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Optimize pose graph and remove bad loop closures


poseGraphUpdated = trimLoopClosures(poseGraphObj,trimParams,solverOptions) optimizes the pose graph to best satisfy the edge constrains and removes any bad loop closure edges based on the residual error parameters specified in trimParams. Create the solverOptions input using the poseGraphSolverOptions function.

The function implements the graduated non-convexity (GNC) method with truncated least squares (TLS) robust cost in combination with the non-minimal pose graph solver [1].


[poseGraphUpdated,trimInfo] = trimLoopClosures(poseGraphObj,trimParams,solverOptions) returns additional information related to the trimming process.


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Optimize a pose graph based on the nodes and edge constraints. Trim loop closed based on their edge residual errors.

Load the data set that contains a 2-D pose graph. Inspect the poseGraph object to view the number of nodes and loop closures.

load grid-2d-posegraph.mat pg
  poseGraph with properties:

               NumNodes: 120
               NumEdges: 193
    NumLoopClosureEdges: 74
     LoopClosureEdgeIDs: [1x74 double]
        LandmarkNodeIDs: [1x0 double]

Plot the pose graph with IDs off. Red lines indicate loop closures identified in the dataset. The poses in the graph should follow a grid pattern, but show evidence of drift over time.

title('Original Pose Graph')

Figure contains an axes. The axes with title Original Pose Graph contains 3 objects of type line.

Optimize the pose grap using the optimizePoseGraph function. By default, this function uses the "builtin-trust-region" solver. Because the pose graph contains some bad loop closures, the resulting pose graph is actual not desirable.

pgOptim = optimizePoseGraph(pg);

Figure contains an axes. The axes contains 225 objects of type line, text.

Look at the edge residual errors for the original pose graph. Large outlier error values at the end indicate bad loop closures.

resErrorVec = edgeResidualErrors(pg);
title('Edge Residual Errors by Edge ID')

Figure contains an axes. The axes with title Edge Residual Errors by Edge ID contains an object of type line.

Certain loop closures should be trimmed from the pose graph based on their residual error. Use the trimLoopClosures function to trim therse bad loop closures. Set the maximum and truncation threshold for the trimmer parameters. This threshold is set based on the measurement accuracy and should be tuned for your system.

trimParams.MaxIterations = 100;
trimParams.TruncationThreshold = 25;

solverOptions = poseGraphSolverOptions; 

Use the trimLoopClosures function with the trimmer parameters and solver options.

[pgNew, trimInfo, debugInfo] = trimLoopClosures(pg,trimParams,solverOptions);

From the trimInfo output, plot the loop closures removed from the optimized pose graph. By plotting with the residual errors plot before, you can see the large error loop closures were removed.

removedLCs = trimInfo.LoopClosuresToRemove;

hold on
title('Edge Residual Errors and Removed Loop Closures')
legend('Residual Errors', 'Removed Loop Closures')
xlabel('Edge IDs')
ylabel('Edge Residual Error')
hold off

Figure contains an axes. The axes with title Edge Residual Errors and Removed Loop Closures contains 45 objects of type line. These objects represent Residual Errors, Removed Loop Closures.

Show the new pose graph with the bad loop closures trimmed.


Figure contains an axes. The axes contains 3 objects of type line.

Input Arguments

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Pose graph, specified as a poseGraph or poseGraph3D object.

Residual error parameters for trimming loop closures, specified as a structure with fields:

  • MaxIterations — Maximum number of iterations allowed for loop closure trimming, specified as a positive integer. In one trimming iteration, the pose graph is optimized based on the solver options and any edges outside the TruncationThreshold are trimmed.

  • TruncationThreshold — Maximum allowed residual error for an edge. This value depends heavily on the pose graph you specify in poseGraphObj. To find a proper threshold based on all the errors, use the edgeResidualErrors function for the pose graph.

Example: struct('MaxIterations',10,'TruncationThreshold',20)

Data Types: struct

Pose graph solver options, specified as a set of parameters generated by calling the poseGraphSolverOptions function. The function generates a set of solver options with default values for the specified pose graph solver type:

pgSolverTrustRegion = poseGraphSolverOptions('builtin-trust-region')
pgSolverTrustRegion = 

TrustRegion (builtin-trust-region-dogleg) options:

               MaxIterations: 300
                     MaxTime: 10
           FunctionTolerance: 1.0000e-08
           GradientTolerance: 5.0000e-09
               StepTolerance: 1.0000e-12
    InitialTrustRegionRadius: 100
               VerboseOutput: 'off'
pgSolverG2o = poseGraphSolverOptions('g2o-levenberg-marquardt')
pgSolverG2o = 

G2oLevenbergMarquardt (g2o-levenberg-marquardt) options:

        MaxIterations: 300
              MaxTime: 10
    FunctionTolerance: 1.0000e-09
        VerboseOutput: 'off'

Modify the options to tune the solver parameters using dot notation.

pgSolverG2o.MaxIterations = 200;

Output Arguments

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Pose graph with trimmed looped closures, specified as a poseGraph or poseGraph3D object.

Information from trimming process, returned as a structure with fields:

  • LoopClosuresToRemove — Loop closure edge IDs to remove from the input poseGraphObj. These loop closures are removed in the output poseGraphUpdated.

  • Iterations — Number of trimming iterations performed.


[1] Yang, Heng, et al. “Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection.” IEEE Robotics and Automation Letters, vol. 5, no. 2, Apr. 2020, pp. 1127–34. (Crossref), doi:10.1109/LRA.2020.2965893.

Introduced in R2020b