Inertial.hh

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/*
 * Copyright (C) 2016 Open Source Robotics Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
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*/
#ifndef GZ_MATH_INERTIAL_HH_
#define GZ_MATH_INERTIAL_HH_
 
#include <optional>
 
#include <gz/math/config.hh>
#include "gz/math/MassMatrix3.hh"
#include "gz/math/Matrix3.hh"
#include "gz/math/Matrix6.hh"
#include "gz/math/Pose3.hh"
 
namespace gz::math
{
  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  //
  template<typename T>
  class Inertial
  {
    public: Inertial()
    {}
 
    public: Inertial(const MassMatrix3<T> &_massMatrix,
                     const Pose3<T> &_pose)
    : massMatrix(_massMatrix), pose(_pose)
    {}
 
    public: Inertial(const MassMatrix3<T> &_massMatrix,
                     const Pose3<T> &_pose,
                     const Matrix6<T> &_addedMass)
    : massMatrix(_massMatrix), pose(_pose), addedMass(_addedMass)
    {}
 
    public: bool SetMassMatrix(const MassMatrix3<T> &_m,
                const T _tolerance = GZ_MASSMATRIX3_DEFAULT_TOLERANCE<T>)
    {
      this->massMatrix = _m;
      return this->massMatrix.IsValid(_tolerance);
    }
 
    public: const MassMatrix3<T> &MassMatrix() const
    {
      return this->massMatrix;
    }
 
    public: bool SetPose(const Pose3<T> &_pose)
    {
      this->pose = _pose;
      return this->massMatrix.IsValid();
    }
 
    public: const Pose3<T> &Pose() const
    {
      return this->pose;
    }
 
    public: bool SetFluidAddedMass(const Matrix6<T> &_m)
    {
      this->addedMass = _m;
      return this->addedMass.value() == this->addedMass.value().Transposed();
    }
 
    public: const std::optional< Matrix6<T> > &FluidAddedMass() const
    {
      return this->addedMass;
    }
 
    public: Matrix3<T> Moi() const
    {
      auto R = Matrix3<T>(this->pose.Rot());
      return R * this->massMatrix.Moi() * R.Transposed();
    }
 
    public: Matrix6<T> BodyMatrix() const
    {
      Matrix6<T> result;
 
      result.SetSubmatrix(Matrix6<T>::TOP_LEFT,
          Matrix3<T>::Identity * this->massMatrix.Mass());
 
      result.SetSubmatrix(Matrix6<T>::BOTTOM_RIGHT, this->Moi());
 
      auto x = this->pose.Pos().X();
      auto y = this->pose.Pos().Y();
      auto z = this->pose.Pos().Z();
      auto skew = Matrix3<T>(
          0, -z, y,
          z, 0, -x,
          -y, x, 0) * this->massMatrix.Mass();
      result.SetSubmatrix(Matrix6<T>::BOTTOM_LEFT, skew);
      result.SetSubmatrix(Matrix6<T>::TOP_RIGHT, skew.Transposed());
 
      return result;
    }
 
    public: Matrix6<T> SpatialMatrix() const
    {
      return this->addedMass.has_value() ?
          this->BodyMatrix() + this->addedMass.value() : this->BodyMatrix();
    }
 
    public: bool SetInertialRotation(const Quaternion<T> &_q)
    {
      auto moi = this->Moi();
      this->pose.Rot() = _q;
      auto R = Matrix3<T>(_q);
      return this->massMatrix.SetMoi(R.Transposed() * moi * R);
    }
 
    public: bool SetMassMatrixRotation(const Quaternion<T> &_q,
                                       const T _tol = 1e-6)
    {
      this->pose.Rot() *= this->MassMatrix().PrincipalAxesOffset(_tol) *
                          _q.Inverse();
      const auto moments = this->MassMatrix().PrincipalMoments(_tol);
      const auto diag = Matrix3<T>(
          moments[0], 0, 0,
          0, moments[1], 0,
          0, 0, moments[2]);
      const auto R = Matrix3<T>(_q);
      return this->massMatrix.SetMoi(R * diag * R.Transposed());
    }
 
    public: bool operator==(const Inertial<T> &_inertial) const
    {
      return (this->pose == _inertial.Pose()) &&
             (this->massMatrix == _inertial.MassMatrix()) &&
             (this->addedMass == _inertial.FluidAddedMass());
    }
 
    public: bool operator!=(const Inertial<T> &_inertial) const
    {
      return !(*this == _inertial);
    }
 
    public: Inertial<T> &operator+=(const Inertial<T> &_inertial)
    {
      T m1 = this->massMatrix.Mass();
      T m2 = _inertial.MassMatrix().Mass();
 
      // Total mass
      T mass = m1 + m2;
 
      // Only continue if total mass is positive
      if (mass <= 0)
      {
        return *this;
      }
 
      auto com1 = this->Pose().Pos();
      auto com2 = _inertial.Pose().Pos();
      // New center of mass location in base frame
      auto com = (m1*com1 + m2*com2) / mass;
 
      // Components of new moment of inertia matrix
      Vector3<T> ixxyyzz;
      Vector3<T> ixyxzyz;
      // First add matrices in base frame
      {
        auto moi = this->Moi() + _inertial.Moi();
        ixxyyzz = Vector3<T>(moi(0, 0), moi(1, 1), moi(2, 2));
        ixyxzyz = Vector3<T>(moi(0, 1), moi(0, 2), moi(1, 2));
      }
      // Then account for parallel axis theorem
      {
        auto dc = com1 - com;
        ixxyyzz.X() += m1 * (std::pow(dc[1], 2) + std::pow(dc[2], 2));
        ixxyyzz.Y() += m1 * (std::pow(dc[2], 2) + std::pow(dc[0], 2));
        ixxyyzz.Z() += m1 * (std::pow(dc[0], 2) + std::pow(dc[1], 2));
        ixyxzyz.X() -= m1 * dc[0] * dc[1];
        ixyxzyz.Y() -= m1 * dc[0] * dc[2];
        ixyxzyz.Z() -= m1 * dc[1] * dc[2];
      }
      {
        auto dc = com2 - com;
        ixxyyzz.X() += m2 * (std::pow(dc[1], 2) + std::pow(dc[2], 2));
        ixxyyzz.Y() += m2 * (std::pow(dc[2], 2) + std::pow(dc[0], 2));
        ixxyyzz.Z() += m2 * (std::pow(dc[0], 2) + std::pow(dc[1], 2));
        ixyxzyz.X() -= m2 * dc[0] * dc[1];
        ixyxzyz.Y() -= m2 * dc[0] * dc[2];
        ixyxzyz.Z() -= m2 * dc[1] * dc[2];
      }
      this->massMatrix = MassMatrix3<T>(mass, ixxyyzz, ixyxzyz);
      this->pose = Pose3<T>(com, Quaternion<T>::Identity);
 
      return *this;
    }
 
   public: Inertial<T> &operator-=(const Inertial<T> &_inertial)
    {
      T m = this->massMatrix.Mass();
      T m2 = _inertial.MassMatrix().Mass();
 
      // Remaining mass
      T m1 = m - m2;
 
      // Only continue if remaining mass is positive
      if (m1 <= 0)
      {
        return *this;
      }
 
      auto com = this->Pose().Pos();
      auto com2 = _inertial.Pose().Pos();
      // Remaining center of mass location in base frame
      auto com1 = (m*com - m2*com2)/m1;
 
      // Components of new moment of inertia matrix
      Vector3<T> ixxyyzz;
      Vector3<T> ixyxzyz;
 
      // First subtract matrices in base frame
      {
        auto moi = this->Moi() - _inertial.Moi();
        ixxyyzz = Vector3<T>(moi(0, 0), moi(1, 1), moi(2, 2));
        ixyxzyz = Vector3<T>(moi(0, 1), moi(0, 2), moi(1, 2));
      }
      // Then account for parallel axis theorem
      {
        auto dc = com1 - com;
        ixxyyzz.X() -= m1 * (std::pow(dc[1], 2) + std::pow(dc[2], 2));
        ixxyyzz.Y() -= m1 * (std::pow(dc[2], 2) + std::pow(dc[0], 2));
        ixxyyzz.Z() -= m1 * (std::pow(dc[0], 2) + std::pow(dc[1], 2));
        ixyxzyz.X() += m1 * dc[0] * dc[1];
        ixyxzyz.Y() += m1 * dc[0] * dc[2];
        ixyxzyz.Z() += m1 * dc[1] * dc[2];
      }
      {
        auto dc = com2 - com;
        ixxyyzz.X() -= m2 * (std::pow(dc[1], 2) + std::pow(dc[2], 2));
        ixxyyzz.Y() -= m2 * (std::pow(dc[2], 2) + std::pow(dc[0], 2));
        ixxyyzz.Z() -= m2 * (std::pow(dc[0], 2) + std::pow(dc[1], 2));
        ixyxzyz.X() += m2 * dc[0] * dc[1];
        ixyxzyz.Y() += m2 * dc[0] * dc[2];
        ixyxzyz.Z() += m2 * dc[1] * dc[2];
      }
      this->massMatrix = MassMatrix3<T>(m1, ixxyyzz, ixyxzyz);
      this->pose = Pose3<T>(com1, Quaternion<T>::Identity);
 
      return *this;
    }
 
    public: const Inertial<T> operator+(const Inertial<T> &_inertial) const
    {
      return Inertial<T>(*this) += _inertial;
    }
 
    public: const Inertial<T> operator-(const Inertial<T> &_inertial) const
    {
      return Inertial<T>(*this) -= _inertial;
    }
 
    private: MassMatrix3<T> massMatrix;
 
    private: Pose3<T> pose;
 
    private: std::optional<Matrix6<T>> addedMass;
  };
 
  typedef Inertial<double> Inertiald;
  typedef Inertial<float> Inertialf;
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_INERTIAL_HH_