# factorPoseSE2AndPointXY

## Description

The `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 `factorGraph`

object.

## Creation

### Description

creates a `F`

= factorPoseSE2AndPointXY(`nodeID`

)`factorPoseSE2AndPointXY`

object, `F`

, with
the node identification numbers property `NodeID`

set to
`nodeID`

.

specifies properties using one or more name-value arguments in addition to the argument
from the previous syntax. For example, `F`

= factorPoseSE2AndPointXY(___,`Name=Value`

)```
factorPoseSE2AndPointXY([1
2],Measurement=[1 5])
```

sets the `Measurement`

property of
the `factorPoseSE2AndPointXY`

object to `[1 5]`

.

## Properties

`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
type `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

*N*,2)

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
`NodeID`

.

If you specify this property as a 2-by-2 matrix when `NodeID`

contains more than one row, the information matrix corresponds to all measurements in
`Measurement`

.

This information matrix is the inverse of the covariance matrix, where the covariance matrix is of the form:

$$\left[\begin{array}{cc}\sigma (x,x)& \sigma (x,y)\\ \sigma (y,x)& \sigma (y,y)\end{array}\right]$$

Each element indicates the covariance between two variables. For
example, *σ(x,y)* is the covariance between *x* and
*y*.

## Object Functions

`nodeType` | Get node type of node in factor graph |

## Examples

### 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);

Create the `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");`

Because the `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.

nodeState(fg,poseIDs,predictedState);

Fix the first pose node. Because the nodes are all relative to each other, they need a known state to be an anchor.

fixNode(fg,0);

**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.

## More About

### 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 |
---|---|

`factorGPS` | `["POSE_SE3"]` |

`factorIMU` | `["POSE_SE3","VEL3","IMU_BIAS","POSE_SE3","VEL3","IMU_BIAS"]` |

`factorCameraSE3AndPointXYZ` | `["POSE_SE3","POINT_XYZ"]` |

`factorPoseSE2AndPointXY` | `["POSE_SE2","POINT_XY"]` |

`factorPoseSE3AndPointXYZ` | `["POSE_SE3","POINT_XYZ"]` |

`factorTwoPoseSE2` | `["POSE_SE2","POSE_SE2"]` |

`factorTwoPoseSE3` | `["POSE_SE3","POSE_SE3"]` |

`factorIMUBiasPrior` | `["IMU_BIAS"]` |

`factorPoseSE3Prior` | `["POSE_SE3"]` |

`factorVelocity3Prior` | `["VEL_3"]` |

For example, `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 `"POSE_SE2"`

and `"POINT_XY"`

, respectively.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

## Version History

**Introduced in R2022b**

### R2023a: Specify multiple factors

The `NodeID`

, `Measurement`

, and
`Information`

properties now accept additional rows to specify
multiple factors.

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