factorGraph
Description
A factorGraph object stores a bipartite graph consisting of
factors connected to variable nodes. The nodes represent the unknown random variables in an
estimation problem, such as robot poses, and the factors represent probabilistic constraints
on those nodes, derived from measurements or prior knowledge. During optimization, the factor
graph uses all the factors and current node states to update the node states.
For more information about factor graph and how to use it, see Factor Graph for SLAM.
Creation
Syntax
Description
fg = factorGraphfactorGraph object.
Properties
Object Functions
Examples
Create a matrix of positions of the landmarks to use for localization, and the real poses of the robot to compare your factor graph estimate against. Use the exampleHelperPlotGroundTruth helper function to visualize the landmark points and the real path of the robot.
gndtruth = [0 0 0;
2 0 pi/2;
2 2 pi;
0 2 pi];
landmarks = [3 0; 0 3];
exampleHelperPlotGroundTruth(gndtruth,landmarks)
Use the exampleHelperSimpleFourPoseGraph helper function to create a factor graph contains four poses related by three 2-D two-pose factors. For more details, see the factorTwoPoseSE2 object page.
fg = exampleHelperSimpleFourPoseGraph(gndtruth);
Create Landmark Factors
Generate node IDs to create two node IDs for two landmarks. The second and third pose nodes observe the first landmark point so they should connect to that landmark with a factor. The third and fourth pose nodes observe the second landmark.
lmIDs = generateNodeID(fg,2); lmFIDs = [1 lmIDs(1); % Pose Node 1 <-> Landmark 1 2 lmIDs(1); % Pose Node 2 <-> Landmark 1 2 lmIDs(2); % Pose Node 2 <-> Landmark 2 3 lmIDs(2)]; % Pose Node 3 <-> Landmark 2
Define the relative position measurements between the position of the poses and their landmarks in the reference frame of the pose node. Then add some noise.
lmFMeasure = [0 -1; % Landmark 1 in pose node 1 reference frame -1 2; % Landmark 1 in pose node 2 reference frame 2 -1; % Landmark 2 in pose node 2 reference frame 0 -1]; % Landmark 2 in pose node 3 reference frame lmFMeasure = lmFMeasure + 0.1*rand(4,2);
Create the landmark factors with those relative measurements and add it to the factor graph.
lmFactor = factorPoseSE2AndPointXY(lmFIDs,Measurement=lmFMeasure); addFactor(fg,lmFactor);
Set the initial state of the landmark nodes to the real position of the landmarks with some noise.
nodeState(fg,lmIDs,landmarks+0.1*rand(2));
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.
rng default
optimize(fg)ans = struct with fields:
InitialCost: 0.0538
FinalCost: 6.2053e-04
NumSuccessfulSteps: 4
NumUnsuccessfulSteps: 0
TotalTime: 8.6100e-04
TerminationType: 0
IsSolutionUsable: 1
OptimizedNodeIDs: [1 2 3 4 5]
FixedNodeIDs: 0
Visualize and Compare Results
Get and store the updated node states for the robot and landmarks. Then plot the results, comparing the factor graph estimate of the robot path to the known ground truth of the robot.
poseIDs = nodeIDs(fg,NodeType="POSE_SE2")poseIDs = 1×4
0 1 2 3
poseStatesOpt = nodeState(fg,poseIDs)
poseStatesOpt = 4×3
0 0 0
2.0815 0.0913 1.5986
1.9509 2.1910 -3.0651
-0.0457 2.0354 -2.9792
landmarkStatesOpt = nodeState(fg,lmIDs)
landmarkStatesOpt = 2×2
3.0031 0.1844
-0.1893 2.9547
handle = show(fg,Orientation="on",OrientationFrameSize=0.5,Legend="on"); grid on; hold on; exampleHelperPlotGroundTruth(gndtruth,landmarks,handle);
More About
Tips
To specify multiple factors and nodes at once for a specific factor type, use the
generateNodeIDfunction and specify the number of factors and the factor type. See thegenerateNodeIDfunction for more details.poseIDPairs = generateNodeID(fg,3,"factorTwoPoseSE2"); ftpse2 = factorTwoPoseSE2(poseIDPairs);You can get the states of all the pose nodes by first using the
nodeIDsfunction and specifying the node type as"POSE_SE2"for SE(2) robot poses and"POSE_SE3"for SE(3) robot poses. Then, use thenodeStatefunction with those node IDs to get the node states of the robot pose nodes.poseIDs = nodeIDs(fg,NodeType="POSE_SE2"); poseStates = nodeState(fg,poseIDs);Check the types of nodes that each factor creates or connects to before adding factors to the factor graph to avoid node type mismatch errors. For a list of expected node types for each factor, see Expected Node Types of Factor Objects.
References
[1] Dellaert, Frank. Factor graphs and GTSAM: A Hands-On Introduction. Georgia: Georgia Tech, September, 2012.
