Use Landmarks and Other Data as Factors

Create a factor graph, and add a prior factor to loosely fix the start pose of the robot by providing an estimate pose.

fg = factorGraph;
rng(2)
pf = factorPoseSE3Prior(1,Measurement=[0 0 0 1 0 0 0]);
addFactor(fg,pf);

Create factorPoseSE3AndXYZ landmark factor objects that relate the first and second pose nodes to the first landmark point, and then add the landmark factors to the factor graph. The landmark factors used here are for SE(3) state space but the process is identical for landmark factors for SE(2) state space. Add some random number to the relative position between the landmark and the ground truth position to simulate real sensor measurements.

% Landmark 1 Factors
measurementlmf1 = landmarks(1,:) - realpos(1,:) + 0.1*rand(1,3);
measurementlmf2 = landmarks(1,:) - realpos(2,:) + 0.1*rand(1,3);
lmf1 = factorPoseSE3AndPointXYZ([1 5],Measurement=measurementlmf1);
lmf2 = factorPoseSE3AndPointXYZ([2 5],Measurement=measurementlmf2);
addFactor(fg,lmf1);
addFactor(fg,lmf2);

Create landmark factors for the second and third landmark points, as well, relating them to the second and third pose nodes and third and fourth pose nodes, respectively. Use the exampleHelperAddNoiseAndAddToFactorGraph helper function to add noise to the measurement for each landmark factor and add the factors to the factor graph. Once you have added all landmark factors to the factor graph, the IDs of the pose nodes are 1, 2, 3, and 4, and the IDs of the landmark nodes are 5, 6, and 7.

% Landmark 2 Factors
lmf3 = factorPoseSE3AndPointXYZ([2 6],Measurement=landmarks(2,:)-realpos(2,:));
lmf4 = factorPoseSE3AndPointXYZ([3 6],Measurement=landmarks(2,:)-realpos(3,:));

% Landmark 3 Factors
lmf5 = factorPoseSE3AndPointXYZ([3 7],Measurement=landmarks(3,:)-realpos(3,:));
lmf6 = factorPoseSE3AndPointXYZ([4 7],Measurement=landmarks(3,:)-realpos(4,:));

exampleHelperAddNoiseAndAddToFactorGraph(fg,[lmf3 lmf4 lmf5 lmf6])

Use relative pose factors to relate consecutive poses, and add the factors to the factor graph. To simulate sensor readings for the measurements of each factor, take the difference between a consecutive pair of ground truth positions, append a quaternion of zero, and add noise.

zeroQuat = [1 0 0 0];
rp1 = factorTwoPoseSE3([1 2],Measurement=[realpos(2,:)-realpos(1,:) zeroQuat]);
rp2 = factorTwoPoseSE3([2 3],Measurement=[realpos(3,:)-realpos(2,:) zeroQuat]);
rp3 = factorTwoPoseSE3([3 4],Measurement=[realpos(4,:)-realpos(3,:) zeroQuat]);
exampleHelperAddNoiseAndAddToFactorGraph(fg,[rp1 rp2 rp3])

Optimize Factor Graph

Optimize the factor graph with the default solver options. The optimization updates the states of all nodes in the factor graph, so the positions of vehicle and the landmarks update.

fgso = factorGraphSolverOptions;
optimize(fg,fgso)

ans = struct with fields:
             InitialCost: 71.6462
               FinalCost: 0.0140
      NumSuccessfulSteps: 5
    NumUnsuccessfulSteps: 0
               TotalTime: 0.0328
         TerminationType: 0
        IsSolutionUsable: 1

Visualize and Compare Results

Get and store the updated node states for the vehicle and landmarks and plot the results, comparing the factor graph estimate of the robot path to the known ground truth of the robot.

fgposopt = [fg.nodeState(1); fg.nodeState(2); fg.nodeState(3); fg.nodeState(4)]

fgposopt = 4×7

   -0.0000    0.0000   -0.0000    1.0000   -0.0000    0.0000    0.0000
    2.0529   -2.0006    0.0528    0.9991    0.0415    0.0115    0.0053
    5.0501    3.0537    0.3775    0.9980    0.0569    0.0210    0.0197
   10.0939    2.3060    0.0984    0.9883    0.1423    0.0465    0.0274

fglmopt = [fg.nodeState(5); fg.nodeState(6); fg.nodeState(7)]

fglmopt = 3×3

    0.0753   -2.9889    0.0527
    3.0294    4.0345    0.5962
    7.1825    1.2102    0.1122

exampleHelperPlotPositionsAndLandmarks(realpos,landmarks,fgposopt,fglmopt)