Help modeling attitude propagation using ModelingToolkit.jl


I am trying to model the attitude propagation with quaternions using ModelingToolkit.jl. I could make a very simple example as shown below:

using ModelingToolkit
using OrdinaryDiffEq
using ReferenceFrameRotations
using StaticArrays

function vectdquat(vq, w)
    q = Quaternion(vq)
    dq = dquat(q, w)
    return @SVector [dq[1], dq[2], dq[3], dq[4]]

@variables t vq[1:4](t) RHS[1:4](t)
@parameters w[1:3]
@register vectdquat(vq, w)
D = Differential(t)

@named att_prop = ODESystem(
    D.(vq) .~ vectdquat(vq, w),

prob = ODEProblem(
    [vq[1] => 1.0, vq[2] => 0.0, vq[3] => 0.0, vq[4] => 0.0],
    (0.0, 100.0),
    [w[1] => 0.05, w[2] => 0.0, w[3] => 0.0]

sol = solve(prob, Tsit5())

Now, I need to add a constraint equation to force the quaternion to be in a unit sphere. It is something like vq .~ vq ./ norm(vq). I tried extending the ODESystem, using a vector of equations (which does not seem to support variables that are vectors), and any other method I could find from the documentation. However, I always get an error when building the ODESystem. Can anyone help me?

That to me looks like an issue with symbolic array handling and worth an issue.

1 Like

I just opened the issue, thanks @ChrisRackauckas ! I am not sure if I opened in the right repository :slight_smile: