SpatialInertia.h

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#ifndef LIBBIOMIMETICS_SPATIALINERTIA_H
#define LIBBIOMIMETICS_SPATIALINERTIA_H

#include "Math/orientation_tools.h"
#include "spatial.h"

#include <cmath>
#include <iostream>
#include <type_traits>

#include <eigen3/Eigen/Dense>

using namespace ori;
using namespace spatial;

template <typename T>
class SpatialInertia {
 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
  SpatialInertia(T mass, const Vec3<T>& com, const Mat3<T>& inertia) {
    Mat3<T> cSkew = vectorToSkewMat(com);
    _inertia.template topLeftCorner<3, 3>() =
        inertia + mass * cSkew * cSkew.transpose();
    _inertia.template topRightCorner<3, 3>() = mass * cSkew;
    _inertia.template bottomLeftCorner<3, 3>() = mass * cSkew.transpose();
    _inertia.template bottomRightCorner<3, 3>() = mass * Mat3<T>::Identity();
  }

  explicit SpatialInertia(const Mat6<T>& inertia) { _inertia = inertia; }

  SpatialInertia() { _inertia = Mat6<T>::Zero(); }

  explicit SpatialInertia(const MassProperties<T>& a) {
    _inertia(0, 0) = a(4);
    _inertia(0, 1) = a(9);
    _inertia(0, 2) = a(8);
    _inertia(1, 0) = a(9);
    _inertia(1, 1) = a(5);
    _inertia(1, 2) = a(7);
    _inertia(2, 0) = a(8);
    _inertia(2, 1) = a(7);
    _inertia(2, 2) = a(6);
    Mat3<T> cSkew = vectorToSkewMat(Vec3<T>(a(1), a(2), a(3)));
    _inertia.template topRightCorner<3, 3>() = cSkew;
    _inertia.template bottomLeftCorner<3, 3>() = cSkew.transpose();
    _inertia.template bottomRightCorner<3, 3>() = a(0) * Mat3<T>::Identity();
  }

  explicit SpatialInertia(const Mat4<T>& P) {
    Mat6<T> I;
    T m = P(3, 3);
    Vec3<T> h = P.template topRightCorner<3, 1>();
    Mat3<T> E = P.template topLeftCorner<3, 3>();
    Mat3<T> Ibar = E.trace() * Mat3<T>::Identity() - E;
    I.template topLeftCorner<3, 3>() = Ibar;
    I.template topRightCorner<3, 3>() = vectorToSkewMat(h);
    I.template bottomLeftCorner<3, 3>() = vectorToSkewMat(h).transpose();
    I.template bottomRightCorner<3, 3>() = m * Mat3<T>::Identity();
    _inertia = I;
  }

  MassProperties<T> asMassPropertyVector() {
    MassProperties<T> a;
    Vec3<T> h = matToSkewVec(_inertia.template topRightCorner<3, 3>());
    a << _inertia(5, 5), h(0), h(1), h(2), _inertia(0, 0), _inertia(1, 1),
        _inertia(2, 2), _inertia(2, 1), _inertia(2, 0), _inertia(1, 0);
    return a;
  }

  const Mat6<T>& getMatrix() const { return _inertia; }

  void setMatrix(const Mat6<T>& mat) { _inertia = mat; }

  void addMatrix(const Mat6<T>& mat) { _inertia += mat; }

  T getMass() { return _inertia(5, 5); }

  Vec3<T> getCOM() {
    T m = getMass();
    Mat3<T> mcSkew = _inertia.template topRightCorner<3, 3>();
    Vec3<T> com = matToSkewVec(mcSkew) / m;
    return com;
  }

  Mat3<T> getInertiaTensor() {
    T m = getMass();
    Mat3<T> mcSkew = _inertia.template topRightCorner<3, 3>();
    Mat3<T> I_rot = _inertia.template topLeftCorner<3, 3>() -
                    mcSkew * mcSkew.transpose() / m;
    return I_rot;
  }

  Mat4<T> getPseudoInertia() {
    Vec3<T> h = matToSkewVec(_inertia.template topRightCorner<3, 3>());
    Mat3<T> Ibar = _inertia.template topLeftCorner<3, 3>();
    T m = _inertia(5, 5);
    Mat4<T> P;
    P.template topLeftCorner<3, 3>() =
        0.5 * Ibar.trace() * Mat3<T>::Identity() - Ibar;
    P.template topRightCorner<3, 1>() = h;
    P.template bottomLeftCorner<1, 3>() = h.transpose();
    P(3, 3) = m;
    return P;
  }

  SpatialInertia flipAlongAxis(CoordinateAxis axis) {
    Mat4<T> P = getPseudoInertia();
    Mat4<T> X = Mat4<T>::Identity();
    if (axis == CoordinateAxis::X)
      X(0, 0) = -1;
    else if (axis == CoordinateAxis::Y)
      X(1, 1) = -1;
    else if (axis == CoordinateAxis::Z)
      X(2, 2) = -1;
    P = X * P * X;
    return SpatialInertia(P);
  }

 private:
  Mat6<T> _inertia;
};

#endif  // LIBBIOMIMETICS_SPATIALINERTIA_H