From f16fd22a5fbbf62b88899038d0bc3a1f557790a8 Mon Sep 17 00:00:00 2001 From: Benjamin Kraft Date: Mon, 10 Oct 2022 16:56:41 +0200 Subject: [PATCH] Positional Constraint for Test Pendulum is working --- Content/Blueprints/BP_TestBot.uasset | Bin 128924 -> 140127 bytes Content/Blueprints/BP_TestCube.uasset | Bin 0 -> 132141 bytes Content/Levels/Main.umap | Bin 633328 -> 634492 bytes Content/Models/cube.obj | 26 +++++++++++ Content/Models/test_base.uasset | Bin 0 -> 91021 bytes Source/PBDRobotics/Joint.cpp | 65 +++++++++++++++----------- Source/PBDRobotics/Joint.h | 14 +++++- Source/PBDRobotics/Link.cpp | 31 ++++++------ Source/PBDRobotics/Robot.cpp | 4 +- Source/PBDRobotics/util.h | 23 ++++++++- 10 files changed, 116 insertions(+), 47 deletions(-) create mode 100644 Content/Blueprints/BP_TestCube.uasset create mode 100644 Content/Models/cube.obj create mode 100644 Content/Models/test_base.uasset diff --git a/Content/Blueprints/BP_TestBot.uasset b/Content/Blueprints/BP_TestBot.uasset 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FirstLocalPosition; +Vector3d UJoint::GetFirstWorldDirection() const{ + return FirstLink->Orientation * FirstLocalPosition; } -Vector3d UJoint::GetSecondWorldPosition() const{ - return SecondLink->Position + SecondLink->Orientation * SecondLocalPosition; +Vector3d UJoint::GetSecondWorldDirection() const{ + return SecondLink->Orientation * SecondLocalPosition; +} + +Vector3d UJoint::GetConnection() const{ + return FirstLink->Position + GetFirstWorldDirection() - (SecondLink->Position + GetSecondWorldDirection()); } Vector3d UJoint::GetFirstWorldAxis() const{ return FirstLink->Orientation * FirstRotateAxis; } + Vector3d UJoint::GetSecondWorldAxis() const{ return SecondLink->Orientation * SecondRotateAxis; } + + void UJoint::SolvePosition(const double H) const{ ULink* L1 = FirstLink; ULink* L2 = SecondLink; // Positional Constraints { - const Vector3d R1 = GetFirstWorldPosition(); - const Vector3d R2 = GetSecondWorldPosition(); - const Vector3d D = R1 - R2; // Original PBD (not R2 - R1), because Impulse P is negated + const Vector3d R1 = GetFirstWorldDirection(); + const Vector3d R2 = GetSecondWorldDirection(); + const Vector3d D = GetConnection(); const Vector3d N = D.normalized(); const double C = D.norm(); const Matrix3d I1 = L1->GetInertia(); @@ -41,7 +48,8 @@ void UJoint::SolvePosition(const double H) const{ const double W1 = L1->GetPositionalInverseMass(R1, N); const double W2 = L2->GetPositionalInverseMass(R2, N); - constexpr double A = 1. / 1000000; // Compliance (inverse of stiffness) + constexpr double A = 1. / 10000000; // Compliance (inverse of stiffness) + const Vector3d P = -C / (W1 + W2 + A / (H * H)) * N; L1->Position += P / M1; @@ -49,20 +57,21 @@ void UJoint::SolvePosition(const double H) const{ Vector3d T1 = I1.inverse() * R1.cross(P); Vector3d T2 = I2.inverse() * R2.cross(P); - Quaterniond Add1 = Quaterniond(0, T1.x(), T1.y(), T1.z()) * L1->Orientation * 0.5; - Quaterniond Add2 = Quaterniond(0, T2.x(), T2.y(), T2.z()) * L2->Orientation * 0.5; - //L1->Orientation = L1->Orientation + Add1; - //L2->Orientation = L2->Orientation- Add2; - //UE_LOG(LogTemp, Log, TEXT("%f %f"), (T1).norm(), T2.norm()); + const Quaterniond Add1 = Quaterniond(0, T1.x(), T1.y(), T1.z()) * L1->Orientation * 0.5; + const Quaterniond Add2 = Quaterniond(0, T2.x(), T2.y(), T2.z()) * L2->Orientation * 0.5; + L1->Orientation = (L1->Orientation + Add1).normalized(); + L2->Orientation = (L2->Orientation - Add2).normalized(); + UE_LOG(LogTemp, Log, TEXT("%f | %f | %f"), C, P.norm(), R2.cross(P).norm()); } // Rotational Constraints { const Vector3d A1 = GetFirstWorldAxis(); const Vector3d A2 = GetSecondWorldAxis(); + assert(A1.norm() == A2.norm() == 1); const Vector3d Q = A1.cross(A2); const Vector3d N = Q.normalized(); - const double Theta = Q.norm(); + const double Theta = UKismetMathLibrary::Asin(Q.norm());// * 180. / PI; const Matrix3d I1 = L1->GetInertia(); const Matrix3d I2 = L2->GetInertia(); @@ -70,16 +79,16 @@ void UJoint::SolvePosition(const double H) const{ const double W1 = L1->GetRotationalInverseMass(N); const double W2 = L2->GetRotationalInverseMass(N); - const double A = 0.000001 / (H * H); - const Vector3d P = -Theta / (W1 + W2 + A) * N; + constexpr double A = 0; //1. / 10000000; + const Vector3d P = Theta / (W1 + W2 + A / (H * H)) * N; Vector3d T1 = I1.inverse() * P; Vector3d T2 = I2.inverse() * P; - T1 = T2 = P; - //L1->Orientation += Quaterniond(0, T1.x(), T1.y(), T1.z()) * L1->Orientation * 0.5; - //L2->Orientation -= Quaterniond(0, T2.x(), T2.y(), T2.z()) * L2->Orientation * 0.5; - - // UE_LOG(LogTemp, Log, TEXT("%f | %f"), W1, W2); + const Quaterniond Add1 = Quaterniond(0, T1.x(), T1.y(), T1.z()) * L1->Orientation * 0.5; + const Quaterniond Add2 = Quaterniond(0, T2.x(), T2.y(), T2.z()) * L2->Orientation * 0.5; + //L1->Orientation = (L1->Orientation + Add1).normalized(); + //L2->Orientation = (L2->Orientation - Add2).normalized(); + //UE_LOG(LogTemp, Log, TEXT("%f | %f | %f | %f"), N.norm(), W1, W2, Q.norm()); } } @@ -92,11 +101,11 @@ void UJoint::SolveVelocity(const double H) const{ const Vector3d V1 = L1->Velocity; const Vector3d V2 = L2->Velocity; - constexpr double MuLin = 100000; // Damping strength - const Vector3d DeltaV = (V2 - V1) * UKismetMathLibrary::Min(MuLin * H, 1); + constexpr double MuLin = 10000; // Damping strength + const Vector3d DeltaV = (V2 - V1) * (MuLin * H < 1 ? MuLin * H : 1); - const Vector3d R1 = GetFirstWorldPosition(); - const Vector3d R2 = GetSecondWorldPosition(); + const Vector3d R1 = GetFirstWorldDirection(); + const Vector3d R2 = GetSecondWorldDirection(); const Vector3d N = (R2 - R1).normalized(); const Matrix3d I1 = L1->GetInertia(); @@ -107,10 +116,10 @@ void UJoint::SolveVelocity(const double H) const{ const Vector3d P = DeltaV / (W1 + W2); - // UE_LOG(LogTemp, Log, TEXT("%f | %f"), (V2 - V1).norm(), MuLin * H); + //UE_LOG(LogTemp, Log, TEXT("%f | %f | %f | %f | %f"), P.norm(), MuLin * H, DeltaV.norm(), (V2 - V1).norm()); - L1->Velocity += P / L1->Mass; - L2->Velocity -= P / L2->Mass; + //L1->Velocity += P / L1->Mass; + //L2->Velocity -= P / L2->Mass; //L1->AngularVelocity += I1.inverse() * R1.cross(P); //L2->AngularVelocity -= I2.inverse() * R2.cross(P); } diff --git a/Source/PBDRobotics/Joint.h b/Source/PBDRobotics/Joint.h index d4ec465..d43c1cf 100644 --- a/Source/PBDRobotics/Joint.h +++ b/Source/PBDRobotics/Joint.h @@ -24,12 +24,22 @@ public: UPROPERTY(BlueprintReadWrite) ULink* SecondLink; + // First Connection point in local space Vector3d FirstLocalPosition; + + // Second Connection point in local space Vector3d SecondLocalPosition; - Vector3d GetFirstWorldPosition() const; - Vector3d GetSecondWorldPosition() const; + // Direction from CenterOfMass to First Connection point + Vector3d GetFirstWorldDirection() const; + + // Direction from CenterOfMass to Second Connection point + Vector3d GetSecondWorldDirection() const; + + // First - Second in World-Space + Vector3d GetConnection() const; + // Vector3d FirstRotateAxis; Vector3d SecondRotateAxis; diff --git a/Source/PBDRobotics/Link.cpp b/Source/PBDRobotics/Link.cpp index b84d99e..7564757 100644 --- a/Source/PBDRobotics/Link.cpp +++ b/Source/PBDRobotics/Link.cpp @@ -12,7 +12,8 @@ using namespace Eigen; Matrix3d ULink::GetInertia() const { - return Orientation.toRotationMatrix() * Inertia_Tensor_Local; + const Matrix3d R = Orientation.toRotationMatrix(); + return R * Inertia_Tensor_Local * R.transpose(); } double ULink::GetPositionalInverseMass(const Vector3d R, const Vector3d N) const{ @@ -31,25 +32,21 @@ void ULink::Setup(){ } void ULink::SetupProperties(){ - Inertia_Tensor_Local = ToEigen(GetInertiaTensor()).asDiagonal(); + + Mass = CalculateMass(); Position = ToEigen(GetComponentLocation()); Velocity = Vector3d::Zero(); - Mass = CalculateMass(); + Inertia_Tensor_Local = ToEigen(GetInertiaTensor()).asDiagonal(); + //Inertia_Tensor_Local = Matrix3d::Identity() * Mass; Orientation = ToEigen(GetComponentQuat()); AngularVelocity = Vector3d::Zero(); if (IsBase){ - Mass = 1e30; - Inertia_Tensor_Local = Vector3d::Ones().asDiagonal() * 1e30; + Mass = 1e50; + Inertia_Tensor_Local = Vector3d::Ones().asDiagonal() * 1e50; } - const Matrix3d I = GetInertia().inverse(); - UE_LOG(LogTemp, Log, TEXT("%s"), *GetName()); - auto log = [this, I](int col){ - UE_LOG(LogTemp, Log, TEXT("%f %f %f"), I(col, 0), I(col, 1), I(col, 2)); - }; - log(0);log(1);log(2); - + Log(GetInertia()); } void ULink::SetupJoints() const { @@ -68,17 +65,23 @@ void ULink::SetupJoints() const { } void ULink::Update(const double H){ - Vector3d ExtTransForce = Vector3d(0, 0, -9.81 * 100) * Mass * 0; + + // Translation + Vector3d ExtTransForce = Vector3d(0, 0, -9.81 * 100) * Mass * 1; if (IsBase) ExtTransForce = Vector3d::Zero(); Last_Position = Position; Velocity += H * ExtTransForce / Mass; Position += H * Velocity; + + // Rotation + const Vector3d ExtRotForce = Vector3d::Zero(); Last_Orientation = Orientation; - // Angle Velocity has no external contributor Vector3d w = AngularVelocity; + AngularVelocity += H * GetInertia().inverse() * (ExtRotForce - w.cross(GetInertia() * w)); + w = AngularVelocity; Orientation = Orientation + Quaterniond(0, w.x(), w.y(), w.z()) * Orientation * 0.5 * H; Orientation.normalize(); } diff --git a/Source/PBDRobotics/Robot.cpp b/Source/PBDRobotics/Robot.cpp index b0aad8c..137db44 100644 --- a/Source/PBDRobotics/Robot.cpp +++ b/Source/PBDRobotics/Robot.cpp @@ -3,6 +3,8 @@ #include "Robot.h" +#include "util.h" + ARobot::ARobot(){ PrimaryActorTick.bCanEverTick = true; @@ -25,7 +27,7 @@ void ARobot::BeginPlay(){ void ARobot::Tick(const float DeltaTime){ Super::Tick(DeltaTime); - constexpr int SubSteps = 30; + constexpr int SubSteps = 10; const double h = DeltaTime / SubSteps; for (int i = 0; i < SubSteps; i++){ for (auto* Link : Parts) diff --git a/Source/PBDRobotics/util.h b/Source/PBDRobotics/util.h index 9b4f420..54a4d42 100644 --- a/Source/PBDRobotics/util.h +++ b/Source/PBDRobotics/util.h @@ -1,6 +1,7 @@ #pragma once #include "Eigen/Dense" +#include inline Vector3d ToEigen(const FVector V){ return Vector3d(V.X, V.Y, V.Z); @@ -30,6 +31,24 @@ inline Quaterniond operator- (const Quaterniond Q1, const Quaterniond Q2){ return Quaterniond(Q1.w() - Q2.w(), Q1.x() - Q2.x(), Q1.y() - Q2.y(), Q1.z() - Q2.z()); } -inline Quaterniond operator-= (const Quaterniond Q1, const Quaterniond Q2){ - return Q1 - Q2; +inline void Log(MatrixXd M){ + assert(M.rows() == 3); + if (M.cols() == 3){ + UE_LOG(LogTemp, Log, TEXT("%f %f %f"), M(0, 0), M(0, 1), M(0, 2)); + UE_LOG(LogTemp, Log, TEXT("%f %f %f"), M(1, 0), M(1, 1), M(1, 2)); + UE_LOG(LogTemp, Log, TEXT("%f %f %f"), M(2, 0), M(2, 1), M(2, 2)); + } + if (M.cols() == 1){ + UE_LOG(LogTemp, Log, TEXT("%f %f %f"), M(0), M(1), M(2)); + } } + +inline void Log(const double V){ + UE_LOG(LogTemp, Log, TEXT("%f"), V); +} + +inline void Log(const char* S){ + UE_LOG(LogTemp, Log, TEXT("%s"), *FString(S)); +} + +