/// <summary>
/// Partial initialisation function
/// Calculates the state vector \vct{y}_{pi} and Jacobians for a new
/// partially-initialised feature from an initial observation.
/// @param hi The initial measurement \vct{h}_i , in this case the (x,y)
/// image location of the feature.
/// </summary>
/// <param name="hi"></param>
/// <param name="xp">The robot position state \vct{x}_p from which the initial observation was made.</param>
public override void func_ypi_and_dypi_by_dxp_and_dypi_by_dhi_and_Ri(Vector hi, Vector xp)
{
// Representation of a line here:
// ypi = (rWi )
// (hLhatWi)
// Form the ray (in camera co-ordinates by unprojecting this image location
Vector3D hLRi = new Vector3D(((Wide_Camera_Point_Feature_Measurement_Model)wide_model).m_camera.Unproject(hi));
//if (Camera_Constants.DEBUGDUMP) Debug.WriteLine("debug hLRi");
// Form hLhatRi from hLRi
// Normalise
Vector3D hLhatRi = hLRi;
hLhatRi.Normalise();
MatrixFixed dhLhatRi_by_dhLRi = MatrixFixed.dvnorm_by_dv(hLRi);
//if (Camera_Constants.DEBUGDUMP) Debug.WriteLine("debug hLhatRi" + hLhatRi);
// Now convert this into a direction in world co-ordinates by rotating
// Form hLhatWi from hLhatRi
// Rotate
((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.func_q(xp);
RotationMatrix RWR = ((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.get_qRES().RotationMatrix();
Vector3D hLhatWi = new Vector3D(RWR * hLhatRi);
//if (Camera_Constants.DEBUGDUMP) Debug.WriteLine("debug hLhatWi" + hLhatWi);
// Extract rW from xp
((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.func_r(xp);
// And form ypiRES
ypiRES.Update(((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.get_rRES().GetVNL3(), 0);
ypiRES.Update(hLhatWi.GetVNL3(), 3);
//if (Camera_Constants.DEBUGDUMP) Debug.WriteLine("debug ypiRES" + ypiRES);
// Form Jacobians dypi_by_dxp and dypi_by_dhi
// dypi_by_dxp = (drWi_by_dr drWi_by_dq )
// (dhLhatWi_by_dr dhLhatWi_by_dq)
// = (I 0 )
// (0 dhLhatWi_by_dq)
// hLhatWi = RWR * hLhatRi
// => dhLhatWi_by_dq = d/dq ( R(qWR) * hLhatRi)
MatrixFixed dhLhatWi_by_dq = MatrixFixed.dRq_times_a_by_dq(((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.get_qRES(), hLhatRi);
// Put dypi_by_dxp together
dypi_by_dxpRES.Fill(0.0f);
dypi_by_dxpRES.Put(0, 0, 1.0f);
dypi_by_dxpRES.Put(1, 1, 1.0f);
dypi_by_dxpRES.Put(2, 2, 1.0f);
dypi_by_dxpRES.Update(dhLhatWi_by_dq, 3, 3);
// cout << "dypi_by_dxpRES" << dypi_by_dxpRES;
// dypi_by_dhi = (drWi_by_dhi )
// (dhLhatWi_by_dhi)
// = (0 )
// (dhLhatWi_by_dhi)
// hLhatWi = RWR * hLhatRi
// Need to work out derivative for this
// dhLhatWi_by_dhi = RWR * dhLhatRi_by_dhLRi * dhLRi_by_dhi
MatrixFixed dhLhatWi_by_dhi = RWR * dhLhatRi_by_dhLRi * ((Wide_Camera_Point_Feature_Measurement_Model)wide_model).m_camera.UnprojectionJacobian();
dypi_by_dhiRES.Fill(0.0f);
dypi_by_dhiRES.Update(dhLhatWi_by_dhi, 3, 0);
// cout << "dypi_by_dhiRES" << dypi_by_dhiRES;
// And construct Ri
func_Ri(hi);
/*
if (Camera_Constants.DEBUGDUMP) Debug.WriteLine("func_ypi: hi = " + hi + "," +
"xp = " + xp + "," +
"ypiRES = " + ypiRES);
*/
}
public override void func_zeroedyi_and_dzeroedyi_by_dxp_and_dzeroedyi_by_dyi(Vector yi, Vector xp)
{
Wide_Camera_Point_Feature_Measurement_Model wm = (Wide_Camera_Point_Feature_Measurement_Model)wide_model;
// Extract cartesian and quaternion components of xp
wm.threed_motion_model.func_r(xp);
wm.threed_motion_model.func_q(xp);
// Extract ri and hhati components of yi = ypi
func_ri(yi);
func_hhati(yi);
// ri part: transformation is just the same as in the normal point case
// zeroedri = RRW(rWi - rW) //commented out in original code
// ri - r
Vector3D yWiminusrW = new Vector3D(riRES - wm.threed_motion_model.get_rRES());
Quaternion qRW = wm.threed_motion_model.get_qRES().Inverse();
MatrixFixed dqRW_by_dq = MatrixFixed.dqbar_by_dq();
// Rotation RRW
RotationMatrix RRW = qRW.RotationMatrix();
// RRW(rWi - rW)
Vector3D zeroedri = new Vector3D(RRW * yWiminusrW);
// Now calculate Jacobians
// dzeroedri_by_dri is RRW
// dzeroedri_by_dhhati = 0
MatrixFixed dzeroedri_by_dri = new MatrixFixed(RRW);
// dzeroedyi_by_dxp:
// dzeroedri_by_dr = -RRW
// dzeroedri_by_dq = d_dq(RRW (ri - r))
MatrixFixed dzeroedri_by_dr = RRW * -1.0f;
MatrixFixed dzeroedri_by_dqRW = MatrixFixed.dRq_times_a_by_dq(qRW, yWiminusrW);
MatrixFixed dzeroedri_by_dq = dzeroedri_by_dqRW * dqRW_by_dq;
// Now for the hhati part (easier...)
// zeroedhhati = RRW hhati
Vector3D zeroedhhati = new Vector3D(RRW * hhatiRES);
// Jacobians
// dzeroedhhati_by_dr = 0
// dzeroedhhati_by_dq = d_dq(RRW hhati)
// dzeroedhhati_by_dhhati = RRW
// dzeroedhhati_by_dri = 0
MatrixFixed dzeroedhhati_by_dqRW = MatrixFixed.dRq_times_a_by_dq(qRW, hhatiRES);
MatrixFixed dzeroedhhati_by_dq = dzeroedhhati_by_dqRW * dqRW_by_dq;
MatrixFixed dzeroedhhati_by_dhhati = new MatrixFixed(RRW);
// And put it all together
zeroedyiRES.Update(zeroedri.GetVNL3(), 0);
zeroedyiRES.Update(zeroedhhati.GetVNL3(), 3);
//cout << "Line: zeroedri = " << zeroedri << "zeroedhhati = " << zeroedhhati;
dzeroedyi_by_dxpRES.Fill(0.0f);
dzeroedyi_by_dxpRES.Update(dzeroedri_by_dr, 0, 0);
dzeroedyi_by_dxpRES.Update(dzeroedri_by_dq, 0, 3);
dzeroedyi_by_dxpRES.Update(dzeroedhhati_by_dq, 3, 3);
dzeroedyi_by_dyiRES.Fill(0.0f);
dzeroedyi_by_dyiRES.Update(dzeroedri_by_dri, 0, 0);
dzeroedyi_by_dyiRES.Update(dzeroedhhati_by_dhhati, 3, 3);
}
public override void func_zeroedyi_and_dzeroedyi_by_dxp_and_dzeroedyi_by_dyi(Vector yi, Vector xp)
{
ThreeD_Motion_Model mm = ((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model;
// Extract cartesian and quaternion components of xp
mm.func_r(xp);
mm.func_q(xp);
Vector3D yWiminusrW = new Vector3D((new Vector3D(yi)) -(mm.get_rRES()));
Quaternion qRES = mm.get_qRES();
Quaternion qRW = qRES.Inverse();
MatrixFixed dqRW_by_dq = MatrixFixed.dqbar_by_dq();
// Rotation RRW
RotationMatrix RRW = qRW.RotationMatrix();
// Position of feature relative to robot in robot frame
Vector3D zeroedyi = new Vector3D(RRW * yWiminusrW);
zeroedyiRES.Update(zeroedyi.GetVNL3());
// Now calculate Jacobians
// dzeroedyi_by_dyi is RRW
dzeroedyi_by_dyiRES.Update(RRW);
// dzeroedyi_by_dxp has 2 partitions:
// dzeroedyi_by_dr (3 * 3)
// dzeroedyi_by_dq (3 * 4)
MatrixFixed dzeroedyi_by_dr = (MatrixFixed)(RRW);
dzeroedyi_by_dr *= -1.0f;
//These should be 3x4 dimension
MatrixFixed dzeroedyi_by_dqRW = MatrixFixed.dRq_times_a_by_dq(qRW, yWiminusrW);
MatrixFixed dzeroedyi_by_dq = dzeroedyi_by_dqRW * dqRW_by_dq;
dzeroedyi_by_dxpRES.Update(dzeroedyi_by_dr, 0, 0);
dzeroedyi_by_dxpRES.Update(dzeroedyi_by_dq, 0, 3);
}
/// <summary>
/// Create a state vector x_v from its component parts. Puts the matrices r, q, v, omega into their right places.
/// </summary>
/// <param name="r"></param>
/// <param name="q"></param>
/// <param name="v"></param>
/// <param name="omega"></param>
/// <param name="xv"></param>
public void compose_xv(ref Vector3D r, ref Quaternion q, ref Vector3D v, ref Vector3D omega, ref Vector xv)
{
xv.Update(r.GetVNL3(), 0);
xv.Update(q.GetRXYZ(), 3);
xv.Update(v.GetVNL3(), 7);
xv.Update(omega.GetVNL3(), 10);
}
// Function to find a region in an image guided by current motion prediction
// which doesn't overlap existing features
public static bool FindNonOverlappingRegion(Scene_Single scene,
Vector local_u,
float delta_t,
Partially_Initialised_Feature_Measurement_Model default_feature_type_for_initialisation,
uint camera_width,
uint camera_height,
uint BOXSIZE,
ref int init_feature_search_ustart,
ref int init_feature_search_vstart,
ref int init_feature_search_ufinish,
ref int init_feature_search_vfinish,
uint FEATURE_INIT_STEPS_TO_PREDICT,
float FEATURE_INIT_DEPTH_HYPOTHESIS,
Random rnd)
{
ThreeD_Motion_Model threed_motion_model = (ThreeD_Motion_Model)scene.get_motion_model();
Vector local_xv = new Vector(scene.get_xv());
for (uint i = 0; i < FEATURE_INIT_STEPS_TO_PREDICT; i++)
{
scene.get_motion_model().func_fv_and_dfv_by_dxv(local_xv, local_u, delta_t);
local_xv.Update(scene.get_motion_model().get_fvRES());
}
threed_motion_model.func_xp(local_xv);
Vector local_xp = new Vector(threed_motion_model.get_xpRES());
threed_motion_model.func_r(local_xp);
Vector3D rW = threed_motion_model.get_rRES();
threed_motion_model.func_q(local_xp);
Quaternion qWR = threed_motion_model.get_qRES();
// yW = rW + RWR hR
Vector3D hR = new Vector3D(0.0f, 0.0f, FEATURE_INIT_DEPTH_HYPOTHESIS);
// Used Inverse + transpose because this was't compiling the normal way
Vector3D yW = new Vector3D(rW + qWR.RotationMatrix() * hR);
// Then project that point into the current camera position
scene.get_motion_model().func_xp(scene.get_xv());
Fully_Initialised_Feature_Measurement_Model fully_init_fmm =
(Fully_Initialised_Feature_Measurement_Model)(default_feature_type_for_initialisation.more_initialised_feature_measurement_model);
Vector yWVNL = yW.GetVNL3();
fully_init_fmm.func_hi_and_dhi_by_dxp_and_dhi_by_dyi(yWVNL, scene.get_motion_model().get_xpRES());
// Now, this defines roughly how much we expect a feature initialised to move
float suggested_u = fully_init_fmm.get_hiRES()[0];
float suggested_v = fully_init_fmm.get_hiRES()[1];
float predicted_motion_u = camera_width / 2.0f - suggested_u;
float predicted_motion_v = camera_height / 2.0f - suggested_v;
// So, the limits of a "safe" region within which we can initialise
// features so that they end up staying within the screen
// (Making the approximation that the whole screen moves like the
// centre point)
int safe_feature_search_ustart = (int)(-predicted_motion_u);
int safe_feature_search_vstart = (int)(-predicted_motion_v);
int safe_feature_search_ufinish = (int)(camera_width - predicted_motion_u);
int safe_feature_search_vfinish = (int)(camera_height - predicted_motion_v);
if (safe_feature_search_ustart < ((int)((BOXSIZE - 1) / 2) + 1))
safe_feature_search_ustart = (int)((BOXSIZE - 1) / 2 + 1);
if (safe_feature_search_ufinish > (int)camera_width - ((int)((BOXSIZE - 1) / 2) + 1))
safe_feature_search_ufinish = (int)(camera_width - (BOXSIZE - 1) / 2 - 1);
if (safe_feature_search_vstart < ((int)((BOXSIZE - 1) / 2) + 1))
safe_feature_search_vstart = (int)((BOXSIZE - 1) / 2 + 1);
if (safe_feature_search_vfinish > (int)camera_height - ((int)((BOXSIZE - 1) / 2) + 1))
safe_feature_search_vfinish = (int)(camera_height - (BOXSIZE - 1) / 2 - 1);
return FindNonOverlappingRegionNoPredict(safe_feature_search_ustart,
safe_feature_search_vstart,
safe_feature_search_ufinish,
safe_feature_search_vfinish,
scene,
ref init_feature_search_ustart,
ref init_feature_search_vstart,
ref init_feature_search_ufinish,
ref init_feature_search_vfinish, rnd);
}
public override void func_xpredef_and_dxpredef_by_dxp_and_dxpredef_by_dxpdef
(Vector xp, Vector xpdef)
{
// Split position state into cartesian and quaternion
// r0, q0: position in original frame
func_r(xp);
func_q(xp);
Vector3D r0 = rRES;
Quaternion q0 = qRES;
// rn, qn: definition of new frame
func_r(xpdef);
func_q(xpdef);
Vector3D rn = rRES;
Quaternion qn = qRES;
Quaternion qnbar = qn.Conjugate();
// Calculate new cartesian part of xp
Vector3D Temp31a = new Vector3D(r0 - rn); // Temp31a is r0 - rn
RotationMatrix Temp33a = qnbar.RotationMatrix();
Vector3D Temp31b = new Vector3D(Temp33a * Temp31a);
// Copy into xpredefRES
xpredefRES[0] = Temp31b.GetX();
xpredefRES[1] = Temp31b.GetY();
xpredefRES[2] = Temp31b.GetZ();
// Calculate new quaternion part of xp
Quaternion Tempqa = qnbar.Multiply(q0);
// Copy into xpredefRES
Vector vecTempqa = Tempqa.GetRXYZ();
xpredefRES.Update(vecTempqa, 3);
// Form Jacobian dxpredef_by_dxpRES
dxpredef_by_dxpRES.Fill(0.0f);
dxpredef_by_dxpRES.Update(Temp33a, 0, 0);
MatrixFixed Temp44a = MatrixFixed.dq3_by_dq1(qnbar);
dxpredef_by_dxpRES.Update(Temp44a, 3, 3);
// Form Jacobian dxpredef_by_dxpdefRES
dxpredef_by_dxpdefRES.Fill(0.0f);
//Temp33a *= -1.0f;
Temp33a = (RotationMatrix)(Temp33a * - 1.0f);
dxpredef_by_dxpdefRES.Update(Temp33a, 0, 0);
Temp44a = MatrixFixed.dq3_by_dq2(q0);
MatrixFixed Temp44b = MatrixFixed.dqbar_by_dq();
MatrixFixed Temp44c = Temp44a * Temp44b;
dxpredef_by_dxpdefRES.Update(Temp44c, 3, 3);
// Top right corner of this Jacobian is tricky because we have to
// differentiate a rotation matrix
// Uses function that does this in bits.cc
// Build this corner in Temp34a
//MatrixFixed temp = new MatrixFixed(3,4);
MatrixFixed Temp34a = MatrixFixed.dRq_times_a_by_dq(qnbar, Temp31a.GetVNL3());
// So far we have drN_by_dqnbar; want _by_dqn
MatrixFixed Temp34b = Temp34a * Temp44b;
// Finally copy into result matrix
dxpredef_by_dxpdefRES.Update(Temp34b, 0, 3);
// cout << "dxpredef_by_dxpdefRES" << dxpredef_by_dxpdefRES;
}
