Merge pull request #138 from JuliaComputing/qcs

Add PrismaticConstraint and suspension test cases

Author: baggepinnen

docs/make.jl

@@ -39,6 +39,7 @@ makedocs(;
                  "Bodies in space" => "examples/space.md",
                  "Gyroscopic effects" => "examples/gyroscopic_effects.md",
                  "Wheels" => "examples/wheel.md",
+                 "Suspension systems" => "examples/suspension.md",
                  "Quadrotor with cable-suspended load" => "examples/quad.md",
              ],
              "Rotations and orientation" => "rotations.md",

docs/src/examples/suspension.md

@@ -0,0 +1,377 @@
+# Quarter-car suspension
+
+A simple suspension system for one wheel, roughly modeled after "Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort", Fernandes et al. 2020.
+
+![suspension system](https://www.researchgate.net/publication/337953665/figure/fig1/AS:941829033828436@1601560948959/Schematic-representation-of-a-vehicle-suspension-system-with-Double-Wishbone-geometry-a_W640.jpg)
+
+We model only the suspension, and excite the system with a force from the ground through a rod connected where the wheel would be. The actuation rod is modeled as a [`SphericalSpherical`](@ref) joint to avoid over constraining the system. We further add a prismatic joint called `body_upright` to hold the "car body" to the world frame. This allows the body to move up and down, but not sideways or rotate.
+
+```@example suspension
+using Multibody
+using ModelingToolkit
+import ModelingToolkitStandardLibrary.Mechanical.TranslationalModelica as Translational
+using Plots
+using OrdinaryDiffEq
+using LinearAlgebra
+using JuliaSimCompiler
+using Test
+
+t = Multibody.t
+D = Differential(t)
+W(args...; kwargs...) = Multibody.world
+
+n = [1, 0, 0]
+AB = 146.5 / 1000
+BC = 233.84 / 1000
+CD = 228.60 / 1000
+DA = 221.43 / 1000
+BP = 129.03 / 1000
+DE = 310.31 / 1000
+t5 = 19.84 |> deg2rad
+
+@mtkmodel QuarterCarSuspension begin
+    @structural_parameters begin
+        spring = true
+        (jc = [0.5, 0.5, 0.5, 0.7])#, [description = "Joint color"]
+        mirror = false
+    end
+    @parameters begin
+        cs = 4000, [description = "Damping constant [Ns/m]"]
+        ks = 44000, [description = "Spring constant [N/m]"]
+        rod_radius = 0.02
+        jr = 0.03, [description = "Radius of revolute joint"]
+    end
+    begin
+        dir = mirror ? -1 : 1
+        rRod1_ia = AB*normalize([0, -0.1, 0.2dir])
+        rRod2_ib = BC*normalize([0, 0.2, 0dir])
+    end
+    @components begin
+        r123 = JointRRR(n_a = n*dir, n_b = n*dir, rRod1_ia, rRod2_ib, rod_radius=0.018, rod_color=jc)
+        r2 = Revolute(; n=n*dir, radius=jr, color=jc)
+        b1 = FixedTranslation(radius = rod_radius, r = CD*normalize([0, -0.1, 0.3dir])) # CD
+        chassis = FixedTranslation(r = DA*normalize([0, 0.2, 0.2*sin(t5)*dir]), render=false)
+        chassis_frame = Frame()
+        
+        if spring
+            springdamper = SpringDamperParallel(c = ks, d = cs, s_unstretched = 1.3*BC, radius=rod_radius) 
+        end
+        if spring
+            spring_mount_F = FixedTranslation(r = 0.7*CD*normalize([0, -0.1, 0.3dir]), render=false) 
+        end
+        if spring
+            spring_mount_E = FixedTranslation(r = 1.3DA*normalize([0, 0.2, 0.2*sin(t5)*dir]), render=true)
+        end
+    end
+    begin
+        A = chassis.frame_b
+        D = chassis.frame_a
+    end
+    @equations begin
+        # Main loop
+        connect(A, r123.frame_a)
+        connect(r123.frame_b, b1.frame_b)
+        connect(b1.frame_a, r2.frame_b)
+        connect(r2.frame_a, D)
+
+        # Spring damper
+        if spring
+            connect(springdamper.frame_b, spring_mount_E.frame_b)
+            connect(b1.frame_a, spring_mount_F.frame_a)
+            connect(D, spring_mount_E.frame_a)
+            connect(springdamper.frame_a, spring_mount_F.frame_b)
+        end
+
+        connect(chassis_frame, chassis.frame_a)
+    end
+end
+
+mirror = false
+@mtkmodel SuspensionWithExcitation begin
+    @structural_parameters begin
+        mirror = false
+    end
+    @parameters begin
+        ms = 1500, [description = "Mass of the car [kg]"]
+        rod_radius = 0.02
+        amplitude = 0.1, [description = "Amplitude of wheel displacement"]
+        freq = 2, [description = "Frequency of wheel displacement"]
+    end
+    begin
+        dir = mirror ? -1 : 1
+    end
+    @components begin
+        world = W()
+        chassis_frame = Frame()
+        suspension = QuarterCarSuspension(; spring=true, mirror, rod_radius)
+
+        wheel_prismatic = Prismatic(n = [0,1,0], axisflange=true, state_priority=100, iscut=false)
+        actuation_rod = SphericalSpherical(radius=rod_radius, r_0 = [0, BC, 0])
+        actuation_position = FixedTranslation(r = [0, 0, CD*dir], render=false)
+        wheel_position = Translational.Position(exact=true)
+
+    end
+    @equations begin
+        wheel_position.s_ref.u ~ amplitude*(sin(2pi*freq*t)) # Displacement of wheel
+        connect(wheel_position.flange, wheel_prismatic.axis)
+
+        connect(world.frame_b, actuation_position.frame_a)
+        connect(actuation_position.frame_b, wheel_prismatic.frame_a)
+        connect(wheel_prismatic.frame_b, actuation_rod.frame_a,)
+        connect(actuation_rod.frame_b, suspension.r123.frame_ib)
+
+        connect(chassis_frame, suspension.chassis_frame)
+    end
+
+end
+
+@mtkmodel SuspensionWithExcitationAndMass begin
+    @structural_parameters begin
+        mirror = false
+    end
+    @parameters begin
+        ms = 1500, [description = "Mass of the car [kg]"]
+        rod_radius = 0.02
+    end
+    begin
+        dir = mirror ? -1 : 1
+    end
+    @components begin
+        world = W()
+        mass = Body(m=ms, r_cm = 0.5DA*normalize([0, 0.2, 0.2*sin(t5)*dir]))
+        excited_suspension = SuspensionWithExcitation(; suspension.spring=true, mirror, rod_radius)
+        body_upright = Prismatic(n = [0, 1, 0], render = false, state_priority=1000)
+    end
+    @equations begin
+        connect(world.frame_b, body_upright.frame_a)
+        connect(body_upright.frame_b, excited_suspension.chassis_frame, mass.frame_a)
+    end
+
+end
+
+@named model = SuspensionWithExcitationAndMass()
+model = complete(model)
+ssys = structural_simplify(IRSystem(model))
+
+defs = [
+    model.body_upright.s => 0.17
+    model.excited_suspension.amplitude => 0.05
+    model.excited_suspension.freq => 10
+    model.excited_suspension.suspension.ks => 30*44000
+    model.excited_suspension.suspension.cs => 30*4000
+    model.ms => 1500/4
+    model.excited_suspension.suspension.springdamper.num_windings => 10
+    # model.r1.phi => -1.0889
+    model.excited_suspension.suspension.r2.phi => -0.6031*(mirror ? -1 : 1)
+    # model.r3.phi => 0.47595
+    model.body_upright.v => 0.14
+]
+
+display(sort(unknowns(ssys), by=string))
+
+prob = ODEProblem(ssys, defs, (0, 2))
+# sol.u[1] = [0.17054946565059462, -0.6015077878288565, 0.274732819217001]
+sol = solve(prob, FBDF(autodiff=true))
+@test SciMLBase.successful_retcode(sol)
+rms(x) = sqrt(sum(abs2, x) / length(x))
+@test rms(sol(0:0.1:2, idxs=model.body_upright.v)) ≈ 2.740 atol=0.01
+```
+```@example suspension
+import GLMakie
+Multibody.render(model, sol, show_axis=false, x=-1, y=0.3, z=0.3, lookat=[0,0.3,0.3], timescale=3, filename="suspension.gif") # Video
+```
+
+![suspension](suspension.gif)
+
+
+# Half-car suspension
+
+In the example below, we extend the previous example to a half-car model with two wheels. We now model the car as a [`BodyShape`](@ref) and attach one suspension system on each side. This time, we let the car rotate around the x-axis to visualize roll effects due to uneven road surfaces. We excite each wheel with similar but slightly different frequencies to produce a beat.
+
+```@example suspension
+@mtkmodel DoubleSuspensionWithExcitationAndMass begin
+    @structural_parameters begin
+        wheel_base = 1
+    end
+    @parameters begin
+        ms = 1500, [description = "Mass of the car [kg]"]
+        rod_radius = 0.02
+    end
+    @components begin
+        world = W()
+        mass = BodyShape(m=ms, r = [0,0,-wheel_base], radius=0.1, color=[0.4, 0.4, 0.4, 0.3])
+        excited_suspension_r = SuspensionWithExcitation(; suspension.spring=true, mirror=false, rod_radius,
+            actuation_position.r = [0, 0, (CD+wheel_base/2)],
+            actuation_rod.r_0 = r_0 = [0, 0.1, 0],
+        )
+        excited_suspension_l = SuspensionWithExcitation(; suspension.spring=true, mirror=true, rod_radius,
+            actuation_position.r = [0, 0, -(CD+wheel_base/2)],
+            actuation_rod.r_0 = r_0 = [0, 0.1, 0],
+        )
+        body_upright = Prismatic(n = [0, 1, 0], render = false, state_priority=1000)
+        body_upright2 = Revolute(n = [1, 0, 0], render = false, state_priority=1000, phi0=0, w0=0)
+        # body_upright = Planar(n = [1, 0, 0], n_x = [0,0,1], render = false, state_priority=1000, radius=0.01)
+    end
+    @equations begin
+        connect(world.frame_b, body_upright.frame_a)
+
+        connect(body_upright.frame_b, body_upright2.frame_a)
+        connect(body_upright2.frame_b, mass.frame_cm)
+
+        # connect(body_upright.frame_b, mass.frame_cm)
+
+        connect(excited_suspension_r.chassis_frame, mass.frame_a)
+        connect(excited_suspension_l.chassis_frame, mass.frame_b)
+    end
+
+end
+
+@named model = DoubleSuspensionWithExcitationAndMass()
+model = complete(model)
+ssys = structural_simplify(IRSystem(model))
+
+defs = [
+    model.excited_suspension_r.amplitude => 0.05
+    model.excited_suspension_r.freq => 10
+    model.excited_suspension_r.suspension.ks => 30*44000
+    model.excited_suspension_r.suspension.cs => 30*4000
+    model.excited_suspension_r.suspension.springdamper.num_windings => 10
+    model.excited_suspension_r.suspension.r2.phi => -0.6031*(1)
+
+    model.excited_suspension_l.amplitude => 0.05
+    model.excited_suspension_l.freq => 9.5
+    model.excited_suspension_l.suspension.ks => 30*44000
+    model.excited_suspension_l.suspension.cs => 30*4000
+    model.excited_suspension_l.suspension.springdamper.num_windings => 10
+    model.excited_suspension_l.suspension.r2.phi => -0.6031*(+1)
+
+    model.ms => 1500/2
+
+    model.body_upright.s => 0.17
+    model.body_upright.v => 0.14
+
+    # model.body_upright.prismatic_y.s => 0.17
+    # model.body_upright.prismatic_y.v => 0.14
+]
+
+display(sort(unknowns(ssys), by=string))
+
+prob = ODEProblem(ssys, defs, (0, 4))
+sol = solve(prob, FBDF(autodiff=true), initializealg = ShampineCollocationInit())
+@test SciMLBase.successful_retcode(sol)
+# first(Multibody.render(model, sol, 0, show_axis=true, x=-1.5, y=0.0, z=0.0))
+```
+
+```@example suspension
+Multibody.render(model, sol, show_axis=false, x=-1.5, y=0.3, z=0.0, lookat=[0,0.1,0.0], timescale=3, filename="suspension_halfcar.gif") # Video
+```
+
+## Adding wheels
+The example below further extends the example from above by adding wheels to the suspension system. The excitation is not modeled as a time-varying surface profile, provided through the `surface` argument to the [`SlippingWheel`](@ref) component.
+The connection between the wheels and the ground form two kinematic loops together with the `body_upright` joint, we thus set both wheels to be cut joints using `iscut=true`.
+```@example suspension
+@mtkmodel ExcitedWheelAssembly begin
+    @structural_parameters begin
+        mirror = false
+    end
+    @parameters begin
+        rod_radius = 0.02
+        amplitude = 0.1, [description = "Amplitude of wheel displacement"]
+        freq = 2, [description = "Frequency of wheel displacement"]
+    end
+    begin
+        dir = mirror ? -1 : 1
+    end
+    @components begin
+        chassis_frame = Frame()
+        suspension = QuarterCarSuspension(; spring=true, mirror, rod_radius)
+
+        wheel = SlippingWheel(
+            radius = 0.2,
+            m = 15,
+            I_axis = 0.06,
+            I_long = 0.12,
+            x0 = 0.0,
+            z0 = 0.0,
+            der_angles = [0, 0, 0],
+            iscut = true, # NOTE: Only used since while we have an "upright joint"
+            surface = (x,z)->amplitude*(sin(2pi*freq*t)), # Excitation from a time-varying surface profile
+        )
+
+    end
+    @equations begin
+        connect(wheel.frame_a, suspension.r123.frame_ib)
+        connect(chassis_frame, suspension.chassis_frame)
+    end
+
+end
+
+@mtkmodel HalfCar begin
+    @structural_parameters begin
+        wheel_base = 1
+    end
+    @parameters begin
+        ms = 1500, [description = "Mass of the car [kg]"]
+        rod_radius = 0.02
+    end
+    @components begin
+        world = W()
+        mass = BodyShape(m=ms, r = [0,0,-wheel_base], radius=0.1, color=[0.4, 0.4, 0.4, 0.3])
+        excited_suspension_r = ExcitedWheelAssembly(; mirror=false, rod_radius)
+        excited_suspension_l = ExcitedWheelAssembly(; mirror=true, rod_radius)
+        body_upright = Prismatic(n = [0, 1, 0], render = false, state_priority=2000, iscut=false)
+        body_upright2 = Revolute(n = [1, 0, 0], render = false, state_priority=2000, phi0=0, w0=0, iscut=false)
+        # body_upright = Planar(n = [1, 0, 0], n_x = [0,0,1], render = false, state_priority=100000, radius=0.01)
+    end
+    @equations begin
+        connect(world.frame_b, body_upright.frame_a)
+        connect(body_upright.frame_b, body_upright2.frame_a)
+        connect(body_upright2.frame_b, mass.frame_cm)
+
+        # connect(body_upright.frame_b, mass.frame_cm)
+
+        connect(excited_suspension_r.chassis_frame, mass.frame_a)
+        connect(excited_suspension_l.chassis_frame, mass.frame_b)
+    end
+
+end
+
+@named model = HalfCar()
+model = complete(model)
+ssys = structural_simplify(IRSystem(model))
+
+defs = [
+    model.excited_suspension_r.amplitude => 0.05
+    model.excited_suspension_r.freq => 10
+    model.excited_suspension_r.suspension.ks => 30*44000
+    model.excited_suspension_r.suspension.cs => 30*4000
+    model.excited_suspension_r.suspension.springdamper.num_windings => 10
+    model.excited_suspension_r.suspension.r2.phi => -0.6031*(1)
+
+    model.excited_suspension_l.amplitude => 0.05
+    model.excited_suspension_l.freq => 9.5
+    model.excited_suspension_l.suspension.ks => 30*44000
+    model.excited_suspension_l.suspension.cs => 30*4000
+    model.excited_suspension_l.suspension.springdamper.num_windings => 10
+    model.excited_suspension_l.suspension.r2.phi => -0.6031*(+1)
+
+    model.ms => 1500
+
+    model.body_upright.s => 0.17
+    model.body_upright.v => 0.14
+
+    # model.body_upright.prismatic_y.s => 0.17
+    # model.body_upright.prismatic_y.v => 0.14
+
+
+    # vec(ori(model.mass.frame_a).R .=> I(3))
+    # vec(ori(model.excited_suspension_r.suspension.r123.jointUSR.frame_a).R .=> I(3))
+]
+
+display(sort(unknowns(ssys), by=string))
+
+prob = ODEProblem(ssys, defs, (0, 4))
+sol = solve(prob, FBDF(autodiff=false), initializealg = ShampineCollocationInit())#, u0 = prob.u0  .+ 1e-6 .* randn.())
+@show SciMLBase.successful_retcode(sol)
+first(Multibody.render(model, sol, 0, show_axis=true, x=-1.5, y=0.0, z=0.0))
+```