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Multibody Robot, compilation and simulation performance

This is a Multibody.jl model of a 6-axis industrial robot with 6 revolute joints. The first three joints are modeled as flexible. The robot is tracking a smooth, predefined reference trajectory.

cd(@__DIR__)
using Pkg
Pkg.activate(".")

using ModelingToolkit
using Multibody
using Multibody: Robot6DOF
using JuliaSimCompiler
using OrdinaryDiffEq
using CairoMakie
using Printf

Setup

time_instantiate = @elapsed @named robot = Robot6DOF()
robot = complete(robot)
time_simplify = @elapsed ssys = structural_simplify(IRSystem(robot))
const C = JuliaSimCompiler.CTarget();
const LLVM = JuliaSimCompiler.llvm.LLVMTarget();
labels = ["Instantiate", "Simplify", "Problem creation", "Solve", "Extract data"]
const u0 = [
        robot.mechanics.r1.phi => deg2rad(-60)
        robot.mechanics.r2.phi => deg2rad(20)
        robot.mechanics.r3.phi => deg2rad(90)
        robot.mechanics.r4.phi => deg2rad(0)
        robot.mechanics.r5.phi => deg2rad(-110)
        robot.mechanics.r6.phi => deg2rad(0)
        robot.axis1.motor.Jmotor.phi => deg2rad(-60) * (-105) 
        robot.axis2.motor.Jmotor.phi => deg2rad(20) * (210)
        robot.axis3.motor.Jmotor.phi => deg2rad(90) * (60)
    ]
const tspan = (0.0, 4.0)
(0.0, 4.0)

Backend Benchmark Definition

function julia_multibody_timings(ssys, target)
    time_prob = @elapsed prob = if target === JuliaSimCompiler.JuliaTarget()
        ODEProblem(ssys, u0, tspan)
    else
        ODEProblem(ssys, target, u0, tspan)
    end
    time_solve = @elapsed sol = solve(prob, Rodas5P(autodiff=false)); # With autodiff=true this takes over 150 seconds
    
    tv = 0:0.01:4
    time_extract_data = @elapsed data = sol(tv, idxs=[
        robot.pathPlanning.controlBus.axisControlBus1.angle
        robot.pathPlanning.controlBus.axisControlBus2.angle
        robot.pathPlanning.controlBus.axisControlBus3.angle
        robot.pathPlanning.controlBus.axisControlBus4.angle
        robot.pathPlanning.controlBus.axisControlBus5.angle
        robot.pathPlanning.controlBus.axisControlBus6.angle
        robot.mechanics.r1.phi
        robot.mechanics.r2.phi
        robot.mechanics.r3.phi
        robot.mechanics.r4.phi
        robot.mechanics.r5.phi
        robot.mechanics.r6.phi
        robot.axis1.controller.feedback1.output.u
        robot.axis2.controller.feedback1.output.u
        robot.axis3.controller.feedback1.output.u
        robot.axis4.controller.feedback1.output.u
        robot.axis5.controller.feedback1.output.u
        robot.axis6.controller.feedback1.output.u
    ]);
    timings = [time_instantiate, time_simplify, time_prob, time_solve, time_extract_data]
end
julia_multibody_timings (generic function with 1 method)
julia_timings = julia_multibody_timings(ssys, JuliaSimCompiler.JuliaTarget())

f = Figure()
xs = 1:length(labels)
points = Makie.Point.(xs .- 0.25, julia_timings .+ 1)
anns = [@sprintf("%3.3g", t) for t in julia_timings]
barplot(f[1,1], julia_timings, axis=(; title="Julia Backend Timings", xticks = (xs, labels), limits = (nothing, (0, maximum(julia_timings)*1.2 + 2))))
annotations!(f[1,1], anns, points)
barplot(f[2,1], julia_timings, axis=(; title="Log Timings", xticks = (xs, labels), yscale=log10))
f

llvm_timings = julia_multibody_timings(ssys, LLVM)

f = Figure()
xs = 1:length(labels)
points = Makie.Point.(xs .- 0.25, llvm_timings .+ 1)
anns = [@sprintf("%3.3g", t) for t in llvm_timings]
barplot(f[1,1], llvm_timings, axis=(; title="LLVM Backend Timings", xticks = (xs, labels), limits = (nothing, (0, maximum(llvm_timings)*1.2 + 2))))
annotations!(f[1,1], anns, points)
barplot(f[2,1], llvm_timings, axis=(; title="Log Timings", xticks = (xs, labels), yscale=log10))
f

c_timings = julia_multibody_timings(ssys, C)

f = Figure()
xs = 1:length(labels)
points = Makie.Point.(xs .- 0.25, c_timings .+ 1)
anns = [@sprintf("%3.3g", t) for t in c_timings]
barplot(f[1,1], c_timings, axis=(; title="C Backend Timings", xticks = (xs, labels), limits = (nothing, (0, maximum(c_timings)*1.2 + 2))))
annotations!(f[1,1], anns, points)
barplot(f[2,1], c_timings, axis=(; title="Log Timings", xticks = (xs, labels), yscale=log10))
f
Error: AssertionError: _is_scalar(x) && _is_scalar(y)

Since the C backend currently errors, it's omitted from the total timings.

OpenModelica

using OMJulia
mod = OMJulia.OMCSession();
OMJulia.sendExpression(mod, "getVersion()")
OMJulia.sendExpression(mod, "installPackage(Modelica)")

@show "Start OpenModelica Timings"

om_total = @elapsed begin
    om_build = @elapsed ModelicaSystem(mod, modelName="Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.FullRobot", library="Modelica")
    om_sim = @elapsed res = sendExpression(mod, "simulate(Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.FullRobot)")
end
@assert res["messages"][1:11] == "LOG_SUCCESS"

OMJulia.quit(mod)
"Start OpenModelica Timings" = "Start OpenModelica Timings"

Comparison

colors = Makie.wong_colors()
labels = ["Build", "Simulate", "Total"]
julia_build = sum(julia_timings[1:3])
julia_sim = sum(julia_timings[4:5])
julia_total = julia_build + julia_sim

llvm_build = sum(llvm_timings[1:3])
llvm_sim = sum(llvm_timings[4:5])
llvm_total = llvm_build + llvm_sim

# c_build = sum(c_timings[1:3])
# c_sim = sum(c_timings[4:5])
# c_total = c_build + c_sim

dymola_build = sum([5.075, 3.912, 4.024])/3
dymola_total = sum([5.267, 4.112, 4.255])/3
dymola_sim = dymola_total - dymola_build

data = [
    julia_build julia_sim julia_total
    llvm_build llvm_sim llvm_total
    # c_build c_sim c_total
    om_build om_sim om_total
    dymola_build dymola_sim dymola_total
]

xs = repeat(1:length(labels), inner=4)
group = repeat([1,2,3,4], outer=3)
fig = Figure()
barplot(fig[1,1], xs, vec(data), dodge=group, color=colors[group], axis=(; title="Timings", xticks = ([1,2,3], labels)))

# Legend
legendentries = ["Julia Backend", "LLVM Backend", #= "C Backend", =# "OpenModelica", "Dymola"]
elements = [PolyElement(polycolor = colors[i]) for i in 1:length(legendentries)]
title = "Contestants"

Legend(fig[1,2], elements, legendentries, title)
fig

Appendix

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/ModelingToolkit","Multibody_Robot.jmd")

Computer Information:

Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores)
Environment:
  JULIA_CPU_THREADS = 128
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953
  JULIA_PKG_SERVER = juliahub.com

Package Information:

Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/ModelingToolkit/Project.toml`
  [6e4b80f9] BenchmarkTools v1.5.0
  [336ed68f] CSV v0.10.14
⌅ [13f3f980] CairoMakie v0.11.11
  [a93c6f00] DataFrames v1.6.1
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⌅ [0c5d862f] Symbolics v5.36.0
  [de0858da] Printf
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

And the full manifest:

Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/ModelingToolkit/Manifest.toml`
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  [2efcf032] SymbolicIndexingInterface v0.3.28
⌃ [19f23fe9] SymbolicLimits v0.2.1
⌅ [d1185830] SymbolicUtils v2.1.2
⌅ [0c5d862f] Symbolics v5.36.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.4.1
  [8290d209] ThreadingUtilities v0.5.2
  [731e570b] TiffImages v0.10.0
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.2
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [a7c27f48] Unityper v0.1.6
  [3d5dd08c] VectorizationBase v0.21.70
  [81def892] VersionParsing v1.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [44d3d7a6] Weave v0.10.12
  [efce3f68] WoodburyMatrices v1.0.0
  [76eceee3] WorkerUtilities v1.6.1
  [ddb6d928] YAML v0.4.12
  [c2297ded] ZMQ v1.3.0
  [6e34b625] Bzip2_jll v1.0.8+1
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.0+2
  [5ae413db] EarCut_jll v2.2.4+0
  [2e619515] Expat_jll v2.6.2+0
  [b22a6f82] FFMPEG_jll v6.1.1+0
  [f5851436] FFTW_jll v3.3.10+0
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.44.0+2
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [905a6f67] Imath_jll v3.1.11+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [dad2f222] LLVMExtra_jll v0.0.29+0
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [dd4b983a] LZO_jll v2.10.2+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [18a262bb] OpenEXR_jll v3.2.4+0
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [36c8627f] Pango_jll v1.52.2+0
  [30392449] Pixman_jll v0.43.4+0
  [f50d1b31] Rmath_jll v0.4.3+0
  [02c8fc9c] XML2_jll v2.13.1+0
  [aed1982a] XSLT_jll v1.1.41+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [8f1865be] ZeroMQ_jll v4.3.5+0
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [b53b4c65] libpng_jll v1.6.43+1
  [075b6546] libsixel_jll v1.10.3+0
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [8bf52ea8] CRC32c
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`