Rible.jl

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Control Hub ​

If Structure describes the robot's "body" — the musculoskeletal system — then ControlHub defines its "nervous system": it specifies what the robot can sense and what it can actuate.

  1. Sensing via Gauges: Gauges define how to extract feature vectors from the complex physical state (coordinates, velocities) for feedback control policies or value functions.

  2. Actuate via Actuators: define how to transform abstract control commands into generalized forces in the physical system.

This architecture allows the same physical model to seamlessly work with different control interfaces, facilitating control algorithm implementations.

2. Actuators ​

All actuators inherit from the abstract type AbstractActuator. An actuator's responsibility is to map the actions to forces applied in the physical system.

  • ExternalForceActuator: the most commonly used concrete implementation, for applying forces or torques at a specific Locus on a body.

Actuator behavior is defined through the following functions:

  • actuate!(bot, policy, state): Top-level entry point. Computes the actions for the entire robot based on the current policy and triggers all sub-actuators.

  • execute!(structure, actuator, u): Executes a single actuator, converting action u to generalized forces and accumulating them into the system force vector.

  • gen_force_actu_jacobian!(∂F∂u, structure, actuator, u): Computes the Jacobian of the generated generalized forces with respect to actions u. This is the foundation for adjoint computations.

3. Gauges ​

Gauges define how the robot observes itself and its environment. All gauges inherit from AbstractGauge.

Captum Gauges vs. Error Gauges ​

To serve both feedback control and optimization solving, Rible classifies gauges into two categories:

CaptumGauge ​

CaptumGauge retrieves raw feedback signals. It is typically fed to a policy function or used for state monitoring.

  • Composition: a Signifier (pointing to a body locus) and a Captum (e.g., PositionCaptum).

  • Output: typically a vector (e.g., a 3D position vector).

Error Gauge ​

ErrorGauge introduces a reference value on top of the observation. It directly computes the deviation between the current state and the reference.

  • Mathematical form: typically computes a weighted squared error

  • Output: a scalar.

  • Usage: ErrorGauge is the atomic building block for constructing Objectives (cost functions for trajectory optimization).

Core Interface: Measurement ​

Gauge computation revolves around the following interface:

  • measure!(out, st, sig, cap): Writes physical attributes (e.g., position or velocity at a specific locus) directly into the output buffer out, based on the concrete Signifier and Captum types.

  • measure_jacobian!(Jq, Jv, Js, st, sig, cap): Computes the Jacobian of the measurement with respect to system generalized coordinates , velocities , and auxiliary variables .

4. Example: Building a Simple Cart-Pole ​

The following demonstrates how to build a ControlHub for a simplified cart-pole system.

Step 1: Physical Structure Setup ​

First, create a physical structure (Structure) for the robot. In this example, we define a cart with a pole.

julia
using Rible
using StaticArrays
using LinearAlgebra
import TypeSortedCollections as TSC

# Physical structure setup (cart, L=1.0)
l = 1.0
mass_locus = Locus(@SVector zeros(3))
loci = [Locus(@SVector zeros(3)), Locus(SVector(0.0, l, 0.0))]
prop_cart = RigidBodyProperty(1, true, 1.0, SMatrix{3,3,Float64}(I), mass_locus, loci)
prop_pole = RigidBodyProperty(2, true, 0.5, SMatrix{3,3,Float64}(I), mass_locus, loci)

cart = RigidBody(prop_cart, RigidBodyState(prop_cart, zeros(3), SMatrix{3,3,Float64}(I), zeros(3), zeros(3)), NC1P3V(zeros(3), zeros(3), SMatrix{3,3,Float64}(I)), nothing)
pole = RigidBody(prop_pole, RigidBodyState(prop_pole, SVector(0.0, l/2, 0.0), SMatrix{3,3,Float64}(I), zeros(3), zeros(3)), NC1P3V(SVector(0.0, l/2, 0.0), SVector(0.0, l/2, 0.0), SMatrix{3,3,Float64}(I)), nothing)

bodies = TSC.TypeSortedCollection([cart, pole])
apparatuses = TSC.TypeSortedCollection(Int[])
st_obj = Structure(bodies, apparatuses, Connectivity(bodies, apparatuses))
Structure{TypeSortedCollections.TypeSortedCollection{Tuple{Vector{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}}, 1}, TypeSortedCollections.TypeSortedCollection{Tuple{}, 0}, Connectivity{Vector{Vector{Int64}}}, Rible.StructureState{CoordinatesState{Float64, Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}}, Vector{CoordinatesState{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, Vector{Float64}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}}}, @NamedTuple{activated_bits::BitVector, persistent_bits::BitVector, friction_coefficients::Vector{Float64}, restitution_coefficients::Vector{Float64}, gaps::Vector{Float64}}, Rible.StructureCache{InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseVector{Float64, Int64}}}}(3, TypeSortedCollections.TypeSortedCollection{Tuple{Vector{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}}, 1}((RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}[RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}(RigidBodyProperty{3, Float64, 9}(true, true, 1, :generic, 1.0, [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}[Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0)]), RigidBodyState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}[Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0])]), NC{3, 3, Float64, 9, 12, 144}(1, 3, LNCData{3, 3, Float64, 9}([0.0, 0.0, 0.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [1 0 … 0 0; 0 1 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], LinearAlgebra.Symmetric{Int64, SparseArrays.SparseMatrixCSC{Int64, Int64}}[[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 2 0; 0 0 … 0 2], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0]], 6, [1, 2, 3, 4, 5, 6]), RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}([1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], StaticArraysCore.SMatrix{3, 12, Float64, 36}[[1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]], InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}(sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1.0, 1.0, 1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 12, 12), sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], false), [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]), nothing), RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}(RigidBodyProperty{3, Float64, 9}(true, true, 2, :generic, 0.5, [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}[Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0)]), RigidBodyState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}[Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 1.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0])]), NC{3, 3, Float64, 9, 12, 144}(1, 3, LNCData{3, 3, Float64, 9}([0.0, 0.0, 0.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [1 0 … 0 0; 0 1 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], LinearAlgebra.Symmetric{Int64, SparseArrays.SparseMatrixCSC{Int64, Int64}}[[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 2 0; 0 0 … 0 2], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0]], 6, [1, 2, 3, 4, 5, 6]), RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}([1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], StaticArraysCore.SMatrix{3, 12, Float64, 36}[[1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]], InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}(sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 12, 12), sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], false), [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]), nothing)],), ([1, 2],)), TypeSortedCollections.TypeSortedCollection{Tuple{}, 0}((), ()), Connectivity{Vector{Vector{Int64}}}(2, 0, 0, 0, 24, 12, 0, 12, 12, 12, 0, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]], [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]], [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]], Vector{Int64}[], Vector{Int64}[], [[1, 2], [3, 4]], Signifier{Int64}[Signifier{Int64}(1, 1), Signifier{Int64}(1, 2), Signifier{Int64}(2, 1), Signifier{Int64}(2, 2)], [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]], 5, 12, 12, 0, 12, Vector{Int64}[], Vector{Int64}[]), Rible.StructureState{CoordinatesState{Float64, Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}}, Vector{CoordinatesState{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, Vector{Float64}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}}}(CoordinatesState{Float64, Vector{Float64}, Vector{Float64}, Vector{Float64}, Vector{Float64}}(0.0, [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0  …  0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float64[], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), CoordinatesState{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, Vector{Float64}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}[CoordinatesState{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, Vector{Float64}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}(0.0, [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float64[], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), CoordinatesState{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, Vector{Float64}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}(0.0, [0.0, 0.5, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float64[], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0])]), (activated_bits = Bool[0, 0, 0, 0], persistent_bits = Bool[0, 0, 0, 0], friction_coefficients = [0.0, 0.0, 0.0, 0.0], restitution_coefficients = [0.0, 0.0, 0.0, 0.0], gaps = [Inf, Inf, Inf, Inf]), Rible.StructureCache{InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseVector{Float64, Int64}}}(InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseVector{Float64, Int64}}(sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [1.0, 1.0, 1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5  …  0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 24, 24), sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0  …  2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], 24, 24), sparse(Int64[], Int64[], Float64[], 24, 24), sparse(Int64[], Int64[], Float64[], 24, 24), sparsevec(Int64[], Float64[], 24), sparsevec(Int64[], Float64[], 24), true)))

Step 2: Define Gauges ​

Next, define two types of gauges: one for observing the cart's state, and one for measuring the pole's position error.

julia
# Define gauges: observation (Captum) and error (Error)
cart_captum = CaptumGauge(1, Signifier(cart, 1), PosVelCaptum())
pole_pos_error = ErrorGauge(1, Signifier(pole, 2), PositionCaptum(), [0.0, l, 0.0])

capta_gauges = TSC.TypeSortedCollection([cart_captum])
error_gauges = TSC.TypeSortedCollection([pole_pos_error])
TypeSortedCollections.TypeSortedCollection{Tuple{Vector{ErrorGauge{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, PositionCaptum, Vector{Float64}}}}, 1}((ErrorGauge{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, PositionCaptum, Vector{Float64}}[ErrorGauge{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, PositionCaptum, Vector{Float64}}(1, Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}(RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}(RigidBodyProperty{3, Float64, 9}(true, true, 2, :generic, 0.5, [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}[Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0)]), RigidBodyState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}[Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 1.5, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0])]), NC{3, 3, Float64, 9, 12, 144}(1, 3, LNCData{3, 3, Float64, 9}([0.0, 0.0, 0.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [1 0 … 0 0; 0 1 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], LinearAlgebra.Symmetric{Int64, SparseArrays.SparseMatrixCSC{Int64, Int64}}[[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 2 0; 0 0 … 0 2], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0]], 6, [1, 2, 3, 4, 5, 6]), RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}([1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], StaticArraysCore.SMatrix{3, 12, Float64, 36}[[1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]], InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}(sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 12, 12), sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], false), [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]), nothing), 2), PositionCaptum(), [0.0, 1.0, 0.0])],), ([1],))

Step 3: Define Actuators ​

Actuators define how action values affect the physical system. Here we define an actuator that applies a horizontal push force on the cart.

julia
# Define actuator: horizontal push force
force_actuator = ExternalForceActuator(
    1, Signifier(cart, 1), NaiveOperator(1), [0; 1.0; 0;;], [0.0]
)
actuators = TSC.TypeSortedCollection([force_actuator])
TypeSortedCollections.TypeSortedCollection{Tuple{Vector{ExternalForceActuator{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, NaiveOperator, Matrix{Float64}, Float64}}}, 1}((ExternalForceActuator{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, NaiveOperator, Matrix{Float64}, Float64}[ExternalForceActuator{Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}, NaiveOperator, Matrix{Float64}, Float64}(1, Signifier{RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}}(RigidBody{3, 3, Float64, 9, NC{3, 3, Float64, 9, 12, 144}, RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}, Nothing}(RigidBodyProperty{3, Float64, 9}(true, true, 1, :generic, 1.0, [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}[Locus{3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0), Locus{3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), 0.0, 0.0)]), RigidBodyState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}[Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 0.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0]), Rible.LocusState{3, 3, Float64, 9}(Rible.CartesianFrame{3, 3, Float64, 9}([0.0, 1.0, 0.0], Rible.Axes{3, Float64, 9}([0.0 0.0 1.0; 1.0 0.0 0.0; 0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0], Rible.ContactState{3, Float64, 9}(false, true, Inf, Rible.Axes{3, Float64, 9}([-0.0 -0.0 1.0; 1.0 -0.0 0.0; -0.0 1.0 0.0]), [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]), [1.0, 0.0, 0.0])]), NC{3, 3, Float64, 9, 12, 144}(1, 3, LNCData{3, 3, Float64, 9}([0.0, 0.0, 0.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]), [1 0 … 0 0; 0 1 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 1 0; 0 0 … 0 1], LinearAlgebra.Symmetric{Int64, SparseArrays.SparseMatrixCSC{Int64, Int64}}[[0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 2 0; 0 0 … 0 2], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0], [0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 0 0; 0 0 … 0 0]], 6, [1, 2, 3, 4, 5, 6]), RigidBodyCache{StaticArraysCore.SMatrix{3, 12, Float64, 36}, InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}, StaticArraysCore.MMatrix{6, 12, Float64, 72}}([1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], StaticArraysCore.SMatrix{3, 12, Float64, 36}[[1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]], InertiaCache{SparseArrays.SparseMatrixCSC{Float64, Int64}, SparseArrays.SparseMatrixCSC{Float64, Int64}, StaticArraysCore.MVector{12, Float64}}(sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1.0, 1.0, 1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 12, 12), sparse([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), sparse(Int64[], Int64[], Float64[], 12, 12), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], false), [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]), nothing), 1), NaiveOperator(1), [0.0; 1.0; 0.0;;], [0.0])],), ([1],))

Step 4: Assemble the Hub and Measure ​

Finally, assemble all components into a ControlHub and demonstrate measurement.

julia
# Assemble Hub and measure
coalition = Coalition(st_obj, capta_gauges, error_gauges, actuators)
hub = ControlHub(st_obj, capta_gauges, error_gauges, actuators, coalition)

# Execute measurements
c = measure(st_obj, cart_captum)
e = measure(st_obj, pole_pos_error)
(c, e)
([0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 0.125)