Factor relating SE(2) position and 2-D point
factorPoseSE2AndPointXY object contains factors that each describe the
relationship between a position in the SE(2) state space and a 2-D landmark point. You can use
this object to add one or more factors to a
F = factorPoseSE2AndPointXY(
the node identification numbers property
NodeID set to
specifies properties using one or more name-value arguments in addition to the argument
from the previous syntax. For example,
F = factorPoseSE2AndPointXY(___,
2],Measurement=[1 5]) sets the
Measurement property of
factorPoseSE2AndPointXY object to
NodeID — Node ID numbers
N-by-2 matrix of nonnegative integers
This property is read-only.
Node ID numbers, specified as an N-by-2 matrix of nonnegative
integers, where N is the total number of desired factors. Each row
represents a factor connecting a node of type,
POSE_SE2 to a node of
POINT_XY in the form [PoseID
PointID], where PoseID is the ID of the
POSE_SE2 node and PointID is the ID of the
POINT_XY node in the factor graph.
If a factor in the
factorPoseSE2AndPointXY object specifies an ID that does not
correspond to a node in the factor graph, the factor graph automatically creates a node
of the required type with that ID and adds it to the factor graph when adding the factor
to the factor graph.
You must specify this property at object creation.
For more information about the expected node types of all supported factors, see Expected Node Types of Factor Objects.
Measurement — Measured relative position
zeros(N,2) (default) | N-by-2 matrix
Measured relative position between the current position and landmark point, specified as an N-by-2 matrix where each row is of the form [dx dy], in meters. N is the total number of factors, and dx and dy are the change in position in x and y, respectively.
Information — Information matrix associated with uncertainty of measurements
eye(2) (default) | 2-by-2 matrix | 2-by-2-by-N array
Information matrix associated with the uncertainty of the measurements, specified as
a 2-by-2 matrix or a 2-by-2-by-N array. N is the
total number of factors specified by the
factorPoseSE2AndPointXY object. Each
information matrix corresponds to the measurements of the corresponding node in
If you specify this property as a 2-by-2 matrix when
contains more than one row, the information matrix corresponds to all measurements in
This information matrix is the inverse of the covariance matrix, where the covariance matrix is of the form:
Each element indicates the covariance between two variables. For example, σ(x,y) is the covariance between x and y.
|Get node type of node in factor graph|
Estimate Poses Using 2-D Pose Factors
Define the ground truth for five robot poses as a loop and create a factor graph.
gndtruth = [0 0 0; 2 0 pi/2; 2 2 pi; 0 2 3*pi 0 0 0]; fg = factorGraph;
Generate the node IDs needed to create three
factorTwoPoseSE2 factors and then manually add the Because node 4 would coincide directly on top of the node 0, instead of specifying a factor that connects node 3 to a new node 4, create a loop closure by adding another factor that relates node 3 to node 0.
poseFIDs = generateNodeID(fg,3,"factorTwoPoseSE2"); poseFIDs = [poseFIDs; 3 0]
poseFIDs = 4×2 0 1 1 2 2 3 3 0
Define the relative measurement between each consecutive pose and add a little noise so the measurement is more like a sensor reading.
relMeasure = [2 0 pi/2; 2 0 pi/2; 2 0 pi/2; 2 0 pi/2] + 0.1*rand(4,3);
factorTwoPoseSE2 factors with the defined relative measurements and then add the factors to the factor graph.
poseFactor = factorTwoPoseSE2(poseFIDs,Measurement=relMeasure); addFactor(fg,poseFactor);
Get the node IDs of all of the SE2 pose nodes in the factor graph.
poseIDs = nodeIDs(fg,NodeType="POSE_SE2");
POSE_SE2 type nodes have a default state of
[0 0 0], you should provide an initial guess for the state. Normally this is from an odometry sensor on the robot. But for this example, use the ground truth with some noise.
predictedState = gndtruth(1:4,:); predictedState(2:4,:) = predictedState(2:4,:) + 0.1*rand(3,3);
Then set the states of the pose nodes to the predicted guess states.
Fix the first pose node. Because the nodes are all relative to each other, they need a known state to be an anchor.
Optimize Factor Graph and Visual Results
Optimize the factor graph with the default solver options. The optimization updates the states of all nodes in the factor graph so the poses of vehicle update.
rng default optimize(fg)
ans = struct with fields: InitialCost: 6.1614 FinalCost: 0.0118 NumSuccessfulSteps: 5 NumUnsuccessfulSteps: 0 TotalTime: 0.0081 TerminationType: 0 IsSolutionUsable: 1 OptimizedNodeIDs: [1 2 3] FixedNodeIDs: 0
Get and store the updated node states for the robot. Then plot the results, comparing the factor graph estimate of the robot path to the known ground truth of the robot.
poseStatesOpt = nodeState(fg,poseIDs)
poseStatesOpt = 4×3 0 0 0 2.0777 0.0689 1.5881 2.0280 2.1646 -3.1137 0.0132 2.0864 -1.6014
figure plot(gndtruth(:,1),gndtruth(:,2),Marker="*",LineWidth=1.5) hold on plot([poseStatesOpt(:,1); 0],[poseStatesOpt(:,2); 0],Marker="*",LineStyle="--",LineWidth=1); legend(["Ground Truth","Opt. Position"]); s2 = se2(poseStatesOpt,"xytheta"); plotTransforms(s2,FrameSize=0.5,FrameAxisLabels="on"); axis padded hold off
Note that the poses do not match perfectly with the ground truth because there are not many factors in this graph that the
optimize function can use to provide a more accurate solution. The accuracy can be improved by using more accurate measurements, accurate initial state guesses, and adding additional factors to add more information for the optimizer to use.
Expected Node Types of Factor Objects
These are the node types that the
NodeID property of each factor object specifies and connects to:
|Factor Object||Expected Node Types of Specified Node IDs|
factorPoseSE2AndPointXY([1 2]) creates a 2-D landmark factor connecting to node IDs 1 and 2. If you try to add that factor to a factor graph that already contains nodes 1 and 2, the factor expects nodes 1 and 2 to be of types
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Version HistoryIntroduced in R2022b
R2023a: Specify multiple factors
Information properties now accept additional rows to specify