add robot benchmark

benchmarks/ModelingToolkit/Multibody_Robot.jmd

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+---
+title: Multibody Robot, compilation and simulation performance
+author: Fredrik Bagge Carlson
+---
+
+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.
+```julia
+cd(@__DIR__)
+using Pkg
+Pkg.activate(".")
+
+using ModelingToolkit
+using Multibody
+using Multibody: Robot6DOF
+using JuliaSimCompiler
+using OrdinaryDiffEq
+using CairoMakie
+using Printf
+
+time_instantiate = @elapsed @named robot = Robot6DOF()
+robot = complete(robot)
+time_simplify = @elapsed ssys = structural_simplify(IRSystem(robot))
+time_prob = @elapsed prob = ODEProblem(ssys, [
+    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)
+], (0.0, 4.0))
+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
+]);
+
+labels = ["Instantiate", "Simplify", "Problem creation", "Solve", "Extract data"]
+timings = [time_instantiate, time_simplify, time_prob, time_solve, time_extract_data]
+f = Figure()
+xs = 1:length(labels)
+points = Makie.Point.(xs .- 0.25, timings .+ 1)
+anns = [@sprintf("%3.3g", t) for t in timings]
+barplot(f[1,1], timings, axis=(; title="Timings", xticks = (xs, labels), limits = (nothing, (0, maximum(timings)*1.2 + 2))))
+
+annotations!(f[1,1], anns, points)
+barplot(f[2,1], timings, axis=(; title="Log Timings", xticks = (xs, labels), yscale=log10))
+f
+```
+
+## OpenModelica
+
+```julia
+using OMJulia
+mod = OMJulia.OMCSession();
+OMJulia.sendExpression(mod, "getVersion()")
+
+@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)
+```
+
+## Comparison
+```julia
+colors = Makie.wong_colors()
+labels = ["Build", "Simulate", "Total"]
+julia_build = time_instantiate + time_simplify + time_prob
+julia_sim = time_solve + time_extract_data
+julia_total = julia_build + julia_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
+    om_build om_sim om_total
+    dymola_build dymola_sim dymola_total
+]
+
+xs = repeat(1:length(labels), inner=3)
+group = repeat([1,2,3], 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", "OpenModelica", "Dymola"]
+elements = [PolyElement(polycolor = colors[i]) for i in 1:length(legendentries)]
+title = "Contestants"
+
+Legend(fig[1,2], elements, legendentries, title)
+fig
+```
+
+
+## Appendix
+
+```julia, echo = false
+using SciMLBenchmarks
+SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])
+```