355 lines
11 KiB
Matlab
355 lines
11 KiB
Matlab
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% GTSAM Copyright 2010, Georgia Tech Research Corporation,
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% Atlanta, Georgia 30332-0415
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% All Rights Reserved
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% Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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%
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% See LICENSE for the license information
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%
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% @brief Estimate trajectory, calibration, landmarks, body-camera offset,
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% IMU
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% @author Chris Beall
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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clear all;
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clc;
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import gtsam.*
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write_video = false;
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if(write_video)
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videoObj = VideoWriter('test.avi');
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videoObj.Quality = 100;
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videoObj.FrameRate = 2;
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open(videoObj);
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end
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%% generate some landmarks
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nrPoints = 8;
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landmarks = {Point3([20 15 1]'),...
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Point3([22 7 -1]'),...
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Point3([20 20 6]'),...
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Point3([24 19 -4]'),...
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Point3([26 17 -2]'),...
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Point3([12 15 4]'),...
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Point3([25 11 -6]'),...
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Point3([23 10 4]')};
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IMU_metadata.AccelerometerSigma = 1e-2;
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IMU_metadata.GyroscopeSigma = 1e-2;
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IMU_metadata.AccelerometerBiasSigma = 1e-6;
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IMU_metadata.GyroscopeBiasSigma = 1e-6;
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IMU_metadata.IntegrationSigma = 1e-1;
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curvature = 5.0;
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transformKey = 1000;
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calibrationKey = 2000;
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steps = 50;
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fg = NonlinearFactorGraph;
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initial = Values;
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%% intial landmarks and camera trajectory shifted in + y-direction
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y_shift = Point3(0,0.5,0);
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% insert shifted points
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for i=1:nrPoints
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initial.insert(100+i,landmarks{i}.compose(y_shift));
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end
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figure(1);
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cla
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hold on;
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%% initial pose priors
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pose_cov = noiseModel.Diagonal.Sigmas([0.1*pi/180; 0.1*pi/180; 0.1*pi/180; 1e-4; 1e-4; 1e-4]);
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%% Actual camera translation coincides with odometry, but -90deg Z-X rotation
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camera_transform = Pose3(Rot3.RzRyRx(-pi/2, 0, -pi/2),y_shift);
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actual_transform = Pose3(Rot3.RzRyRx(-pi/2, 0, -pi/2),Point3());
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trans_cov = noiseModel.Diagonal.Sigmas([1*pi/180; 1*pi/180; 1*pi/180; 20; 1e-6; 1e-6]);
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move_forward = Pose3(Rot3(),Point3(1,0,0));
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move_circle = Pose3(Rot3.RzRyRx(0.0,0.0,curvature*pi/180),Point3(1,0,0));
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covariance = noiseModel.Diagonal.Sigmas([5*pi/180; 5*pi/180; 5*pi/180; 0.05; 0.05; 0.05]);
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z_cov = noiseModel.Diagonal.Sigmas([1.0;1.0]);
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%% calibration initialization
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K = Cal3_S2(900,900,0,640,480);
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K_corrupt = Cal3_S2(910,890,0,650,470);
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K_cov = noiseModel.Diagonal.Sigmas([20; 20; 0.001; 20; 20]);
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cheirality_exception_count = 0;
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isamParams = gtsam.ISAM2Params;
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isamParams.setFactorization('QR');
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isam = ISAM2(isamParams);
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currentIMUPoseGlobal = Pose3();
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%% Get initial conditions for the estimated trajectory
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currentVelocityGlobal = [1;0;0]; % the vehicle is stationary at the beginning
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currentBias = imuBias.ConstantBias(zeros(3,1), zeros(3,1));
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sigma_init_v = noiseModel.Isotropic.Sigma(3, 1.0);
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sigma_init_b = noiseModel.Isotropic.Sigmas([ 0.100; 0.100; 0.100; 5.00e-05; 5.00e-05; 5.00e-05 ]);
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sigma_between_b = [ IMU_metadata.AccelerometerBiasSigma * Matrix::Ones(3,1); IMU_metadata.GyroscopeBiasSigma * Matrix::Ones(3,1) ];
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g = [0;0;-9.8];
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w_coriolis = [0;0;0];
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for i=1:steps
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t = i-1;
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currentVelKey = symbol('v',i);
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currentBiasKey = symbol('b',i);
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initial.insert(currentVelKey, currentVelocityGlobal);
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initial.insert(currentBiasKey, currentBias);
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if i==1
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% Pose Priors
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fg.add(PriorFactorPose3(1, Pose3(),pose_cov));
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fg.add(PriorFactorPose3(2, Pose3(Rot3(),Point3(1,0,0)),pose_cov));
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% insert first
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initial.insert(1, Pose3());
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% camera transform
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initial.insert(transformKey,camera_transform);
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fg.add(PriorFactorPose3(transformKey,camera_transform,trans_cov));
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% calibration
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initial.insert(2000, K_corrupt);
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fg.add(PriorFactorCal3_S2(calibrationKey,K_corrupt,K_cov));
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% velocity and bias evolution
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fg.add(PriorFactorVector(currentVelKey, currentVelocityGlobal, sigma_init_v));
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fg.add(PriorFactorConstantBias(currentBiasKey, currentBias, sigma_init_b));
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result = initial;
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end
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if i == 2
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fg.add(PriorFactorPose3(2, Pose3(Rot3(),Point3(1,0,0)),pose_cov));
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fg.add(PriorFactorLieVector(currentVelKey, currentVelocityGlobal, sigma_init_v));
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fg.add(PriorFactorConstantBias(currentBiasKey, currentBias, sigma_init_b));
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end
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if i > 1
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if i < 11
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step = move_forward;
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else
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step = move_circle;
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end
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initial.insert(i,result.at(i-1).compose(step));
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fg.add(BetweenFactorPose3(i-1,i, step, covariance));
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deltaT = 1;
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logmap = Pose3.Logmap(step);
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omega = logmap(1:3);
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velocity = logmap(4:6);
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%% Simulate IMU measurements, considering Coriolis effect
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% (in this simple example we neglect gravity and there are no other forces acting on the body)
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acc_omega = imuSimulator.calculateIMUMeas_coriolis( ...
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omega, omega, velocity, velocity, deltaT);
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[ currentIMUPoseGlobal, currentVelocityGlobal ] = imuSimulator.integrateTrajectory( ...
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currentIMUPoseGlobal, omega, velocity, velocity, deltaT);
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currentSummarizedMeasurement = gtsam.ImuFactorPreintegratedMeasurements( ...
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currentBias, IMU_metadata.AccelerometerSigma.^2 * eye(3), ...
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IMU_metadata.GyroscopeSigma.^2 * eye(3), IMU_metadata.IntegrationSigma.^2 * eye(3));
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accMeas = acc_omega(1:3)-g;
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omegaMeas = acc_omega(4:6);
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currentSummarizedMeasurement.integrateMeasurement(accMeas, omegaMeas, deltaT);
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%% create IMU factor
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fg.add(ImuFactor( ...
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i-1, currentVelKey-1, ...
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i, currentVelKey, ...
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currentBiasKey, currentSummarizedMeasurement, g, w_coriolis));
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% Bias evolution as given in the IMU metadata
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fg.add(BetweenFactorConstantBias(currentBiasKey-1, currentBiasKey, imuBias.ConstantBias(zeros(3,1), zeros(3,1)), ...
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noiseModel.Diagonal.Sigmas(sqrt(steps) * sigma_between_b)));
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end
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% generate some camera measurements
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cam_pose = currentIMUPoseGlobal.compose(actual_transform);
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% gtsam.plotPose3(cam_pose);
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cam = SimpleCamera(cam_pose,K);
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i
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% result
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for j=1:nrPoints
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% All landmarks seen in every frame
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try
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z = cam.project(landmarks{j});
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fg.add(TransformCalProjectionFactorCal3_S2(z, z_cov, i, transformKey, 100+j, calibrationKey, false, true));
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catch
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cheirality_exception_count = cheirality_exception_count + 1;
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end % end try/catch
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end
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if i > 1
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disp('ISAM Update');
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isam.update(fg, initial);
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result = isam.calculateEstimate();
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%% reset
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initial = Values;
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fg = NonlinearFactorGraph;
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currentVelocityGlobal = isam.calculateEstimate(currentVelKey);
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currentBias = isam.calculateEstimate(currentBiasKey);
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%% Compute some marginals
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marginal = isam.marginalCovariance(calibrationKey);
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marginal_fx(i)=sqrt(marginal(1,1));
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marginal_fy(i)=sqrt(marginal(2,2));
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%% Compute condition number
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isam_fg = isam.getFactorsUnsafe();
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isam_values = isam.getLinearizationPoint();
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gfg = isam_fg.linearize(isam_values);
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mat = gfg.jacobian();
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c(i) = cond(mat, 2);
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mat = gfg.augmentedJacobian();
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augmented_c(i)= cond(mat, 2);
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for f=0:isam_fg.size()-1
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nonlinear_factor = isam_fg.at(f);
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if strcmp(class(nonlinear_factor),'gtsam.TransformCalProjectionFactorCal3_S2')
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gaussian_factor = nonlinear_factor.linearize(isam_values);
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A = gaussian_factor.getA();
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b = gaussian_factor.getb();
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% Column 17 (fy) in jacobian
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A_col = A(:,17);
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if A_col(2) == 0
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% pause
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disp('Cheirality Exception!');
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end
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end
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end
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end
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hold off;
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clf;
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figure(1);
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subplot(5,1,1:2);
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hold on;
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%% plot the integrated IMU frame (not from
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gtsam.plotPose3(currentIMUPoseGlobal, [], 2);
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%% plot results
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result_camera_transform = result.at(transformKey);
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for j=1:i
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gtsam.plotPose3(result.at(j),[],0.5);
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gtsam.plotPose3(result.at(j).compose(result_camera_transform),[],0.5);
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end
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xlabel('x (m)');
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ylabel('y (m)');
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title(sprintf('Curvature %g deg, iteration %g', curvature, i));
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axis([0 20 0 20 -10 10]);
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view(-37,40);
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% axis equal
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for l=101:100+nrPoints
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plotPoint3(result.at(l),'g');
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end
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ty = result.at(transformKey).translation().y();
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fx = result.at(calibrationKey).fx();
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fy = result.at(calibrationKey).fy();
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px = result.at(calibrationKey).px();
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py = result.at(calibrationKey).py();
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text(1,5,5,sprintf('Y-Transform(0.0): %0.2f',ty));
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text(1,5,3,sprintf('fx(900): %.0f',fx));
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text(1,5,1,sprintf('fy(900): %.0f',fy));
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fxs(i) = fx;
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fys(i) = fy;
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pxs(i) = px;
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pys(i) = py;
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subplot(5,1,3);
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hold on;
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plot(1:steps,repmat(K.fx,1,steps),'r--');
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p(1) = plot(1:i,fxs,'r','LineWidth',2);
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plot(1:steps,repmat(K.fy,1,steps),'g--');
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p(2) = plot(1:i,fys,'g','LineWidth',2);
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if i > 1
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plot(2:i,fxs(2:i) + marginal_fx(2:i),'r-.');
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plot(2:i,fxs(2:i) - marginal_fx(2:i),'r-.');
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plot(2:i,fys(2:i) + marginal_fy(2:i),'g-.');
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plot(2:i,fys(2:i) - marginal_fy(2:i),'g-.');
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subplot(5,1,5);
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hold on;
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title('Condition Number');
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plot(2:i,c(2:i),'b-');
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plot(2:i,augmented_c(2:i),'r-');
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axis([0 steps 0 max(c(2:i))*1.1]);
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% figure(2);
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% plotBayesTree(isam);
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end
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legend(p, 'f_x', 'f_y', 'Location', 'SouthWest');
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% legend(p, 'f_x', 'f_x''', 'f_y', 'f_y''', 'Location', 'SouthWest');
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%% plot principal points
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subplot(5,1,4);
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hold on;
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plot(1:steps,repmat(K.px,1,steps),'r--');
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pp(1) = plot(1:i,pxs,'r','LineWidth',2);
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plot(1:steps,repmat(K.py,1,steps),'g--');
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pp(2) = plot(1:i,pys,'g','LineWidth',2);
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title('Principal Point');
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legend(pp, 'p_x', 'p_y', 'Location', 'SouthWest');
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if(write_video)
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currFrame = getframe(gcf);
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writeVideo(videoObj, currFrame)
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else
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pause(0.1);
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end
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end
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if(write_video)
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close(videoObj);
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end
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fprintf('Cheirality Exception count: %d\n', cheirality_exception_count);
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disp('Transform after optimization');
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result.at(transformKey)
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disp('Calibration after optimization');
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result.at(calibrationKey)
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disp('Bias after optimization');
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currentBias
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