spatial.h

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#ifndef LIBBIOMIMETICS_SPATIAL_H
#define LIBBIOMIMETICS_SPATIAL_H

#include "Math/orientation_tools.h"

#include <eigen3/Eigen/Dense>

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

namespace spatial {
using namespace ori;
enum class JointType { Prismatic, Revolute, FloatingBase, Nothing };

template <typename T>
SXform<T> spatialRotation(CoordinateAxis axis, T theta) {
  static_assert(std::is_floating_point<T>::value,
                "must use floating point value");
  RotMat<T> R = coordinateRotation(axis, theta);
  SXform<T> X = SXform<T>::Zero();
  X.template topLeftCorner<3, 3>() = R;
  X.template bottomRightCorner<3, 3>() = R;
  return X;
}

template <typename T>
auto motionCrossMatrix(const Eigen::MatrixBase<T>& v) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  Mat6<typename T::Scalar> m;
  m << 0, -v(2), v(1), 0, 0, 0, v(2), 0, -v(0), 0, 0, 0, -v(1), v(0), 0, 0, 0,
      0,

      0, -v(5), v(4), 0, -v(2), v(1), v(5), 0, -v(3), v(2), 0, -v(0), -v(4),
      v(3), 0, -v(1), v(0), 0;
  return m;
}

template <typename T>
auto forceCrossMatrix(const Eigen::MatrixBase<T>& v) {
  Mat6<typename T::Scalar> f;
  f << 0, -v(2), v(1), 0, -v(5), v(4), v(2), 0, -v(0), v(5), 0, -v(3), -v(1),
      v(0), 0, -v(4), v(3), 0, 0, 0, 0, 0, -v(2), v(1), 0, 0, 0, v(2), 0, -v(0),
      0, 0, 0, -v(1), v(0), 0;
  return f;
}

template <typename T>
auto motionCrossProduct(const Eigen::MatrixBase<T>& a,
                        const Eigen::MatrixBase<T>& b) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  SVec<typename T::Scalar> mv;
  mv << a(1) * b(2) - a(2) * b(1), a(2) * b(0) - a(0) * b(2),
      a(0) * b(1) - a(1) * b(0),
      a(1) * b(5) - a(2) * b(4) + a(4) * b(2) - a(5) * b(1),
      a(2) * b(3) - a(0) * b(5) - a(3) * b(2) + a(5) * b(0),
      a(0) * b(4) - a(1) * b(3) + a(3) * b(1) - a(4) * b(0);
  return mv;
}

template <typename T>
auto forceCrossProduct(const Eigen::MatrixBase<T>& a,
                       const Eigen::MatrixBase<T>& b) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  SVec<typename T::Scalar> mv;
  mv << b(2) * a(1) - b(1) * a(2) - b(4) * a(5) + b(5) * a(4),
      b(0) * a(2) - b(2) * a(0) + b(3) * a(5) - b(5) * a(3),
      b(1) * a(0) - b(0) * a(1) - b(3) * a(4) + b(4) * a(3),
      b(5) * a(1) - b(4) * a(2), b(3) * a(2) - b(5) * a(0),
      b(4) * a(0) - b(3) * a(1);
  return mv;
}

template <typename T>
auto sxformToHomogeneous(const Eigen::MatrixBase<T>& X) {
  static_assert(T::ColsAtCompileTime == 6 && T::RowsAtCompileTime == 6,
                "Must have 6x6 matrix");
  Mat4<typename T::Scalar> H = Mat4<typename T::Scalar>::Zero();
  RotMat<typename T::Scalar> R = X.template topLeftCorner<3, 3>();
  Mat3<typename T::Scalar> skewR = X.template bottomLeftCorner<3, 3>();
  H.template topLeftCorner<3, 3>() = R;
  H.template topRightCorner<3, 1>() = matToSkewVec(skewR * R.transpose());
  H(3, 3) = 1;
  return H;
}

template <typename T>
auto homogeneousToSXform(const Eigen::MatrixBase<T>& H) {
  static_assert(T::ColsAtCompileTime == 4 && T::RowsAtCompileTime == 4,
                "Must have 4x4 matrix");
  Mat3<typename T::Scalar> R = H.template topLeftCorner<3, 3>();
  Vec3<typename T::Scalar> translate = H.template topRightCorner<3, 1>();
  Mat6<typename T::Scalar> X = Mat6<typename T::Scalar>::Zero();
  X.template topLeftCorner<3, 3>() = R;
  X.template bottomLeftCorner<3, 3>() = vectorToSkewMat(translate) * R;
  X.template bottomRightCorner<3, 3>() = R;
  return X;
}

template <typename T, typename T2>
auto createSXform(const Eigen::MatrixBase<T>& R,
                  const Eigen::MatrixBase<T2>& r) {
  static_assert(T::ColsAtCompileTime == 3 && T::RowsAtCompileTime == 3,
                "Must have 3x3 matrix");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 3,
                "Must have 3x1 matrix");
  Mat6<typename T::Scalar> X = Mat6<typename T::Scalar>::Zero();
  X.template topLeftCorner<3, 3>() = R;
  X.template bottomRightCorner<3, 3>() = R;
  X.template bottomLeftCorner<3, 3>() = -R * vectorToSkewMat(r);
  return X;
}

template <typename T>
auto rotationFromSXform(const Eigen::MatrixBase<T>& X) {
  static_assert(T::ColsAtCompileTime == 6 && T::RowsAtCompileTime == 6,
                "Must have 6x6 matrix");
  RotMat<typename T::Scalar> R = X.template topLeftCorner<3, 3>();
  return R;
}

template <typename T>
auto translationFromSXform(const Eigen::MatrixBase<T>& X) {
  static_assert(T::ColsAtCompileTime == 6 && T::RowsAtCompileTime == 6,
                "Must have 6x6 matrix");
  RotMat<typename T::Scalar> R = rotationFromSXform(X);
  Vec3<typename T::Scalar> r =
      -matToSkewVec(R.transpose() * X.template bottomLeftCorner<3, 3>());
  return r;
}

template <typename T>
auto invertSXform(const Eigen::MatrixBase<T>& X) {
  static_assert(T::ColsAtCompileTime == 6 && T::RowsAtCompileTime == 6,
                "Must have 6x6 matrix");
  RotMat<typename T::Scalar> R = rotationFromSXform(X);
  Vec3<typename T::Scalar> r =
      -matToSkewVec(R.transpose() * X.template bottomLeftCorner<3, 3>());
  SXform<typename T::Scalar> Xinv = createSXform(R.transpose(), -R * r);
  return Xinv;
}

template <typename T>
SVec<T> jointMotionSubspace(JointType joint, CoordinateAxis axis) {
  Vec3<T> v(0, 0, 0);
  SVec<T> phi = SVec<T>::Zero();
  if (axis == CoordinateAxis::X)
    v(0) = 1;
  else if (axis == CoordinateAxis::Y)
    v(1) = 1;
  else
    v(2) = 1;

  if (joint == JointType::Prismatic)
    phi.template bottomLeftCorner<3, 1>() = v;
  else if (joint == JointType::Revolute)
    phi.template topLeftCorner<3, 1>() = v;
  else
    throw std::runtime_error("Unknown motion subspace");

  return phi;
}

template <typename T>
Mat6<T> jointXform(JointType joint, CoordinateAxis axis, T q) {
  Mat6<T> X = Mat6<T>::Zero();
  if (joint == JointType::Revolute) {
    X = spatialRotation(axis, q);
  } else if (joint == JointType::Prismatic) {
    Vec3<T> v(0, 0, 0);
    if (axis == CoordinateAxis::X)
      v(0) = q;
    else if (axis == CoordinateAxis::Y)
      v(1) = q;
    else if (axis == CoordinateAxis::Z)
      v(2) = q;

    X = createSXform(RotMat<T>::Identity(), v);
  } else {
    throw std::runtime_error("Unknown joint xform\n");
  }
  return X;
}

template <typename T>
Mat3<typename T::Scalar> rotInertiaOfBox(typename T::Scalar mass,
                                         const Eigen::MatrixBase<T>& dims) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 3,
                "Must have 3x1 vector");
  Mat3<typename T::Scalar> I =
      Mat3<typename T::Scalar>::Identity() * dims.norm() * dims.norm();
  for (int i = 0; i < 3; i++) I(i, i) -= dims(i) * dims(i);
  I = I * mass / 12;
  return I;
}

template <typename T, typename T2>
auto spatialToLinearVelocity(const Eigen::MatrixBase<T>& v,
                             const Eigen::MatrixBase<T2>& x) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 3,
                "Must have 3x1 vector");
  Vec3<typename T::Scalar> vsAng = v.template topLeftCorner<3, 1>();
  Vec3<typename T::Scalar> vsLin = v.template bottomLeftCorner<3, 1>();
  Vec3<typename T::Scalar> vLinear = vsLin + vsAng.cross(x);
  return vLinear;
}

template <typename T>
auto spatialToAngularVelocity(const Eigen::MatrixBase<T>& v) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  Vec3<typename T::Scalar> vsAng = v.template topLeftCorner<3, 1>();
  return vsAng;
}

template <typename T, typename T2>
auto spatialToLinearAcceleration(const Eigen::MatrixBase<T>& a,
                                 const Eigen::MatrixBase<T2>& v) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 6,
                "Must have 6x1 vector");

  Vec3<typename T::Scalar> acc;
  // classical accleration = spatial linear acc + omega x v
  acc = a.template tail<3>() + v.template head<3>().cross(v.template tail<3>());
  return acc;
}

template <typename T, typename T2, typename T3>
auto spatialToLinearAcceleration(const Eigen::MatrixBase<T>& a,
                                 const Eigen::MatrixBase<T2>& v,
                                 const Eigen::MatrixBase<T3>& x) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 6,
                "Must have 6x1 vector");
  static_assert(T3::ColsAtCompileTime == 1 && T3::RowsAtCompileTime == 3,
                "Must have 3x1 vector");

  Vec3<typename T::Scalar> alin_x = spatialToLinearVelocity(a, x);
  Vec3<typename T::Scalar> vlin_x = spatialToLinearVelocity(v, x);

  // classical accleration = spatial linear acc + omega x v
  Vec3<typename T::Scalar> acc = alin_x + v.template head<3>().cross(vlin_x);
  return acc;
}

template <typename T, typename T2>
auto sXFormPoint(const Eigen::MatrixBase<T>& X,
                 const Eigen::MatrixBase<T2>& p) {
  static_assert(T::ColsAtCompileTime == 6 && T::RowsAtCompileTime == 6,
                "Must have 6x6 vector");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 3,
                "Must have 3x1 vector");

  Mat3<typename T::Scalar> R = rotationFromSXform(X);
  Vec3<typename T::Scalar> r = translationFromSXform(X);
  Vec3<typename T::Scalar> Xp = R * (p - r);
  return Xp;
}

template <typename T, typename T2>
auto forceToSpatialForce(const Eigen::MatrixBase<T>& f,
                         const Eigen::MatrixBase<T2>& p) {
  static_assert(T::ColsAtCompileTime == 1 && T::RowsAtCompileTime == 3,
                "Must have 3x1 vector");
  static_assert(T2::ColsAtCompileTime == 1 && T2::RowsAtCompileTime == 3,
                "Must have 3x1 vector");
  SVec<typename T::Scalar> fs;
  fs.template topLeftCorner<3, 1>() = p.cross(f);
  fs.template bottomLeftCorner<3, 1>() = f;
  return fs;
}

}  // namespace spatial

#endif  // LIBBIOMIMETICS_SPATIAL_H