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/*
APM_AHRS_DCM.cpp
AHRS system using DCM matrices
Based on DCM code by Doug Weibel, Jordi Mu�oz and Jose Julio. DIYDrones.com
Adapted for the general ArduPilot AHRS interface by Andrew Tridgell
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public License
as published by the Free Software Foundation; either version 2.1
of the License, or (at your option) any later version.
*/
#include "AP_AHRS.h"
#include "output.h"
#include "profiler.h"
#include "analog.h"
#include "debug.h"
#include <stdio.h>
// this is the speed in cm/s above which we first get a yaw lock with
// the GPS
#define GPS_SPEED_MIN 300
// this is the speed in cm/s at which we stop using drift correction
// from the GPS and wait for the ground speed to get above GPS_SPEED_MIN
#define GPS_SPEED_RESET 100
// run a full DCM update round
void
AP_AHRS_DCM::update(int16_t attitude[3], float delta_t)
{
// Get current values for gyros
_gyro_vector = gyro_attitude;
_accel_vector = accel;
// Integrate the DCM matrix using gyro inputs
matrix_update(delta_t);
// Normalize the DCM matrix
normalize();
// Perform drift correction
//setCurrentProfiledActivity(DRIFT_CORRECTION);
drift_correction(delta_t);
// paranoid check for bad values in the DCM matrix
//setCurrentProfiledActivity(CHECK_MATRIX);
check_matrix();
// Calculate pitch, roll, yaw for stabilization and navigation
//setCurrentProfiledActivity(EULER_ANGLES);
euler_angles();
//setCurrentProfiledActivity(ANGLESOUTPUT);
attitude[0] = roll * INT16DEG_PI_FACTOR;
attitude[1] = pitch* INT16DEG_PI_FACTOR;
attitude[2] = yaw * INT16DEG_PI_FACTOR;
// Just for info:
int16_t sensor = degrees(roll) * 10;
debugOut.analog[0] = sensor;
sensor = degrees(pitch) * 10;
debugOut.analog[1] = sensor;
sensor = degrees(yaw) * 10;
if (sensor < 0)
sensor += 3600;
debugOut.analog[2] = sensor;
}
// update the DCM matrix using only the gyros
void
AP_AHRS_DCM::matrix_update(float _G_Dt)
{
//setCurrentProfiledActivity(MATRIX_UPDATE1);
// _omega_integ_corr is used for _centripetal correction
// (theoretically better than _omega)
_omega_integ_corr = _gyro_vector + _omega_I;
// Equation 16, adding proportional and integral correction terms
_omega = _omega_integ_corr + _omega_P + _omega_yaw_P;
// this is a replacement of the DCM matrix multiply (equation
// 17), with known zero elements removed and the matrix
// operations inlined. This runs much faster than the original
// version of this code, as the compiler was doing a terrible
// job of realising that so many of the factors were in common
// or zero. It also uses much less stack, as we no longer need
// two additional local matrices
Vector3f r = _omega * _G_Dt;
//setCurrentProfiledActivity(MATRIX_UPDATE2);
_dcm_matrix.rotate(r);
}
// adjust an accelerometer vector for known acceleration forces
void
AP_AHRS_DCM::accel_adjust(Vector3f &accel)
{
float veloc;
// compensate for linear acceleration. This makes a
// surprisingly large difference in the pitch estimate when
// turning, plus on takeoff and landing
//float acceleration = _gps->acceleration();
//accel.x -= acceleration;
// compensate for centripetal acceleration
veloc = 0; //_gps->ground_speed * 0.01;
// We are working with a modified version of equation 26 as
// our IMU object reports acceleration in the positive axis
// direction as positive
// Equation 26 broken up into separate pieces
accel.y -= _omega_integ_corr.z * veloc;
accel.z += _omega_integ_corr.y * veloc;
}
/*
reset the DCM matrix and omega. Used on ground start, and on
extreme errors in the matrix
*/
void
AP_AHRS_DCM::reset(bool recover_eulers)
{
if (_compass != NULL) {
_compass->null_offsets_disable();
}
// reset the integration terms
_omega_I.zero();
_omega_P.zero();
_omega_yaw_P.zero();
_omega_integ_corr.zero();
_omega.zero();
// if the caller wants us to try to recover to the current
// attitude then calculate the dcm matrix from the current
// roll/pitch/yaw values
if (recover_eulers && !isnan(roll) && !isnan(pitch) && !isnan(yaw)) {
_dcm_matrix.from_euler(roll, pitch, yaw);
} else {
// otherwise make it flat
_dcm_matrix.from_euler(0, 0, 0);
}
if (_compass != NULL) {
_compass->null_offsets_enable(); // This call is needed to restart the nulling
// Otherwise the reset in the DCM matrix can mess up
// the nulling
}
}
/*
check the DCM matrix for pathological values
*/
void
AP_AHRS_DCM::check_matrix(void)
{
if (_dcm_matrix.is_nan()) {
//Serial.printf("ERROR: DCM matrix NAN\n");
printf("ERROR: DCM matrix NAN\n");
renorm_blowup_count++;
reset(true);
return;
}
// some DCM matrix values can lead to an out of range error in
// the pitch calculation via asin(). These NaN values can
// feed back into the rest of the DCM matrix via the
// error_course value.
if (!(_dcm_matrix.c.x < 1.0 &&
_dcm_matrix.c.x > -1.0)) {
// We have an invalid matrix. Force a normalisation.
renorm_range_count++;
normalize();
if (_dcm_matrix.is_nan() ||
fabs(_dcm_matrix.c.x) > 10) {
// normalisation didn't fix the problem! We're
// in real trouble. All we can do is reset
//Serial.printf("ERROR: DCM matrix error. _dcm_matrix.c.x=%f\n",
// _dcm_matrix.c.x);
printf("ERROR: DCM matrix error. _dcm_matrix.c.x=%f\n", (double)_dcm_matrix.c.x);
renorm_blowup_count++;
reset(true);
}
}
}
// renormalise one vector component of the DCM matrix
// this will return false if renormalization fails
bool
AP_AHRS_DCM::renorm(Vector3f const &a, Vector3f &result)
{
float renorm_val;
// numerical errors will slowly build up over time in DCM,
// causing inaccuracies. We can keep ahead of those errors
// using the renormalization technique from the DCM IMU paper
// (see equations 18 to 21).
// For APM we don't bother with the taylor expansion
// optimisation from the paper as on our 2560 CPU the cost of
// the sqrt() is 44 microseconds, and the small time saving of
// the taylor expansion is not worth the potential of
// additional error buildup.
// Note that we can get significant renormalisation values
// when we have a larger delta_t due to a glitch eleswhere in
// APM, such as a I2c timeout or a set of EEPROM writes. While
// we would like to avoid these if possible, if it does happen
// we don't want to compound the error by making DCM less
// accurate.
renorm_val = 1.0 / a.length();
// keep the average for reporting
_renorm_val_sum += renorm_val;
_renorm_val_count++;
if (!(renorm_val < 2.0 && renorm_val > 0.5)) {
// this is larger than it should get - log it as a warning
renorm_range_count++;
if (!(renorm_val < 1.0e6 && renorm_val > 1.0e-6)) {
// we are getting values which are way out of
// range, we will reset the matrix and hope we
// can recover our attitude using drift
// correction before we hit the ground!
//Serial.printf("ERROR: DCM renormalisation error. renorm_val=%f\n",
// renorm_val);
printf("ERROR: DCM renormalisation error. renorm_val=%f\n", (double)renorm_val);
renorm_blowup_count++;
return false;
}
}
result = a * renorm_val;
return true;
}
/*************************************************
Direction Cosine Matrix IMU: Theory
William Premerlani and Paul Bizard
Numerical errors will gradually reduce the orthogonality conditions expressed by equation 5
to approximations rather than identities. In effect, the axes in the two frames of reference no
longer describe a rigid body. Fortunately, numerical error accumulates very slowly, so it is a
simple matter to stay ahead of it.
We call the process of enforcing the orthogonality conditions �renormalization�.
*/
void
AP_AHRS_DCM::normalize(void)
{
float error;
Vector3f t0, t1, t2;
//setCurrentProfiledActivity(MATRIX_NORMALIZE1);
error = _dcm_matrix.a * _dcm_matrix.b; // eq.18
t0 = _dcm_matrix.a - (_dcm_matrix.b * (0.5f * error)); // eq.19
t1 = _dcm_matrix.b - (_dcm_matrix.a * (0.5f * error)); // eq.19
t2 = t0 % t1;
//setCurrentProfiledActivity(MATRIX_NORMALIZE2);
if (!renorm(t0, _dcm_matrix.a) ||
!renorm(t1, _dcm_matrix.b) ||
!renorm(t2, _dcm_matrix.c)) {
// Our solution is blowing up and we will force back
// to last euler angles
reset(true);
}
}
// perform drift correction. This function aims to update _omega_P and
// _omega_I with our best estimate of the short term and long term
// gyro error. The _omega_P value is what pulls our attitude solution
// back towards the reference vector quickly. The _omega_I term is an
// attempt to learn the long term drift rate of the gyros.
//
// This function also updates _omega_yaw_P with a yaw correction term
// from our yaw reference vector
void
AP_AHRS_DCM::drift_correction(float deltat)
{
float error_course = 0;
Vector3f accel;
Vector3f error;
float error_norm = 0;
float yaw_deltat = 0;
accel = _accel_vector;
// if enabled, use the GPS to correct our accelerometer vector
// for centripetal forces
if(_centripetal &&
_gps != NULL &&
_gps->status() == GPS::GPS_OK) {
accel_adjust(accel);
}
//*****Roll and Pitch***************
// normalise the accelerometer vector to a standard length
// this is important to reduce the impact of noise on the
// drift correction, as very noisy vectors tend to have
// abnormally high lengths. By normalising the length we
// reduce their impact.
float accel_length = accel.length();
accel *= (_gravity / accel_length);
if (accel.is_inf()) {
// we can't do anything useful with this sample
_omega_P.zero();
return;
}
// calculate the error, in m/s^2, between the attitude
// implied by the accelerometers and the attitude
// in the current DCM matrix
error = _dcm_matrix.c % accel;
// Limit max error to limit the effect of noisy values
// on the algorithm. This limits the error to about 11
// degrees
error_norm = error.length();
if (error_norm > 2) {
error *= (2 / error_norm);
}
// we now want to calculate _omega_P and _omega_I. The
// _omega_P value is what drags us quickly to the
// accelerometer reading.
_omega_P = error * _kp_roll_pitch;
// the _omega_I is the long term accumulated gyro
// error. This determines how much gyro drift we can
// handle.
_omega_I_sum += error * (_ki_roll_pitch * deltat);
_omega_I_sum_time += deltat;
// these sums support the reporting of the DCM state via MAVLink
_error_rp_sum += error_norm;
_error_rp_count++;
// yaw drift correction
// we only do yaw drift correction when we get a new yaw
// reference vector. In between times we rely on the gyros for
// yaw. Avoiding this calculation on every call to
// update_DCM() saves a lot of time
if (_compass && _compass->use_for_yaw()) {
if (_compass->last_update != _compass_last_update) {
yaw_deltat = 1.0e-6*(_compass->last_update - _compass_last_update);
if (_have_initial_yaw && yaw_deltat < 2.0) {
// Equation 23, Calculating YAW error
// We make the gyro YAW drift correction based
// on compass magnetic heading
error_course = (_dcm_matrix.a.x * _compass->heading_y) - (_dcm_matrix.b.x * _compass->heading_x);
_compass_last_update = _compass->last_update;
} else {
// this is our first estimate of the yaw,
// or the compass has come back online after
// no readings for 2 seconds.
//
// construct a DCM matrix based on the current
// roll/pitch and the compass heading.
// First ensure the compass heading has been
// calculated
_compass->calculate(_dcm_matrix);
// now construct a new DCM matrix
_compass->null_offsets_disable();
_dcm_matrix.from_euler(roll, pitch, _compass->heading);
_compass->null_offsets_enable();
_have_initial_yaw = true;
_compass_last_update = _compass->last_update;
error_course = 0;
}
}
} else if (_gps && _gps->status() == GPS::GPS_OK) {
if (_gps->last_fix_time != _gps_last_update) {
// Use GPS Ground course to correct yaw gyro drift
if (_gps->ground_speed >= GPS_SPEED_MIN) {
yaw_deltat = 1.0e-3*(_gps->last_fix_time - _gps_last_update);
if (_have_initial_yaw && yaw_deltat < 2.0) {
float course_over_ground_x = cos(ToRad(_gps->ground_course/100.0));
float course_over_ground_y = sin(ToRad(_gps->ground_course/100.0));
// Equation 23, Calculating YAW error
error_course = (_dcm_matrix.a.x * course_over_ground_y) - (_dcm_matrix.b.x * course_over_ground_x);
_gps_last_update = _gps->last_fix_time;
} else {
// when we first start moving, set the
// DCM matrix to the current
// roll/pitch values, but with yaw
// from the GPS
if (_compass) {
_compass->null_offsets_disable();
}
_dcm_matrix.from_euler(roll, pitch, ToRad(_gps->ground_course));
if (_compass) {
_compass->null_offsets_enable();
}
_have_initial_yaw = true;
error_course = 0;
_gps_last_update = _gps->last_fix_time;
}
} else if (_gps->ground_speed >= GPS_SPEED_RESET) {
// we are not going fast enough to use GPS for
// course correction, but we won't reset
// _have_initial_yaw yet, instead we just let
// the gyro handle yaw
error_course = 0;
} else {
// we are moving very slowly. Reset
// _have_initial_yaw and adjust our heading
// rapidly next time we get a good GPS ground
// speed
error_course = 0;
_have_initial_yaw = false;
}
}
}
// see if there is any error in our heading relative to the
// yaw reference. This will be zero most of the time, as we
// only calculate it when we get new data from the yaw
// reference source
if (yaw_deltat == 0 || error_course == 0) {
// we don't have a new reference heading. Slowly
// decay the _omega_yaw_P to ensure that if we have
// lost the yaw reference sensor completely we don't
// keep using a stale offset
_omega_yaw_P *= 0.97;
goto check_sum_time;
}
// ensure the course error is scaled from -PI to PI
if (error_course > PI) {
error_course -= 2*PI;
} else if (error_course < -PI) {
error_course += 2*PI;
}
// Equation 24, Applys the yaw correction to the XYZ rotation of the aircraft
// this gives us an error in radians
error = _dcm_matrix.c * error_course;
// Adding yaw correction to proportional correction vector. We
// allow the yaw reference source to affect all 3 components
// of _omega_yaw_P as we need to be able to correctly hold a
// heading when roll and pitch are non-zero
_omega_yaw_P = error * _kp_yaw;
// add yaw correction to integrator correction vector, but
// only for the z gyro. We rely on the accelerometers for x
// and y gyro drift correction. Using the compass or GPS for
// x/y drift correction is too inaccurate, and can lead to
// incorrect builups in the x/y drift. We rely on the
// accelerometers to get the x/y components right
_omega_I_sum.z += error.z * (_ki_yaw * yaw_deltat);
// we keep the sum of yaw error for reporting via MAVLink.
_error_yaw_sum += error_course;
_error_yaw_count++;
check_sum_time:
if (_omega_I_sum_time > 10) {
// every 10 seconds we apply the accumulated
// _omega_I_sum changes to _omega_I. We do this to
// prevent short term feedback between the P and I
// terms of the controller. The _omega_I vector is
// supposed to refect long term gyro drift, but with
// high noise it can start to build up due to short
// term interactions. By summing it over 10 seconds we
// prevent the short term interactions and can apply
// the slope limit more accurately
float drift_limit = _gyro_drift_limit * _omega_I_sum_time;
_omega_I_sum.x = constrain(_omega_I_sum.x, -drift_limit, drift_limit);
_omega_I_sum.y = constrain(_omega_I_sum.y, -drift_limit, drift_limit);
_omega_I_sum.z = constrain(_omega_I_sum.z, -drift_limit, drift_limit);
_omega_I += _omega_I_sum;
// zero the sum
_omega_I_sum.zero();
_omega_I_sum_time = 0;
}
}
// calculate the euler angles which will be used for high level
// navigation control
void
AP_AHRS_DCM::euler_angles(void)
{
_dcm_matrix.to_euler(&roll, &pitch, &yaw);
}
/* reporting of DCM state for MAVLink */
// average error_roll_pitch since last call
float AP_AHRS_DCM::get_error_rp(void)
{
if (_error_rp_count == 0) {
// this happens when telemetry is setup on two
// serial ports
return _error_rp_last;
}
_error_rp_last = _error_rp_sum / _error_rp_count;
_error_rp_sum = 0;
_error_rp_count = 0;
return _error_rp_last;
}
// average error_yaw since last call
float AP_AHRS_DCM::get_error_yaw(void)
{
if (_error_yaw_count == 0) {
// this happens when telemetry is setup on two
// serial ports
return _error_yaw_last;
}
_error_yaw_last = _error_yaw_sum / _error_yaw_count;
_error_yaw_sum = 0;
_error_yaw_count = 0;
return _error_yaw_last;
}