*x(7)*0.5; % zs_FR
x(51) + b*x(9) - tf*x(7)*0.5; % zs_RL
x(51) + b*x(9) + tf*x(7)*0.5; % zs_RR
x(51) - a*x(10) + tf*0.5*(1/x(8)); % zsR_FL
x(51) - a*x(10) - tf*0.5*(1/x(8)); % zsR_FR
x(51) + b*x(10) - tf*0.5*(1/x(8)); % zsR_RL
x(51) + b*x(10) + tf*0.5*(1/x(8)); % zsR_RR
];
% x_handle=@(x)[x(1)+(x(2)*dt)+e(1);x(2)+e(2);x(3)+(x(4)*dt)+e(3);x(4)+e(4);x(5)+(x(6)*dt)+e(5);x(6)+e(6); x(7)+x(8)*dt+e(7); x(8)+e(8); x(9)+(x(10)*dt)+e(9); x(10)+e(10);x(11)+(x(12)*dt)+e(11);x(12)+e(12); x(13)+e(13)];
% x_handle_dash=@(x)[x(1)+(x(2)*dt)+e(1);x(2)+e(2);x(3)+(x(4)*dt)+e(3);x(4)+e(4);x(5)+(x(6)*dt)+e(5);x(6)+e(6); x(7)+x(8)*dt+e(7); x(8)+e(8); x(9)+(x(10)*dt)+e(9); x(10)+e(10);x(11)+(x(12)*dt)+e(11);x(12)+e(12); x(13)+e(13)];
% y_handle=@(x)[x(2)/dt;x(4)/dt;x(6)/dt]; % measurement equation
y_handle=@(x)[x(1)+d(1);x(3)+d(2);x(5)+d(3);x(7)+d(4);x(9)+d(5);x(11)+d(6);x(1)+d(7);x(3)+d(8);x(5)+d(9)];
% y_handle_dash=@(x)[x(1)+d(7);x(3)+d(8);x(5)+d(9)];
% x
% meas
% P
% y_handle
% Q_proc
% R_meas
[x, P] = ekf(x_handle,x,P,y_handle,meas,Q_proc,R_meas);
% [x_dash, P_dash] = ekf(x_handle_dash,x_dash,P_dash,y_handle_dash,meas_dash,Q_proc,R_meas_dash);
Rekf = eul2rotm([x(9) x(5) x(7)]);
% disp([x(9) x(5) x(7)]);
Tekf = [x(1);x(11);x(3)];
Tr_ekf_total{k} = [Rekf Tekf; 0 0 0 1];
% disp(rotm2eul(Tr_ekf_total{k}(1:3,1:3)));
x_store(:,k-1) = x; % save estimate
% x_store_dash(:,k-1) = x_dash;
end
pause(0.05); refresh;
% output statistics
num_matches = visualOdometryMonoMex('num_matches');
num_inliers = visualOdometryMonoMex('num_inliers');
disp(['Frame: ' num2str(frame)]);
% disp(['Frame: ' num2str(frame) ...
% ', Matches: ' num2str(num_matches) ...
% ', Inliers: ' num2str(100*num_inliers/num_matches,'%.1f') ,' %']);
end
% figure;
% for k=1:3 % plot results
% subplot(3,1,k)
% hold on;
% % plot(1:NN, meas_store(k,:), '-', 1:NN, x_store(k,:), '--')
% % plot(1:NN, gt(k,:), 'b-')
% plot(1:NN, gt(k,:), 'b-',1:NN, x_store(2*k-1,:), 'r--', 1:NN, gt_meas(k,:), 'g--');
% % plot(1:NN, x_store(k,:), '--')
% end
% figure;
% for k=2:NN
% plot([Tr_total{k-1}(1,4) Tr_total{k}(1,4)], ...
% [Tr_total{k-1}(3,4) Tr_total{k}(3,4)],'-xb','LineWidth',1)
% hold on;
% end
% plot(gt(1,1:NN), gt(2,1:NN), 'r--', 'LineWidth',2);
% axis equal;
% hold on;
% figure;
% for k=2:NN-1
% % plot([gt(1,k+1-1) gt(1,k+1)],...
% % [gt(2,k+1-1) gt(2,k+1)],'-ro','LineWidth',1)
% % hold on;
% plot([x_store(1,k-1) x_store(1,k)], ...
% [x_store(3,k-1) x_store(3,k)],'-g+','LineWidth',1)
% hold on;
% theta = x_store(5,k);
% r = 1; % magnitude (length) of arrow to plot
% x = x_store(1,k); y = x_store(3,k);
% u = r * cos(theta); % convert polar (theta,r) to cartesian
% v = r * sin(theta);
% quiver(x,y,u,v);
% hold on;
% plot([gt_meas(1,k+1-1) gt_meas(1,k+1)],...
% [gt_meas(2,k+1-1) gt_meas(2,k+1)],'-bx','LineWidth',1)
% hold on;
% end
% xlabel('X');
% ylabel('Y');
% hold off;
figure
for k=1:3 % plot results
subplot(5,1,k)
plot(1:NN, gt(k,:), 'b-', 1:NN, x_store(2*k-1,:), 'r--')
end
subplot(5,1,4)
plot(1:NN, velX, 'b-', 1:NN, x_store(2,:),'r--');
subplot(5,1,5)
plot(1:NN, velY, 'b-', 1:NN, x_store(4,:),'r--');
for k=2:NN-1
estDevX(k-1) = abs((x_store(1,k-1)-gt(1,k+1-1)));
estDevY(k-1) = abs((x_store(3,k-1)-gt(2,k+1-1)));
estDevVX(k-1) = abs((x_store(2, k-1)-velX(k)));
estDevVY(k-1) = abs((x_store(4, k-1)-velY(k)));
% estDevX_dash(k-1) = abs((x_store_dash(1,k-1)-gt(1,k+1-1))/gt(1,k+1-1));
% estDevY_dash(k-1) = abs((x_store_dash(3,k-1)-gt(2,k+1-1))/gt(2,k+1-1));
measDevX(k-1) = abs((gt_meas(1,k+1-1)-gt(1,k+1-1)));
measDevY(k-1) = abs((gt_meas(2,k+1-1)-gt(2,k+1-1)));
end
% Relative Percent Difference
mEDX = mean(estDevX);
mEDY = mean(estDevY);
mEDVX = mean(estDevVX);
mEDVY = mean(estDevVY);
% mEDX_dash = mean(estDevX_dash);
% mEDY_dash = mean(estDevY_dash);
mMDX = mean(measDevX);
mMDY = mean(measDevY);
max(estDevVX);
max(estDevVY);
%{
figure;
for k=2:NN-1
% plot([gt(1,k+1-1) gt(1,k+1)],...
% [gt(2,k+1-1) gt(2,k+1)],'-ro','LineWidth',1)
% hold on;
plot([x_store_dash(1,k-1) x_store_dash(1,k)], ...
[x_store_dash(3,k-1) x_store_dash(3,k)],'-g+','LineWidth',1)
hold on;
plot([x_store(1,k-1) x_store(1,k)], ...
[x_store(3,k-1) x_store(3,k)],'-r+','LineWidth',1)
hold on;
% theta = x_store(5,k);
% r = 1; % magnitude (length) of arrow to plot
% x = x_store(1,k); y = x_store(3,k);
% u = r * cos(theta); % convert polar (theta,r) to cartesian
% v = r * sin(theta);
% quiver(x,y,u,v);
% hold on;
plot([gt_meas(1,k+1-1) gt_meas(1,k+1)],...
[gt_meas(2,k+1-1) gt_meas(2,k+1)],'-bx','LineWidth',1)
hold on;
end
xlabel('X');
ylabel('Y');
hold off;
%}
% figure;
% plot(1:NN, gt_meas(3,:),'b-',1:NN, x_store(5,:), 'r--');
% figure;
% for k=1:3 % plot results
% subplot(3,1,k)
% hold on;
% plot(1:NN, meas_store(k,:), 'b-')
% end
%
% % figure;
% % for k=1:3
% % subplot(3,1,k)
% % plot(1:NN, radtodeg(eulAng(k,:)), '-')
% % end
% % release visual odometry
%
% figure;
% plot(gt(2,:)-gt(2,1), gt(1,:)-gt(1,1), 'b')
% axis equal
% figure;
% plot(X03(1:200,4),X03(1:200,12), 'b')
% axis equal
% figure;
% for k=1:3 % plot results
% subplot(3,1,k)
% hold on;
% % plot(1:NN, meas_store(k,:), '-', 1:NN, x_store(k,:), '--')
% % plot(1:NN, gt(k,:), 'b-')
% plot(1:NN, gt_m(k,:), 'b-',1:NN, gt_meas(k,:), 'r--');
% % plot(1:NN, x_store(k,:), '--')
% end
visualOdometryMonoMex('close');