Vector6d logmap_se3(Matrix4d T){
    Matrix3d R, Id3 = Matrix3d::Identity();
    Vector3d Vt, t, w;
    Matrix3d V = Matrix3d::Identity(), w_hat = Matrix3d::Zero();
    Vector6d x;
    Vt << T(0,3), T(1,3), T(2,3);
    w  << 0.f, 0.f, 0.f;
    R = T.block(0,0,3,3);
    double cosine = (R.trace() - 1.f)/2.f;
    if(cosine > 1.f)
        cosine = 1.f;
    else if (cosine < -1.f)
        cosine = -1.f;
    double sine = sqrt(1.0-cosine*cosine);
    if(sine > 1.f)
        sine = 1.f;
    else if (sine < -1.f)
        sine = -1.f;
    double theta  = acos(cosine);
    if( theta > 0.000001 ){
        w_hat = theta*(R-R.transpose())/(2.f*sine);
        w = skewcoords(w_hat);
        Matrix3d s;
        s = skew(w) / theta;
        V = Id3 + s * (1.f-cosine) / theta + s * s * (theta - sine) / theta;
    }
    t = V.inverse() * Vt;
    x.head(3) = t;
    x.tail(3) = w;
    return x;
}

Vector6d gc_Rt_to_wt( pose_t Rt ) {
  Vector6d wt;
  wt.head(3) = gc_Rodriguez( Rt.R );
  wt.tail(3) = Rt.t;

  return wt;
}

Vector6d gc_asd_to_av(Vector4d asd) {
  Vector6d av;

  Vector3d aa = asd.head(3);

  // double d_inv = asd(3);

  // double sig_d_inv = (1.0 - exp(-asd(3))) / (2.0 * (1.0 + exp(-asd(3))));

  // double sig_d_inv = -log(1.0/asd(3) - 1.0);
  // double sig_d_inv = log( (2.0 * asd(3) + 1.0) / (1.0 - 2.0*asd(3)) );
  // double sig_d_inv = atan(asd(3)) / 2.0;
  // double sig_d_inv = atan2(asd(3), 1.0) / 2.0;
  // double sig_d_inv = atan2(asd(3), 1.0);

  // double sig_d_inv = atan2(asd(3), 1.0) * 1.0;
  
  // double sig_d_inv = tan(4.0 * asd(3));
  double sig_d_inv = log(asd(3));
  // cout << "sig_d_inv = " << sig_d_inv << endl;

  // double sig_d_inv = cos(asd(3)) / sin(asd(3));

  // double sig_d_inv = sin(asd(3)) / cos(asd(3));
  // double sig_d_inv = sin(asd(3)) / cos(asd(3));

  Matrix3d R = gc_Rodriguez(aa);

  // av.head(3) = R.col(2) / sig_d_inv;
  av.head(3) = R.col(2) * sig_d_inv;
  av.tail(3) = R.col(0);

  return av;
}

static Vector6d apply(const Matrix4d &T, const Vector6d &q, double w) {
	Vector6d q_t;
	q_t << q.head(3), w, 0, 0;
	q_t.head(4) = T * q_t.head(4);
	q_t.tail(3) = q.tail(3);
	return q_t;
}

/*!
 * This function is implemented in order to not use any external
 * mapping functions. The function was build completely from pieces of
 * code of the old cartesianStateDerivativeModel in order to use
 * completely different, but also verified methods of constructing a
 * stateDerivative from the total accelerations.
 * \param currentState The current state.
 * \param accelerations Total sum of accelerations.
 * \return stateDerivative
 */
Vector6d mapCartesian( const Vector6d& cartesianState, const Eigen::Vector3d& acceleration )
{
    
    // {{{ Snippets from cartesianStateDerivativeModel.h
    typedef Vector6d CartesianStateDerivativeType;

    // Declare Cartesian state derivative size.
    unsigned int stateDerivativeSize = cartesianState.rows( );

    // Declare Cartesian state derivative of the same size as Cartesian state.
    CartesianStateDerivativeType cartesianStateDerivative
	= CartesianStateDerivativeType::Zero( stateDerivativeSize );

    // Set derivative of position components to current Cartesian velocity.
    cartesianStateDerivative.segment( 0, stateDerivativeSize / 2 )
	= cartesianState.segment( stateDerivativeSize / 2, stateDerivativeSize / 2 );

    // Add transformed acceleration to state derivative.
    cartesianStateDerivative.segment( stateDerivativeSize / 2, stateDerivativeSize / 2 )
	+= acceleration;

    // Return assembled state derivative.
    return cartesianStateDerivative;

    // }}} End Snippets from cartesianStateDerivativeModel.h
}

/* ******************************************************************************************** */
void computeTorques (const Vector6d& state, double& ul, double& ur) {

	// Set reference based on the mode
	Vector6d refState;
	if(locoMode == 1 || locoMode == 2) refState << 0.0, 0.0, state0(2), 0.0, state0(4), 0.0;
	else {
		ul = ur = 0.0;
		return;
	}

	// Set the gains
	Vector6d K;
	if(locoMode == 1) K = K_stand;
	else if(locoMode == 2) K = K_bal;
	else assert(false);
	if(dbg) cout << "K: " << K.transpose() << endl;

	// Compute the error
	Vector6d error = state - refState;
	if(dbg) cout << "error: " << error.transpose() << endl;

	// Compute the forward and spin torques 
	double u_x = K(2)*error(2) + K(3)*error(3);
	double u_spin = K.bottomLeftCorner<2,1>().dot(error.bottomLeftCorner<2,1>());
	double u_theta = K.topLeftCorner<2,1>().dot(error.topLeftCorner<2,1>());

	// Limit the output torques
	if(dbg) printf("u_theta: %lf, u_x: %lf, u_spin: %lf\n", u_theta, u_x, u_spin);
	u_spin = max(-10.0, min(10.0, u_spin));
	ul = u_theta + u_x + u_spin;
	ur = u_theta + u_x - u_spin;
	ul = max(-50.0, min(50.0, ul));
	ur = max(-50.0, min(50.0, ur));
}

Vector6d gc_aid_to_av(Vector4d aid) {

  Vector6d av;
  Vector3d aa = aid.head(3);
  double d = 1.0 / aid(3);
  Matrix3d R = gc_Rodriguez(aa);
  av.head(3) = R.col(2) * d;
  av.tail(3) = R.col(0);

//  Vector6d av;
//  double a = aid[0];
//  double b = aid[1];
//  double g = aid[2];
//  double t = aid[3];
//
//  double s1 = sin(a);
//  double c1 = cos(a);
//  double s2 = sin(b);
//  double c2 = cos(b);
//  double s3 = sin(g);
//  double c3 = cos(g);
//
//  Matrix3d R;
//  R <<
//      c2 * c3,   s1 * s2 * c3 - c1 * s3,   c1 * s2 * c3 + s1 * s3,
//      c2 * s3,   s1 * s2 * s3 + c1 * c3,   c1 * s2 * s3 - s1 * c3,
//      -s2,                  s1 * c2,                  c1 * c2;
//
//  double d = 1.0 / t;
//  av.head(3) = -R.col(2) * d;
//  av.tail(3) = R.col(1);

  return av;
}

Vector4d gc_av_to_orth(Vector6d av) {
  Vector4d orth;

  Vector3d a = av.head(3);
  Vector3d v = av.tail(3);  // v
  Vector3d n = a.cross(v);  // n

  Vector3d x = n / n.norm();
  Vector3d y = v / v.norm();
  Vector3d z = x.cross(y);

  orth[0] = atan2( y(2), z(2) );
  orth[1] = asin( - x(2) );
  orth[2] = atan2( x(1), x(0) );

  Vector2d w( n.norm(), v.norm() );
  w = w / w.norm();

  orth[3] = asin( w(1) );

//   MatrixXd A(3,2), Q, R;
// 
//   A.col(0) = n;
//   A.col(1) = v;
// 
//   Eigen::FullPivHouseholderQR<MatrixXd> qr(A);
//   // Q = qr.householderQ();
//   Q = qr.matrixQ();
//   R = qr.matrixQR().triangularView<Upper>();
//   // std::cout << Q << "\n\n" << R << "\n\n" << Q * R - A << "\n";
// 
// //  double sigma1 = R(0,0);
// //  double sigma2 = R(1,1);
// 
// //  cout << "\ntheta from sigma1 = " << acos(sigma1) << endl;
// //  cout << "theta from sigma2 = " << asin(sigma2) << endl;
// 
// // cout << "\nsigma1 = " << sigma1<< endl;
// // cout << "sigma2 = " << sigma2<< endl;
// 
// // sigma2 /= sqrt(sigma1*sigma1 + sigma2*sigma2);
// 
//   Vector3d x = Q.col(0);
//   Vector3d y = Q.col(1);
//   Vector3d z = Q.col(2);
// 
//   orth[0] = atan2( y(2), z(2) );
//   orth[1] = asin( - x(2) );
//   orth[2] = atan2( x(1), x(0) );
//   // orth[3] = asin(sigma2);
// 
//   Vector2d w( n.norm(), v.norm() );
//   w = w / w.norm();
//   orth[3] = asin( w(1) );

  return orth;
}

Vector4d gc_av_to_asd(Vector6d av) {
  Vector4d asd;

  Vector3d a = av.head(3);
  Vector3d x = av.tail(3);  // v
  Vector3d y = a.cross(x);  // n

//  Vector2d w(y.norm(), x.norm());
//  w /= w.norm();
//  asd(3) = asin(w(1));
  
  double depth = x.norm() / y.norm();
  // double sig_d = log( (2.0*depth + 1.0) / (1.0 - 2.0*depth));

//  double quotient = depth / 0.5;
//  int integer_quotient = (int)quotient;
//  double floating_quotient = quotient - (double)integer_quotient;
//  depth = depth * floating_quotient;
//  double sig_d = log(2.0*depth + 1.0) - log(1.0 - 2.0*depth);

// double sig_d = atan(1.0 / (1.0*depth) );
// double sig_d = atan(depth);
// double sig_d = atan2(1.0, depth);
// double sig_d = atan(depth);

// double sig_d = atan2(1.0, depth) / 4.0;
  double sig_d = 1.0 / exp(-depth);
  asd(3) = sig_d;
  // cout << "sig_d = " << sig_d << endl;

  // asd(3) = depth;

  // double sig_d = tan(1.0/depth);
  // double sig_d = tan(2.0/depth);
  // double sig_d = tan(2.0*depth);
  // double sig_d = (1.0 - exp(-1.0/depth)) / (2.0*(1.0 + exp(-1.0/depth)));
  // double sig_d = (1.0 - exp(-depth)) / (2.0*(1.0 + exp(-depth)));
  // double sig_d = 1.0 / (1.0 + exp(-1.0/depth));
  // double sig_d = 1.0 / (1.0 + exp(-depth));

  x /= x.norm();
  y /= y.norm();
  Vector3d z = x.cross(y);

  Matrix3d R;
  R.col(0) = x;
  R.col(1) = y;
  R.col(2) = z;

  Vector3d aa = gc_Rodriguez(R);

  asd(0) = aa(0);
  asd(1) = aa(1);
  asd(2) = aa(2);

  return asd;
}

void ForceSensor::voltage2FT() {
  SetToZero(wrench_);

  Vector6d result_voltage = voltage_ADC_ - bias_;

  Vector6d force = conversion_matrix * result_voltage;
  force = force.array() * conversion_scale.array();

  for (int i = 0; i < 6; i++) {
    wrench_[i] = force(i);
  }
}

Vector6d gc_plk_to_pose( Vector6d plk_w, pose_t T ) {
  Vector3d nw = plk_w.head(3);
  Vector3d vw = plk_w.tail(3);

  Vector3d nc = T.R * nw + gc_skew_symmetric(T.t) * T.R * vw;
  Vector3d vc = T.R * vw;

  Vector6d plk_c;
  plk_c.head(3) = nc;
  plk_c.tail(3) = vc;
  return plk_c;
}

void RollPitchYawFloatingJoint::motionSubspaceDotTimesV(const Eigen::Ref<const VectorXd>& q, const Eigen::Ref<const VectorXd>& v,
    Vector6d& motion_subspace_dot_times_v,
    Gradient<Vector6d, Eigen::Dynamic>::type* dmotion_subspace_dot_times_vdq,
    Gradient<Vector6d, Eigen::Dynamic>::type* dmotion_subspace_dot_times_vdv) const
{
  motion_subspace_dot_times_v.resize(TWIST_SIZE, 1);
  auto rpy = q.middleRows<RPY_SIZE>(SPACE_DIMENSION);
  double roll = rpy(0);
  double pitch = rpy(1);
  double yaw = rpy(2);

  auto pd = v.middleRows<SPACE_DIMENSION>(0);
  double xd = pd(0);
  double yd = pd(1);
  double zd = pd(2);

  auto rpyd = v.middleRows<RPY_SIZE>(SPACE_DIMENSION);
  double rolld = rpyd(0);
  double pitchd = rpyd(1);
  double yawd = rpyd(2);

  using namespace std;
  double cr = cos(roll);
  double sr = sin(roll);
  double cp = cos(pitch);
  double sp = sin(pitch);
  double cy = cos(yaw);
  double sy = sin(yaw);

  motion_subspace_dot_times_v.transpose() << -pitchd * yawd * cp, rolld * yawd * cp * cr - pitchd * yawd * sp * sr - pitchd * rolld * sr, -pitchd * rolld * cr - pitchd * yawd * cr * sp - rolld * yawd * cp * sr, yd * (yawd * cp * cy - pitchd * sp * sy) - xd * (pitchd * cy * sp + yawd * cp * sy)
      - pitchd * zd * cp, zd * (rolld * cp * cr - pitchd * sp * sr) + xd * (rolld * (sr * sy + cr * cy * sp) - yawd * (cr * cy + sp * sr * sy) + pitchd * cp * cy * sr) - yd * (rolld * (cy * sr - cr * sp * sy) + yawd * (cr * sy - cy * sp * sr) - pitchd * cp * sr * sy), xd
      * (rolld * (cr * sy - cy * sp * sr) + yawd * (cy * sr - cr * sp * sy) + pitchd * cp * cr * cy) - zd * (pitchd * cr * sp + rolld * cp * sr) + yd * (yawd * (sr * sy + cr * cy * sp) - rolld * (cr * cy + sp * sr * sy) + pitchd * cp * cr * sy);

  if (dmotion_subspace_dot_times_vdq) {
    dmotion_subspace_dot_times_vdq->resize(motion_subspace_dot_times_v.rows(), getNumPositions());
    dmotion_subspace_dot_times_vdq->transpose() << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -pitchd * rolld * cr - pitchd * yawd * cr * sp - rolld * yawd * cp * sr, pitchd * rolld * sr + pitchd * yawd * sp * sr - rolld * yawd * cp * cr, 0.0, xd
        * (rolld * (cr * sy - cy * sp * sr) + yawd * (cy * sr - cr * sp * sy) + pitchd * cp * cr * cy) - zd * (pitchd * cr * sp + rolld * cp * sr) + yd * (-rolld * (cr * cy + sp * sr * sy) + yawd * (sr * sy + cr * cy * sp) + pitchd * cp * cr * sy), -zd * (rolld * cp * cr - pitchd * sp * sr)
        - xd * (rolld * (sr * sy + cr * cy * sp) - yawd * (cr * cy + sp * sr * sy) + pitchd * cp * cy * sr) + yd * (rolld * (cy * sr - cr * sp * sy) + yawd * (cr * sy - cy * sp * sr) - pitchd * cp * sr * sy), pitchd * yawd * sp, -pitchd * yawd * cp * sr - rolld * yawd * cr * sp, rolld * yawd * sp
        * sr - pitchd * yawd * cp * cr, -xd * (pitchd * cp * cy - yawd * sp * sy) - yd * (pitchd * cp * sy + yawd * cy * sp) + pitchd * zd * sp, -zd * (pitchd * cp * sr + rolld * cr * sp) - xd * (-rolld * cp * cr * cy + pitchd * cy * sp * sr + yawd * cp * sr * sy)
        + yd * (rolld * cp * cr * sy + yawd * cp * cy * sr - pitchd * sp * sr * sy), -zd * (pitchd * cp * cr - rolld * sp * sr) - xd * (pitchd * cr * cy * sp + rolld * cp * cy * sr + yawd * cp * cr * sy) - yd * (-yawd * cp * cr * cy + pitchd * cr * sp * sy + rolld * cp * sr * sy), 0.0, 0.0, 0.0, -xd
        * (yawd * cp * cy - pitchd * sp * sy) - yd * (pitchd * cy * sp + yawd * cp * sy), yd * (rolld * (sr * sy + cr * cy * sp) - yawd * (cr * cy + sp * sr * sy) + pitchd * cp * cy * sr) + xd * (rolld * (cy * sr - cr * sp * sy) + yawd * (cr * sy - cy * sp * sr) - pitchd * cp * sr * sy), yd
        * (rolld * (cr * sy - cy * sp * sr) + yawd * (cy * sr - cr * sp * sy) + pitchd * cp * cr * cy) - xd * (-rolld * (cr * cy + sp * sr * sy) + yawd * (sr * sy + cr * cy * sp) + pitchd * cp * cr * sy);
  }

  if (dmotion_subspace_dot_times_vdv) {
    dmotion_subspace_dot_times_vdv->resize(motion_subspace_dot_times_v.rows(), getNumVelocities());
    dmotion_subspace_dot_times_vdv->transpose() << 0.0, 0.0, 0.0, -pitchd * cy * sp - yawd * cp * sy, rolld * (sr * sy + cr * cy * sp) - yawd * (cr * cy + sp * sr * sy) + pitchd * cp * cy * sr, rolld * (cr * sy - cy * sp * sr) + yawd * (cy * sr - cr * sp * sy) + pitchd * cp * cr * cy, 0.0, 0.0, 0.0, yawd * cp
        * cy - pitchd * sp * sy, -rolld * (cy * sr - cr * sp * sy) - yawd * (cr * sy - cy * sp * sr) + pitchd * cp * sr * sy, -rolld * (cr * cy + sp * sr * sy) + yawd * (sr * sy + cr * cy * sp) + pitchd * cp * cr * sy, 0.0, 0.0, 0.0, -pitchd * cp, rolld * cp * cr - pitchd * sp * sr, -pitchd * cr
        * sp - rolld * cp * sr, 0.0, -pitchd * sr + yawd * cp * cr, -pitchd * cr - yawd * cp * sr, 0.0, xd * (sr * sy + cr * cy * sp) - yd * (cy * sr - cr * sp * sy) + zd * cp * cr, xd * (cr * sy - cy * sp * sr) - yd * (cr * cy + sp * sr * sy) - zd * cp * sr, -yawd * cp, -sr * (rolld + yawd * sp), -cr
        * (rolld + yawd * sp), -zd * cp - xd * cy * sp - yd * sp * sy, sr * (-zd * sp + xd * cp * cy + yd * cp * sy), cr * (-zd * sp + xd * cp * cy + yd * cp * sy), -pitchd * cp, rolld * cp * cr - pitchd * sp * sr, -pitchd * cr * sp - rolld * cp * sr, cp * (yd * cy - xd * sy), -xd
        * (cr * cy + sp * sr * sy) - yd * (cr * sy - cy * sp * sr), xd * (cy * sr - cr * sp * sy) + yd * (sr * sy + cr * cy * sp);
  }
}

void QuaternionFloatingJoint::motionSubspaceDotTimesV(const Eigen::Ref<const VectorXd>& q, const Eigen::Ref<const VectorXd>& v,
    Vector6d& motion_subspace_dot_times_v,
    Gradient<Vector6d, Eigen::Dynamic>::type* dmotion_subspace_dot_times_vdq,
    Gradient<Vector6d, Eigen::Dynamic>::type* dmotion_subspace_dot_times_vdv) const
{
  motion_subspace_dot_times_v.setZero();
  if (dmotion_subspace_dot_times_vdq) {
    dmotion_subspace_dot_times_vdq->setZero(motion_subspace_dot_times_v.size(), getNumPositions());
  }
  if (dmotion_subspace_dot_times_vdv) {
    dmotion_subspace_dot_times_vdv->setZero(motion_subspace_dot_times_v.size(), getNumVelocities());
  }
}

/// The main loop
void run() {

	// start some timers
	Vector6d state;	
	size_t c_ = 0;
	struct timespec t_now, t_prev = aa_tm_now();
	int lastLocoMode = locoMode;
	while(!somatic_sig_received) {

		pthread_mutex_lock(&mutex);
		dbg = (c_++ % 20 == 0);
		if(dbg) cout << "\nmode: " << locoMode << endl;
		
		// Update times
		t_now = aa_tm_now();						
		double dt = (double)aa_tm_timespec2sec(aa_tm_sub(t_now, t_prev));	
		t_prev = t_now;
		if(dbg) cout << "dt: " << dt << endl;

		// Get the locomotion state 
		getState(state, dt); 
		if(dbg) cout << "state: " << state.transpose() << endl;

		// Check if the arm has reached the goal position or if the body is moving
		bool armReached = (fabs(hw->arms[LEFT]->pos[0] - (-1.8)) < 0.05);
		bool baseMoved = (hw->imu > -1.8);
		if(dbg) cout << "armReached: " << armReached << ", baseMoved: " << baseMoved << endl;
		if((armReached || baseMoved) && (locoMode == 0)) {
			locoMode = 1;
			state0 = state;
		}
		if(dbg) cout << "state0: " << state0.transpose() << endl;

		// Switch the mode if necessary
		switchModes(state);

		// Compute the torques based on the state and the mode
		double ul, ur;
		computeTorques(state, ul, ur);
	
		// Apply the torque
		double input [2] = {ul, ur};
		if(dbg) cout << "start: " << start << "\nu: {" << ul << ", " << ur << "}" << endl;
		if(!start) input[0] = input[1] = 0.0;
//		somatic_motor_cmd(&daemon_cx, hw->amc, SOMATIC__MOTOR_PARAM__MOTOR_CURRENT, input, 2, NULL);

		// Update the locomotion mode
		lastLocoMode = locoMode;
		pthread_mutex_unlock(&mutex);
	}
}

Vector6d gc_line_to_pose(Vector6d line_w, pose_t T) {
  Vector6d line_c;

  Vector3d cp0, dv0;
  cp0 = line_w.head(3);
  dv0 = line_w.tail(3);

  Vector3d cp1 = gc_point_to_pose( T, cp0 );
  Vector3d dv1 = T.R * dv0;

  line_c.head(3) = cp1;
  line_c.tail(3) = dv1;

  return line_c;
}

template <typename PointSource, typename PointTarget> inline void
pcl::GeneralizedIterativeClosestPoint<PointSource, PointTarget>::OptimizationFunctorWithIndices::fdf (const Vector6d& x, double& f, Vector6d& g)
{
  Eigen::Matrix4f transformation_matrix = gicp_->base_transformation_;
  gicp_->applyState(transformation_matrix, x);
  f = 0;
  g.setZero ();
  Eigen::Matrix3d R = Eigen::Matrix3d::Zero ();
  const int m = static_cast<const int> (gicp_->tmp_idx_src_->size ());
  for (int i = 0; i < m; ++i)
  {
    // The last coordinate, p_src[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_src = gicp_->tmp_src_->points[(*gicp_->tmp_idx_src_)[i]].getVector4fMap ();
    // The last coordinate, p_tgt[3] is guaranteed to be set to 1.0 in registration.hpp
    Vector4fMapConst p_tgt = gicp_->tmp_tgt_->points[(*gicp_->tmp_idx_tgt_)[i]].getVector4fMap ();
    Eigen::Vector4f pp (transformation_matrix * p_src);
    // The last coordiante is still guaranteed to be set to 1.0
    Eigen::Vector3d res (pp[0] - p_tgt[0], pp[1] - p_tgt[1], pp[2] - p_tgt[2]);
    // temp = M*res
    Eigen::Vector3d temp (gicp_->mahalanobis((*gicp_->tmp_idx_src_)[i]) * res);
    // Increment total error
    f+= double(res.transpose() * temp);
    // Increment translation gradient
    // g.head<3> ()+= 2*M*res/num_matches (we postpone 2/num_matches after the loop closes)
    g.head<3> ()+= temp;
    pp = gicp_->base_transformation_ * p_src;
    Eigen::Vector3d p_src3 (pp[0], pp[1], pp[2]);
    // Increment rotation gradient
    R+= p_src3 * temp.transpose();    
  }
  f/= double(m);
  g.head<3> ()*= double(2.0/m);
  R*= 2.0/m;
  gicp_->computeRDerivative(x, R, g);
}

pair<Matrix4d, Matrix4d> C3Trajectory::transformation_pair(const Vector6d &q) {
	Matrix4d R;
	R.block<3,3>(0, 0) = AttitudeHelpers::EulerToRotation(q.tail(3));
	R.block<1,3>(3, 0).fill(0);
	R.block<3,1>(0, 3).fill(0);
	R(3, 3) = 1;

	Matrix4d T = Matrix4d::Identity();
	T.block<3,1>(0, 3) = -q.head(3);

	pair<Matrix4d, Matrix4d> result;
	result.first = R.transpose()*T; // NED -> BODY

	T.block<3,1>(0, 3) = q.head(3);
	result.second = T*R; // BODY -> NED

	return result;
}

Matrix4d expmap_se3(Vector6d x){
    Matrix3d R, V, s, I = Matrix3d::Identity();
    Vector3d t, w;
    Matrix4d T = Matrix4d::Identity();
    w = x.tail(3);
    t = x.head(3);
    double theta = w.norm();
    if( theta < 0.000001 )
        R = I;
    else{
        s = skew(w)/theta;
        R = I + s * sin(theta) + s * s * (1.0f-cos(theta));
        V = I + s * (1.0f - cos(theta)) / theta + s * s * (theta - sin(theta)) / theta;
        t = V * t;
    }
    T.block(0,0,3,4) << R, t;
    return T;
}

//! Determine aerodynamic coefficients of a single vehicle part.
Vector6d HypersonicLocalInclinationAnalysis::determinePartCoefficients(
        const int partNumber, const boost::array< int, 3 > independentVariableIndices )
{
    // Declare and determine angles of attack and sideslip for analysis.
    double angleOfAttack =  dataPointsOfIndependentVariables_[ 1 ]
            [ independentVariableIndices[ 1 ] ];

    double angleOfSideslip =  dataPointsOfIndependentVariables_[ 2 ]
            [ independentVariableIndices[ 2 ] ];

    // Declare partCoefficient vector.
    Vector6d partCoefficients = Vector6d::Zero( );

    // Check whether the inclinations of the vehicle part have already been computed.
    if ( previouslyComputedInclinations_.count( std::pair< double, double >(
                                                    angleOfAttack, angleOfSideslip ) ) == 0 )
    {
        // Determine panel inclinations for part.
        determineInclinations( angleOfAttack, angleOfSideslip );

        // Add panel inclinations to container
        previouslyComputedInclinations_[ std::pair< double, double >(
                    angleOfAttack, angleOfSideslip ) ] = inclination_;
    }

    else
    {
        // Fetch inclinations from container
        inclination_ = previouslyComputedInclinations_[ std::pair< double, double >(
                    angleOfAttack, angleOfSideslip ) ];
    }

    // Set pressureCoefficient_ array for given independent variables.
    determinePressureCoefficients( partNumber, independentVariableIndices );

    // Calculate force coefficients from pressure coefficients.
    partCoefficients.segment( 0, 3 ) = calculateForceCoefficients( partNumber );

    // Calculate moment coefficients from pressure coefficients.
    partCoefficients.segment( 3, 3 ) = calculateMomentCoefficients( partNumber );

    return partCoefficients;
}

/// Read file for gains
void readGains () {

	// Get the gains
	Vector6d* kgains [] = {&K_stand, &K_bal};
	ifstream file ("/home/cerdogan/Documents/Software/project/krang/iser/data/gains-03.txt");
	assert(file.is_open());
	char line [1024];
	for(size_t k_idx = 0; k_idx < 2; k_idx++) {
		*kgains[k_idx] = Vector6d::Zero();
		file.getline(line, 1024);
		std::stringstream stream(line, std::stringstream::in);
		size_t i = 0;
		double newDouble;
		while ((i < 6) && (stream >> newDouble)) (*kgains[k_idx])(i++) = newDouble;
	}
	cout << "K_stand: " << K_stand.transpose() << endl;
	cout << "K_bal: " << K_bal.transpose() << endl;
	file.close();
}