Variables in Caesar.jl

You can check for the latest variable types by running the following in your terminal:

using RoME, Caesar

The variables and factors in Caesar should be sufficient for a variety of robotic applications, however, users can easily extend the framework (without changing the core code). This can even be done out-of-library at runtime after a construction of a factor graph has started! See Custom Variables and Custom Factors for more details.

Basic Variables

Default variables in IncrementalInference

struct ContinuousScalar <: InferenceVariable

Most basic continuous scalar variable in a ::DFG.AbstractDFG object.


  • TODO Consolidate with ContinuousEuclid{1}

2D Variables

The current variables types are:

struct Point2 <: InferenceVariable

XY Euclidean manifold variable node softtype.

struct Pose2 <: InferenceVariable

Pose2 is a SE(2) mechanization of two Euclidean translations and one Circular rotation, used for general 2D SLAM.

struct DynPoint2 <: InferenceVariable

Dynamic point in 2D space with velocity components: x, y, dx/dt, dy/dt

struct DynPose2 <: InferenceVariable

Dynamic pose variable with velocity components: x, y, theta, dx/dt, dy/dt


  • The SE2E2_Manifold definition used currently is a hack to simplify the transition to Manifolds.jl, see #244
  • Replaced SE2E2_Manifold hack with ProductManifold(SpecialEuclidean(2), TranslationGroup(2)), confirm if it is correct.

3D Variables

struct Point3 <: InferenceVariable

XYZ Euclidean manifold variable node softtype.


p3 = Point3()
struct Pose3 <: InferenceVariable

Pose3 is currently a Euler angle mechanization of three Euclidean translations and three Circular rotation.


  • Work in progress on AMP3D for proper non-Euler angle on-manifold operations.
  • TODO the AMP upgrade is aimed at resolving 3D to Quat/SE3/SP3 – current Euler angles will be replaced
mutable struct InertialPose3 <: AbstractRelativeRoots

Inertial Odometry version of preintegration procedure and used as a factor between InertialPose3 types for inertial navigation in factor graphs.


Please open an issue with JuliaRobotics/RoME.jl for specific requests, problems, or suggestions. Contributions are also welcome. There might be more variable types in Caesar/RoME/IIF not yet documented here.

Factors in Caesar.jl

You can check for the latest factor types by running the following in your terminal:

using RoME, Caesar
println("- Singletons (priors): ")
println("- Pairwise (variable constraints): ")
println("- Pairwise (variable minimization constraints): ")

Priors (Absolute Data)

Defaults in IncrementalInference.jl:

struct Prior{T<:SamplableBelief} <: AbstractPrior

Default prior on all dimensions of a variable node in the factor graph. Prior is not recommended when non-Euclidean dimensions are used in variables.

struct PartialPrior{T<:SamplableBelief, P<:Tuple} <: AbstractPrior

Partial prior belief (absolute data) on any variable, given <:SamplableBelief and which dimensions of the intended variable.


  • If using AMP.ManifoldKernelDensity, don't double partial. Only define the partial in this PartialPrior container.
    • Future TBD, consider using AMP.getManifoldPartial for more general abstraction.

Some of the most common priors (unary factors) in Caesar.jl/RoME.jl include:

mutable struct PriorPolar{T1<:SamplableBelief, T2<:SamplableBelief} <: AbstractPrior

Prior belief on any Polar related variable.

mutable struct PriorPoint2{T<:SamplableBelief} <: AbstractPrior

Direction observation information of a Point2 variable.

Missing docstring.

Missing docstring for PriorPose2. Check Documenter's build log for details.

mutable struct PriorPoint3{T} <: AbstractPrior

Direction observation information of a Point3 variable.

struct PriorPose3{T<:SamplableBelief, P} <: AbstractPrior

Direct observation information of Pose3 variable type.

Relative Likelihoods (Relative Data)

Defaults in IncrementalInference.jl:

struct LinearRelative{N, T<:SamplableBelief} <: AbstractRelativeRoots

Default linear offset between two scalar variables.

\[X_2 = X_1 + η_Z\]

Existing n-ary factors in Caesar.jl/RoME.jl/IIF.jl include:

mutable struct PolarPolar{T1<:SamplableBelief, T2<:SamplableBelief} <: AbstractRelativeRoots

Linear offset factor of IIF.SamplableBelief between two Polar variables.

mutable struct Point2Point2{D<:SamplableBelief} <: AbstractRelativeRoots
struct Pose2Point2{T<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Bearing and Range constraint from a Pose2 to Point2 variable.

struct Pose2Point2Bearing{B<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Single dimension bearing constraint from Pose2 to Point2 variable.

mutable struct Pose2Point2BearingRange{B<:SamplableBelief, R<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Bearing and Range constraint from a Pose2 to Point2 variable.

mutable struct Pose2Point2Range{T<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Range only measurement from Pose2 to Point2 variable.

mutable struct VelPose2VelPose2{T1<:SamplableBelief, T2<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize
mutable struct DynPose2Pose2{T<:SamplableBelief} <: AbstractRelativeRoots
struct Pose3Pose3{T<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Rigid transform factor between two Pose3 compliant variables.

mutable struct PriorPose3ZRP{T1<:SamplableBelief, T2<:SamplableBelief} <: AbstractPrior

Partial prior belief on Z, Roll, and Pitch of a Pose3.

Missing docstring.

Missing docstring for PartialPriorRollPitchZ. Check Documenter's build log for details.

Missing docstring.

Missing docstring for PartialPose3XYYaw. Check Documenter's build log for details.

struct Pose3Pose3XYYaw{T<:SamplableBelief} <: IncrementalInference.AbstractManifoldMinimize

Partial factor between XY and Yaw of two Pose3 variables.

wR2 = wR1*1R2 = wR1*(1Rψ*Rθ*Rϕ)
wRz = wR1*1Rz
zRz = wRz \ wR(Δψ)

M_R = SO(3)
δ(α,β,γ) = vee(M_R, R_0, log(M_R, R_0, zRz))

M = SE(3)
p0 = identity_element(M)
δ(x,y,z,α,β,γ) = vee(M, p0, log(M, p0, zRz))

Extending Caesar with New Variables and Factors

A question that frequently arises is how to design custom variables and factors to solve a specific type of graph. One strength of Caesar is the ability to incorporate new variables and factors at will. Please refer to Adding Factors for more information on creating your own factors.