vrpn_IMU_SimpleCombiner::vrpn_IMU_SimpleCombiner
(const char * name, vrpn_Connection * trackercon,
vrpn_Tracker_IMU_Params *params,
float update_rate, bool report_changes)
: vrpn_Tracker(name, trackercon),
d_update_interval(update_rate ? (1 / update_rate) : 1.0),
d_report_changes(report_changes)
{
// Set the restoration rates for gravity and north.
// These are the fraction of the way to full restoration that should
// occur over one second.
d_gravity_restore_rate = 0.9;
d_north_restore_rate = 0.9;
// Hook up the parameters for acceleration and rotational velocity
d_acceleration.params = params->d_acceleration;
d_rotational_vel.params = params->d_rotational_vel;
// Magetometers by definition produce unit vectors and
// have their axes as (x,y,z) so we just have to specify
// the name here and the others are all set to pass the
// values through.
d_magnetometer.params.name = params->d_magnetometer_name;
for (int i = 0; i < 3; i++) {
d_magnetometer.params.channels[i] = i;
d_magnetometer.params.offsets[i] = 0;
d_magnetometer.params.scales[i] = 1;
}
//--------------------------------------------------------------------
// Open analog remotes for any channels that have non-NULL names.
// If the name starts with the "*" character, use tracker
// connection rather than getting a new connection for it.
// Set up callbacks to handle updates to the analog values.
setup_vector(&d_acceleration, handle_analog_update);
setup_vector(&d_rotational_vel, handle_analog_update);
setup_vector(&d_magnetometer, handle_analog_update);
//--------------------------------------------------------------------
// Set the current timestamp to "now", the current orientation to identity
// and the angular rotation velocity to zero.
vrpn_gettimeofday(&d_prevtime, NULL);
d_prev_update_time = d_prevtime;
vrpn_Tracker::timestamp = d_prevtime;
q_vec_set(pos, 0, 0, 0);
q_from_axis_angle(d_quat, 0, 0, 1, 0);
q_vec_set(vel, 0, 0, 0);
q_from_axis_angle(vel_quat, 0, 0, 1, 0);
vel_quat_dt = 1;
}
/// Interpolates the values at three 2D points to the
/// location of a third point.
static double interpolate(double p1X, double p1Y, double val1, double p2X,
double p2Y, double val2, double p3X, double p3Y,
double val3, double pointX, double pointY) {
// Fit a plane to three points, using their values as the
// third dimension.
q_vec_type p1, p2, p3;
q_vec_set(p1, p1X, p1Y, val1);
q_vec_set(p2, p2X, p2Y, val2);
q_vec_set(p3, p3X, p3Y, val3);
// The normalized cross product of the vectors from the first
// point to each of the other two is normal to this plane.
q_vec_type v1, v2;
q_vec_subtract(v1, p2, p1);
q_vec_subtract(v2, p3, p1);
q_vec_type ABC;
q_vec_cross_product(ABC, v1, v2);
if (q_vec_magnitude(ABC) == 0) {
// We can't get a normal, degenerate points, just return the first
// value.
return val1;
}
q_vec_normalize(ABC, ABC);
// Solve for the D associated with the plane by filling back
// in one of the points. This is done by taking the dot product
// of the ABC vector with the first point. We then solve for D.
// AX + BY + CZ + D = 0; D = -(AX + BY + CZ)
double D = -q_vec_dot_product(ABC, p1);
// Evaluate the plane equations at our input point, which will interpolate
// or extrapolate our values.
// We're solving for Z in this case, so we get
// CZ = -(AX + BY + D); Z = -(AX + BY + D)/C;
return -(ABC[0] * pointX + ABC[1] * pointY + D) / ABC[2];
}
void vrpn_IMU_SimpleCombiner::update_matrix_based_on_values(double time_interval)
{
//==================================================================
// Adjust the orientation based on the rotational velocity, which is
// measured in the rotated coordinate system. We need to rotate the
// difference vector back to the canonical orientation, apply the
// orientation change there, and then rotate back.
// Be sure to scale by the time value.
q_type forward, inverse;
q_copy(forward, d_quat);
q_invert(inverse, forward);
// Remember that Euler angles in Quatlib have rotation around Z in
// the first term. Compute the time-scaled delta transform in
// canonical space.
q_type delta;
q_from_euler(delta,
time_interval * d_rotational_vel.values[Q_Z],
time_interval * d_rotational_vel.values[Q_Y],
time_interval * d_rotational_vel.values[Q_X]);
// Bring the delta back into canonical space
q_type canonical;
q_mult(canonical, delta, inverse);
q_mult(canonical, forward, canonical);
q_mult(d_quat, canonical, d_quat);
//==================================================================
// To the extent that the acceleration vector's magnitude is equal
// to the expected gravity, rotate the orientation so that the vector
// points downward. This is measured in the rotated coordinate system,
// so we need to rotate back to canonical orientation and apply
// the difference there and then rotate back. The rate of rotation
// should be as specified in the gravity-rotation-rate parameter so
// we don't swing the head around too quickly but only slowly re-adjust.
double accel = sqrt(
d_acceleration.values[0] * d_acceleration.values[0] +
d_acceleration.values[1] * d_acceleration.values[1] +
d_acceleration.values[2] * d_acceleration.values[2] );
double diff = fabs(accel - 9.80665);
// Only adjust if we're close enough to the expected gravity
// @todo In a more complicated IMU tracker, base this on state and
// error estimates from a Kalman or other filter.
double scale = 1.0 - diff;
if (scale > 0) {
// Get a new forward and inverse matrix from the current, just-
// rotated matrix.
q_copy(forward, d_quat);
// Change how fast we adjust based on how close we are to the
// expected value of gravity. Then further scale this by the
// amount of time since the last estimate.
double gravity_scale = scale * d_gravity_restore_rate * time_interval;
// Rotate the gravity vector by the estimated transform.
// We expect this direction to match the global down (-Y) vector.
q_vec_type gravity_global;
q_vec_set(gravity_global, d_acceleration.values[0],
d_acceleration.values[1], d_acceleration.values[2]);
q_vec_normalize(gravity_global, gravity_global);
q_xform(gravity_global, forward, gravity_global);
//printf(" XXX Gravity: %lg, %lg, %lg\n", gravity_global[0], gravity_global[1], gravity_global[2]);
// Determine the rotation needed to take gravity and rotate
// it into the direction of -Y.
q_vec_type neg_y;
q_vec_set(neg_y, 0, -1, 0);
q_type rot;
q_from_two_vecs(rot, gravity_global, neg_y);
// Scale the rotation by the fraction of the orientation we
// should remove based on the time that has passed, how well our
// gravity vector matches expected, and the specified rate of
// correction.
static q_type identity = { 0, 0, 0, 1 };
q_type scaled_rot;
q_slerp(scaled_rot, identity, rot, gravity_scale);
//printf("XXX Scaling gravity vector by %lg\n", gravity_scale);
// Rotate by this angle.
q_mult(d_quat, scaled_rot, d_quat);
//==================================================================
// If we are getting compass data, and to the extent that the
// acceleration vector's magnitude is equal to the expected gravity,
// compute the cross product of the cross product to find the
// direction of north perpendicular to down. This is measured in
// the rotated coordinate system, so we need to rotate back to the
// canonical orientation and do the comparison there.
// The fraction of rotation should be as specified in the
// magnetometer-rotation-rate parameter so we don't swing the head
// around too quickly but only slowly re-adjust.
if (d_magnetometer.ana != NULL) {
// Get a new forward and inverse matrix from the current, just-
// rotated matrix.
q_copy(forward, d_quat);
// Find the North vector that is perpendicular to gravity by
// clearing its Y axis to zero and renormalizing.
q_vec_type magnetometer;
q_vec_set(magnetometer, d_magnetometer.values[0],
d_magnetometer.values[1], d_magnetometer.values[2]);
q_vec_type magnetometer_global;
q_xform(magnetometer_global, forward, magnetometer);
magnetometer_global[Q_Y] = 0;
q_vec_type north_global;
q_vec_normalize(north_global, magnetometer_global);
//printf(" XXX north_global: %lg, %lg, %lg\n", north_global[0], north_global[1], north_global[2]);
// Determine the rotation needed to take north and rotate it
// into the direction of negative Z.
q_vec_type neg_z;
q_vec_set(neg_z, 0, 0, -1);
q_from_two_vecs(rot, north_global, neg_z);
// Change how fast we adjust based on how close we are to the
// expected value of gravity. Then further scale this by the
// amount of time since the last estimate.
double north_rate = scale * d_north_restore_rate * time_interval;
// Scale the rotation by the fraction of the orientation we
// should remove based on the time that has passed, how well our
// gravity vector matches expected, and the specified rate of
// correction.
static q_type identity = { 0, 0, 0, 1 };
q_slerp(scaled_rot, identity, rot, north_rate);
// Rotate by this angle.
q_mult(d_quat, scaled_rot, d_quat);
}
}
//==================================================================
// Compute and store the velocity information
// This will be in the rotated coordinate system, so we need to
// rotate back to the identity orientation before storing.
// Convert from radians/second into a quaternion rotation as
// rotated in a hundredth of a second and set the rotational
// velocity dt to a hundredth of a second so that we don't
// risk wrapping.
// Remember that Euler angles in Quatlib have rotation around Z in
// the first term. Compute the time-scaled delta transform in
// canonical space.
q_from_euler(delta,
1e-2 * d_rotational_vel.values[Q_Z],
1e-2 * d_rotational_vel.values[Q_Y],
1e-2 * d_rotational_vel.values[Q_X]);
// Bring the delta back into canonical space
q_mult(canonical, delta, inverse);
q_mult(vel_quat, forward, canonical);
vel_quat_dt = 1e-2;
}
void vrpn_Tracker_AnalogFly::update_matrix_based_on_values
(double time_interval)
{
double tx,ty,tz, rx,ry,rz; // Translation (m/s) and rotation (rad/sec)
q_matrix_type diffM; // Difference (delta) matrix
// For absolute trackers, the interval is treated as "1", so that the
// translations and rotations are unscaled;
if (d_absolute) { time_interval = 1.0; };
// compute the translation and rotation
tx = d_x.value * time_interval;
ty = d_y.value * time_interval;
tz = d_z.value * time_interval;
rx = d_sx.value * time_interval * (2*VRPN_PI);
ry = d_sy.value * time_interval * (2*VRPN_PI);
rz = d_sz.value * time_interval * (2*VRPN_PI);
// Build a rotation matrix, then add in the translation
q_euler_to_col_matrix(diffM, rz, ry, rx);
diffM[3][0] = tx; diffM[3][1] = ty; diffM[3][2] = tz;
// While the clutch is not engaged, we don't move. Record that
// the clutch was off so that we know later when it is re-engaged.
if (!d_clutch_engaged) {
d_clutch_was_off = true;
return;
}
// When the clutch becomes re-engaged, we store the current matrix
// multiplied by the inverse of the present differential matrix so that
// the first frame of the mouse-hold leaves us in the same location.
// For the absolute matrix, this re-engages new motion at the previous
// location.
if (d_clutch_engaged && d_clutch_was_off) {
d_clutch_was_off = false;
q_type diff_orient;
// This is backwards, because Euler angles have rotation about Z first...
q_from_euler(diff_orient, rz, ry, rx);
q_xyz_quat_type diff;
q_vec_set(diff.xyz, tx, ty, tz);
q_copy(diff.quat, diff_orient);
q_xyz_quat_type diff_inverse;
q_xyz_quat_invert(&diff_inverse, &diff);
q_matrix_type di_matrix;
q_to_col_matrix(di_matrix, diff_inverse.quat);
di_matrix[3][0] = diff_inverse.xyz[0];
di_matrix[3][1] = diff_inverse.xyz[1];
di_matrix[3][2] = diff_inverse.xyz[2];
q_matrix_mult(d_clutchMatrix, di_matrix, d_currentMatrix);
}
// Apply the matrix.
if (d_absolute) {
// The difference matrix IS the current matrix. Catenate it
// onto the clutch matrix. If there is no clutching happening,
// this matrix will always be the identity so this will just
// copy the difference matrix.
q_matrix_mult(d_currentMatrix, diffM, d_clutchMatrix);
} else {
// Multiply the current matrix by the difference matrix to update
// it to the current time.
if (d_worldFrame) {
// If using world frame:
// 1. Separate out the translation and add to the differential translation
tx += d_currentMatrix[3][0];
ty += d_currentMatrix[3][1];
tz += d_currentMatrix[3][2];
diffM[3][0] = 0; diffM[3][1] = 0; diffM[3][2] = 0;
d_currentMatrix[3][0] = 0; d_currentMatrix[3][1] = 0; d_currentMatrix[3][2] = 0;
// 2. Compose the rotations.
q_matrix_mult(d_currentMatrix, d_currentMatrix, diffM);
// 3. Put the new translation back in the matrix.
d_currentMatrix[3][0] = tx; d_currentMatrix[3][1] = ty; d_currentMatrix[3][2] = tz;
} else {
q_matrix_mult(d_currentMatrix, diffM, d_currentMatrix);
}
}
// Finally, convert the matrix into a pos/quat
// and copy it into the tracker position and quaternion structures.
convert_matrix_to_tracker();
}
int vrpn_Tracker_DeadReckoning_Rotation::test(void)
{
// Construct a loopback connection to be used by all of our objects.
vrpn_Connection *c = vrpn_create_server_connection("loopback:");
// Create a tracker server to be the initator and a dead-reckoning
// rotation tracker to use it as a base; have it predict 1 second
// into the future.
vrpn_Tracker_Server *t0 = new vrpn_Tracker_Server("Tracker0", c, 2);
vrpn_Tracker_DeadReckoning_Rotation *t1 =
new vrpn_Tracker_DeadReckoning_Rotation("Tracker1", c, "*Tracker0", 2, 1);
// Create a remote tracker to listen to t1 and set up its callbacks for
// position and velocity reports. They will fill in the static structures
// listed above with whatever values they receive.
vrpn_Tracker_Remote *tr = new vrpn_Tracker_Remote("Tracker1", c);
tr->register_change_handler(&poseResponse, handle_test_tracker_report);
tr->register_change_handler(&velResponse, handle_test_tracker_velocity_report);
// Set up the values in the pose and velocity responses with incorrect values
// so that things will fail if the class does not perform as expected.
q_vec_set(poseResponse.pos, 1, 1, 1);
q_make(poseResponse.quat, 0, 0, 1, 0);
poseResponse.time.tv_sec = 0;
poseResponse.time.tv_usec = 0;
poseResponse.sensor = -1;
// Send a pose report from sensors 0 and 1 on the original tracker that places
// them at (1,1,1) and with the identity rotation. We should get a response for
// each of them so we should end up with the sensor-1 response matching what we
// sent, with no change in position or orientation.
q_vec_type pos = { 1, 1, 1 };
q_type quat = { 0, 0, 0, 1 };
struct timeval firstSent;
vrpn_gettimeofday(&firstSent, NULL);
t0->report_pose(0, firstSent, pos, quat);
t0->report_pose(1, firstSent, pos, quat);
t0->mainloop();
t1->mainloop();
c->mainloop();
tr->mainloop();
if ( (poseResponse.time.tv_sec != firstSent.tv_sec + 1)
|| (poseResponse.sensor != 1)
|| (q_vec_distance(poseResponse.pos, pos) > 1e-10)
|| (poseResponse.quat[Q_W] != 1)
)
{
std::cerr << "vrpn_Tracker_DeadReckoning_Rotation::test(): Got unexpected"
<< " initial response: pos (" << poseResponse.pos[Q_X] << ", "
<< poseResponse.pos[Q_Y] << ", " << poseResponse.pos[Q_Z] << "), quat ("
<< poseResponse.quat[Q_X] << ", " << poseResponse.quat[Q_Y] << ", "
<< poseResponse.quat[Q_Z] << ", " << poseResponse.quat[Q_W] << ")"
<< " from sensor " << poseResponse.sensor
<< " at time " << poseResponse.time.tv_sec << ":" << poseResponse.time.tv_usec
<< std::endl;
delete tr;
delete t1;
delete t0;
c->removeReference();
return 1;
}
// Send a second tracker report for sensor 0 coming 0.4 seconds later that has
// translated to position (2,1,1) and rotated by 0.4 * 90 degrees around Z.
// This should cause a prediction for one second later than this new pose
// message that has rotated by very close to 1.4 * 90 degrees.
q_vec_type pos2 = { 2, 1, 1 };
q_type quat2;
double angle2 = 0.4 * 90 * M_PI / 180.0;
q_from_axis_angle(quat2, 0, 0, 1, angle2);
struct timeval p4Second = { 0, 400000 };
struct timeval firstPlusP4 = vrpn_TimevalSum(firstSent, p4Second);
t0->report_pose(0, firstPlusP4, pos2, quat2);
t0->mainloop();
t1->mainloop();
c->mainloop();
tr->mainloop();
double x, y, z, angle;
q_to_axis_angle(&x, &y, &z, &angle, poseResponse.quat);
if ((poseResponse.time.tv_sec != firstPlusP4.tv_sec + 1)
|| (poseResponse.sensor != 0)
|| (q_vec_distance(poseResponse.pos, pos2) > 1e-10)
|| !isClose(x, 0) || !isClose(y, 0) || !isClose(z, 1)
|| !isClose(angle, 1.4 * 90 * M_PI / 180.0)
)
{
std::cerr << "vrpn_Tracker_DeadReckoning_Rotation::test(): Got unexpected"
<< " predicted pose response: pos (" << poseResponse.pos[Q_X] << ", "
<< poseResponse.pos[Q_Y] << ", " << poseResponse.pos[Q_Z] << "), quat ("
<< poseResponse.quat[Q_X] << ", " << poseResponse.quat[Q_Y] << ", "
<< poseResponse.quat[Q_Z] << ", " << poseResponse.quat[Q_W] << ")"
<< " from sensor " << poseResponse.sensor
<< std::endl;
delete tr;
delete t1;
delete t0;
c->removeReference();
return 2;
}
// Send a velocity report for sensor 1 that has has translation by (1,0,0)
// and rotating by 0.4 * 90 degrees per 0.4 of a second around Z.
// This should cause a prediction for one second later than the first
// report that has rotated by very close to 90 degrees. The translation
// should be ignored, so the position should be the original position.
q_vec_type vel = { 0, 0, 0 };
t0->report_pose_velocity(1, firstPlusP4, vel, quat2, 0.4);
t0->mainloop();
t1->mainloop();
c->mainloop();
tr->mainloop();
q_to_axis_angle(&x, &y, &z, &angle, poseResponse.quat);
if ((poseResponse.time.tv_sec != firstSent.tv_sec + 1)
|| (poseResponse.sensor != 1)
|| (q_vec_distance(poseResponse.pos, pos) > 1e-10)
|| !isClose(x, 0) || !isClose(y, 0) || !isClose(z, 1)
|| !isClose(angle, 90 * M_PI / 180.0)
)
{
std::cerr << "vrpn_Tracker_DeadReckoning_Rotation::test(): Got unexpected"
<< " predicted velocity response: pos (" << poseResponse.pos[Q_X] << ", "
<< poseResponse.pos[Q_Y] << ", " << poseResponse.pos[Q_Z] << "), quat ("
<< poseResponse.quat[Q_X] << ", " << poseResponse.quat[Q_Y] << ", "
<< poseResponse.quat[Q_Z] << ", " << poseResponse.quat[Q_W] << ")"
<< " from sensor " << poseResponse.sensor
<< std::endl;
delete tr;
delete t1;
delete t0;
c->removeReference();
return 3;
}
// To test the behavior of the prediction code when we're moving around more
// than one axis, and when we're starting from a non-identity orientation,
// set sensor 1 to be rotated 180 degrees around X. Then send a velocity
// report that will produce a rotation of 180 degrees around Z. The result
// should match a prediction of 180 degrees around Y (plus or minus 180, plus
// or minus Y axis are all equivalent).
struct timeval oneSecond = { 1, 0 };
struct timeval firstPlusOne = vrpn_TimevalSum(firstSent, oneSecond);
q_type quat3;
q_from_axis_angle(quat3, 1, 0, 0, M_PI);
t0->report_pose(1, firstPlusOne, pos, quat3);
q_type quat4;
q_from_axis_angle(quat4, 0, 0, 1, M_PI);
t0->report_pose_velocity(1, firstPlusOne, vel, quat4, 1.0);
t0->mainloop();
t1->mainloop();
c->mainloop();
tr->mainloop();
q_to_axis_angle(&x, &y, &z, &angle, poseResponse.quat);
if ((poseResponse.time.tv_sec != firstPlusOne.tv_sec + 1)
|| (poseResponse.sensor != 1)
|| (q_vec_distance(poseResponse.pos, pos) > 1e-10)
|| !isClose(x, 0) || !isClose(fabs(y), 1) || !isClose(z, 0)
|| !isClose(fabs(angle), M_PI)
)
{
std::cerr << "vrpn_Tracker_DeadReckoning_Rotation::test(): Got unexpected"
<< " predicted pose + velocity response: pos (" << poseResponse.pos[Q_X] << ", "
<< poseResponse.pos[Q_Y] << ", " << poseResponse.pos[Q_Z] << "), quat ("
<< poseResponse.quat[Q_X] << ", " << poseResponse.quat[Q_Y] << ", "
<< poseResponse.quat[Q_Z] << ", " << poseResponse.quat[Q_W] << ")"
<< " from sensor " << poseResponse.sensor
<< std::endl;
delete tr;
delete t1;
delete t0;
c->removeReference();
return 4;
}
// To test the behavior of the prediction code when we're moving around more
// than one axis, and when we're starting from a non-identity orientation,
// set sensor 0 to start out at identity. Then in one second it will be
// rotated 180 degrees around X. Then in another second it will be rotated
// additionally by 90 degrees around Z; the prediction should be another
// 90 degrees around Z, which should turn out to compose to +/-180 degrees
// around +/- Y, as in the velocity case above.
// To make this work, we send a sequence of three poses, one second apart,
// starting at the original time. We do this on sensor 0, which has never
// had a velocity report, so that it will be using the pose-only prediction.
struct timeval firstPlusTwo = vrpn_TimevalSum(firstPlusOne, oneSecond);
q_from_axis_angle(quat3, 1, 0, 0, M_PI);
t0->report_pose(0, firstSent, pos, quat);
t0->report_pose(0, firstPlusOne, pos, quat3);
q_from_axis_angle(quat4, 0, 0, 1, M_PI / 2);
q_type quat5;
q_mult(quat5, quat4, quat3);
t0->report_pose(0, firstPlusTwo, pos, quat5);
t0->mainloop();
t1->mainloop();
c->mainloop();
tr->mainloop();
q_to_axis_angle(&x, &y, &z, &angle, poseResponse.quat);
if ((poseResponse.time.tv_sec != firstPlusTwo.tv_sec + 1)
|| (poseResponse.sensor != 0)
|| (q_vec_distance(poseResponse.pos, pos) > 1e-10)
|| !isClose(x, 0) || !isClose(fabs(y), 1.0) || !isClose(z, 0)
|| !isClose(fabs(angle), M_PI)
)
{
std::cerr << "vrpn_Tracker_DeadReckoning_Rotation::test(): Got unexpected"
<< " predicted pose + pose response: pos (" << poseResponse.pos[Q_X] << ", "
<< poseResponse.pos[Q_Y] << ", " << poseResponse.pos[Q_Z] << "), quat ("
<< poseResponse.quat[Q_X] << ", " << poseResponse.quat[Q_Y] << ", "
<< poseResponse.quat[Q_Z] << ", " << poseResponse.quat[Q_W] << ")"
<< " from sensor " << poseResponse.sensor
<< "; axis = (" << x << ", " << y << ", " << z << "), angle = "
<< angle
<< std::endl;
delete tr;
delete t1;
delete t0;
c->removeReference();
return 5;
}
// Done; delete our objects and return 0 to indicate that
// everything worked.
delete tr;
delete t1;
delete t0;
c->removeReference();
return 0;
}