147 lines
5.8 KiB
Matlab
147 lines
5.8 KiB
Matlab
import gtsam.*;
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deltaT = 0.001;
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summarizedDeltaT = 0.1;
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timeElapsed = 1;
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times = 0:deltaT:timeElapsed;
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omega = [0;0;2*pi];
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velocity = [1;0;0];
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summaryTemplate = gtsam.ImuFactorPreintegratedMeasurements( ...
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gtsam.imuBias.ConstantBias([0;0;0], [0;0;0]), ...
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1e-3 * eye(3), 1e-3 * eye(3), 1e-3 * eye(3));
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%% Set initial conditions for the true trajectory and for the estimates
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% (one estimate is obtained by integrating in the body frame, the other
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% by integrating in the navigation frame)
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% Initial state (body)
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currentPoseGlobal = Pose3;
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currentVelocityGlobal = velocity;
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% Initial state estimate (integrating in navigation frame)
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currentPoseGlobalIMUnav = currentPoseGlobal;
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currentVelocityGlobalIMUnav = currentVelocityGlobal;
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% Initial state estimate (integrating in the body frame)
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currentPoseGlobalIMUbody = currentPoseGlobal;
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currentVelocityGlobalIMUbody = currentVelocityGlobal;
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%% Prepare data structures for actual trajectory and estimates
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% Actual trajectory
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positions = zeros(3, length(times)+1);
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positions(:,1) = currentPoseGlobal.translation;
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poses(1).p = positions(:,1);
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poses(1).R = currentPoseGlobal.rotation.matrix;
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% Trajectory estimate (integrated in the navigation frame)
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positionsIMUnav = zeros(3, length(times)+1);
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positionsIMUnav(:,1) = currentPoseGlobalIMUbody.translation;
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posesIMUnav(1).p = positionsIMUnav(:,1);
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posesIMUnav(1).R = poses(1).R;
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% Trajectory estimate (integrated in the body frame)
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positionsIMUbody = zeros(3, length(times)+1);
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positionsIMUbody(:,1) = currentPoseGlobalIMUbody.translation;
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posesIMUbody(1).p = positionsIMUbody(:,1);
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posesIMUbody(1).R = poses(1).R;
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%% Solver object
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isamParams = ISAM2Params;
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isamParams.setRelinearizeSkip(1);
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isam = gtsam.ISAM2(isamParams);
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initialValues = Values;
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initialValues.insert(symbol('x',0), currentPoseGlobal);
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initialValues.insert(symbol('v',0), LieVector(currentVelocityGlobal));
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initialValues.insert(symbol('b',0), imuBias.ConstantBias([0;0;0],[0;0;0]));
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initialFactors = NonlinearFactorGraph;
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initialFactors.add(PriorFactorPose3(symbol('x',0), ...
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currentPoseGlobal, noiseModel.Isotropic.Sigma(6, 1.0)));
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initialFactors.add(PriorFactorLieVector(symbol('v',0), ...
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LieVector(currentVelocityGlobal), noiseModel.Isotropic.Sigma(3, 1.0)));
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initialFactors.add(PriorFactorConstantBias(symbol('b',0), ...
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imuBias.ConstantBias([0;0;0],[0;0;0]), noiseModel.Isotropic.Sigma(6, 1.0)));
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%% Main loop
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i = 2;
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lastSummaryTime = 0;
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lastSummaryIndex = 0;
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currentSummarizedMeasurement = ImuFactorPreintegratedMeasurements(summaryTemplate);
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for t = times
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%% Create the actual trajectory, using the velocities and
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% accelerations in the inertial frame to compute the positions
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[ currentPoseGlobal, currentVelocityGlobal ] = imuSimulator.integrateTrajectory( ...
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currentPoseGlobal, omega, velocity, velocity, deltaT);
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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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%% Accumulate preintegrated measurement
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currentSummarizedMeasurement.integrateMeasurement(acc_omega(1:3), acc_omega(4:6), deltaT);
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%% Update solver
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if t - lastSummaryTime >= summarizedDeltaT
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% Create IMU factor
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initialFactors.add(ImuFactor( ...
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symbol('x',lastSummaryIndex), symbol('v',lastSummaryIndex), ...
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symbol('x',lastSummaryIndex+1), symbol('v',lastSummaryIndex+1), ...
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symbol('b',0), currentSummarizedMeasurement, [0;0;1], [0;0;0], ...
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noiseModel.Isotropic.Sigma(9, 1e-6)));
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% Predict movement in a straight line (bad initialization)
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if lastSummaryIndex > 0
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initialPose = isam.calculateEstimate(symbol('x',lastSummaryIndex)) ...
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.compose(Pose3(Rot3, Point3( velocity * t - lastSummaryTime) ));
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initialVel = isam.calculateEstimate(symbol('v',lastSummaryIndex));
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else
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initialPose = Pose3;
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initialVel = LieVector(velocity);
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end
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initialValues.insert(symbol('x',lastSummaryIndex+1), initialPose);
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initialValues.insert(symbol('v',lastSummaryIndex+1), initialVel);
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% Update solver
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isam.update(initialFactors, initialValues);
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initialFactors = NonlinearFactorGraph;
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initialValues = Values;
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lastSummaryIndex = lastSummaryIndex + 1;
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lastSummaryTime = t;
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currentSummarizedMeasurement = ImuFactorPreintegratedMeasurements(summaryTemplate);
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end
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%% Integrate in the body frame
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[ currentPoseGlobalIMUbody, currentVelocityGlobalIMUbody ] = imuSimulator.integrateIMUTrajectory_bodyFrame( ...
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currentPoseGlobalIMUbody, currentVelocityGlobalIMUbody, acc_omega, deltaT, velocity);
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%% Integrate in the navigation frame
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[ currentPoseGlobalIMUnav, currentVelocityGlobalIMUnav ] = imuSimulator.integrateIMUTrajectory_navFrame( ...
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currentPoseGlobalIMUnav, currentVelocityGlobalIMUnav, acc_omega, deltaT);
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%% Store data in some structure for statistics and plots
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positions(:,i) = currentPoseGlobal.translation;
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positionsIMUbody(:,i) = currentPoseGlobalIMUbody.translation;
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positionsIMUnav(:,i) = currentPoseGlobalIMUnav.translation;
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% -
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poses(i).p = positions(:,i);
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posesIMUbody(i).p = positionsIMUbody(:,i);
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posesIMUnav(i).p = positionsIMUnav(:,i);
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% -
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poses(i).R = currentPoseGlobal.rotation.matrix;
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posesIMUbody(i).R = currentPoseGlobalIMUbody.rotation.matrix;
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posesIMUnav(i).R = currentPoseGlobalIMUnav.rotation.matrix;
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i = i + 1;
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end
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figure(1)
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hold on;
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plot(positions(1,:), positions(2,:), '-b');
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plot(positionsIMUbody(1,:), positionsIMUbody(2,:), '-r');
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plot(positionsIMUnav(1,:), positionsIMUnav(2,:), ':k');
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plot3DTrajectory(isam.calculateEstimate, 'g-');
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axis equal;
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legend('true trajectory', 'traj integrated in body', 'traj integrated in nav')
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