/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*- /* * APM_AHRS_DCM.cpp * * AHRS system using DCM matrices * * Based on DCM code by Doug Weibel, Jordi Muñoz and Jose Julio. DIYDrones.com * * Adapted for the general ArduPilot AHRS interface by Andrew Tridgell This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . */ #include #include extern const AP_HAL::HAL& hal; // 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 // the limit (in degrees/second) beyond which we stop integrating // omega_I. At larger spin rates the DCM PI controller can get 'dizzy' // which results in false gyro drift. See // http://gentlenav.googlecode.com/files/fastRotations.pdf #define SPIN_RATE_LIMIT 20 // run a full DCM update round void AP_AHRS_DCM::update(void) { float delta_t; // tell the IMU to grab some data _ins->update(); // ask the IMU how much time this sensor reading represents delta_t = _ins->get_delta_time(); // if the update call took more than 0.2 seconds then discard it, // otherwise we may move too far. This happens when arming motors // in ArduCopter if (delta_t > 0.2f) { _ra_sum.zero(); _ra_deltat = 0; return; } // Get current values for gyros _gyro_vector = _ins->get_gyro(); _accel_vector = _ins->get_accel(); // Integrate the DCM matrix using gyro inputs matrix_update(delta_t); // Normalize the DCM matrix normalize(); // Perform drift correction drift_correction(delta_t); // paranoid check for bad values in the DCM matrix check_matrix(); // Calculate pitch, roll, yaw for stabilization and navigation euler_angles(); } // update the DCM matrix using only the gyros void AP_AHRS_DCM::matrix_update(float _G_Dt) { // note that we do not include the P terms in _omega. This is // because the spin_rate is calculated from _omega.length(), // and including the P terms would give positive feedback into // the _P_gain() calculation, which can lead to a very large P // value _omega = _gyro_vector + _omega_I; _dcm_matrix.rotate((_omega + _omega_P + _omega_yaw_P) * _G_Dt); } /* * 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) { // reset the integration terms _omega_I.zero(); _omega_P.zero(); _omega_yaw_P.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); } } /* * 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"); 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 < 1.0f && _dcm_matrix.c.x > -1.0f)) { // We have an invalid matrix. Force a normalisation. renorm_range_count++; normalize(); if (_dcm_matrix.is_nan() || fabsf(_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); 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 = 1.0f / a.length(); // keep the average for reporting _renorm_val_sum += renorm_val; _renorm_val_count++; if (!(renorm_val < 2.0f && renorm_val > 0.5f)) { // this is larger than it should get - log it as a warning renorm_range_count++; if (!(renorm_val < 1.0e6f && renorm_val > 1.0e-6f)) { // 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); 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 ÒrenormalizationÓ. */ void AP_AHRS_DCM::normalize(void) { float error; Vector3f t0, t1, t2; 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; // c= a x b // eq.20 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); } } // produce a yaw error value. The returned value is proportional // to sin() of the current heading error in earth frame float AP_AHRS_DCM::yaw_error_compass(void) { Vector3f mag = Vector3f(_compass->mag_x, _compass->mag_y, _compass->mag_z); // get the mag vector in the earth frame Vector2f rb = _dcm_matrix.mulXY(mag); rb.normalize(); if (rb.is_inf()) { // not a valid vector return 0.0; } // update vector holding earths magnetic field (if required) if( _last_declination != _compass->get_declination() ) { _last_declination = _compass->get_declination(); _mag_earth.x = cosf(_last_declination); _mag_earth.y = sinf(_last_declination); } // calculate the error term in earth frame // calculate the Z component of the cross product of rb and _mag_earth return rb % _mag_earth; } // the _P_gain raises the gain of the PI controller // when we are spinning fast. See the fastRotations // paper from Bill. float AP_AHRS_DCM::_P_gain(float spin_rate) { if (spin_rate < ToRad(50)) { return 1.0f; } if (spin_rate > ToRad(500)) { return 10.0f; } return spin_rate/ToRad(50); } // return true if we have and should use GPS bool AP_AHRS_DCM::have_gps(void) const { if (!_gps || _gps->status() <= GPS::NO_FIX || !_gps_use) { return false; } return true; } // return true if we should use the compass for yaw correction bool AP_AHRS_DCM::use_compass(void) { if (!_compass || !_compass->use_for_yaw()) { // no compass available return false; } if (!_flags.fly_forward || !have_gps()) { // we don't have any alterative to the compass return true; } if (_gps->ground_speed_cm < GPS_SPEED_MIN) { // we are not going fast enough to use the GPS return true; } // if the current yaw differs from the GPS yaw by more than 45 // degrees and the estimated wind speed is less than 80% of the // ground speed, then switch to GPS navigation. This will help // prevent flyaways with very bad compass offsets int32_t error = abs(wrap_180_cd(yaw_sensor - _gps->ground_course_cd)); if (error > 4500 && _wind.length() < _gps->ground_speed_cm*0.008f) { if (hal.scheduler->millis() - _last_consistent_heading > 2000) { // start using the GPS for heading if the compass has been // inconsistent with the GPS for 2 seconds return false; } } else { _last_consistent_heading = hal.scheduler->millis(); } // use the compass return true; } // yaw drift correction using the compass or GPS // this function prodoces the _omega_yaw_P vector, and also // contributes to the _omega_I.z long term yaw drift estimate void AP_AHRS_DCM::drift_correction_yaw(void) { bool new_value = false; float yaw_error; float yaw_deltat; if (use_compass()) { /* we are using compass for yaw */ if (_compass->last_update != _compass_last_update) { yaw_deltat = (_compass->last_update - _compass_last_update) * 1.0e-6f; _compass_last_update = _compass->last_update; // we force an additional compass read() // here. This has the effect of throwing away // the first compass value, which can be bad if (!_flags.have_initial_yaw && _compass->read()) { float heading = _compass->calculate_heading(_dcm_matrix); _dcm_matrix.from_euler(roll, pitch, heading); _omega_yaw_P.zero(); _flags.have_initial_yaw = true; } new_value = true; yaw_error = yaw_error_compass(); } } else if (_flags.fly_forward && have_gps()) { /* we are using GPS for yaw */ if (_gps->last_fix_time != _gps_last_update && _gps->ground_speed_cm >= GPS_SPEED_MIN) { yaw_deltat = (_gps->last_fix_time - _gps_last_update) * 1.0e-3f; _gps_last_update = _gps->last_fix_time; new_value = true; float gps_course_rad = ToRad(_gps->ground_course_cd * 0.01f); float yaw_error_rad = gps_course_rad - yaw; yaw_error = sinf(yaw_error_rad); /* reset yaw to match GPS heading under any of the following 3 conditions: 1) if we have reached GPS_SPEED_MIN and have never had yaw information before 2) if the last time we got yaw information from the GPS is more than 20 seconds ago, which means we may have suffered from considerable gyro drift 3) if we are over 3*GPS_SPEED_MIN (which means 9m/s) and our yaw error is over 60 degrees, which means very poor yaw. This can happen on bungee launch when the operator pulls back the plane rapidly enough then on release the GPS heading changes very rapidly */ if (!_flags.have_initial_yaw || yaw_deltat > 20 || (_gps->ground_speed_cm >= 3*GPS_SPEED_MIN && fabsf(yaw_error_rad) >= 1.047f)) { // reset DCM matrix based on current yaw _dcm_matrix.from_euler(roll, pitch, gps_course_rad); _omega_yaw_P.zero(); _flags.have_initial_yaw = true; yaw_error = 0; } } } if (!new_value) { // we don't have any new yaw information // slowly decay _omega_yaw_P to cope with loss // of our yaw source _omega_yaw_P *= 0.97f; return; } // convert the error vector to body frame float error_z = _dcm_matrix.c.z * yaw_error; // the spin rate changes the P gain, and disables the // integration at higher rates float spin_rate = _omega.length(); // update the proportional control to drag the // yaw back to the right value. We use a gain // that depends on the spin rate. See the fastRotations.pdf // paper from Bill Premerlani _omega_yaw_P.z = error_z * _P_gain(spin_rate) * _kp_yaw; if (_flags.fast_ground_gains) { _omega_yaw_P.z *= 8; } // don't update the drift term if we lost the yaw reference // for more than 2 seconds if (yaw_deltat < 2.0f && spin_rate < ToRad(SPIN_RATE_LIMIT)) { // also add to the I term _omega_I_sum.z += error_z * _ki_yaw * yaw_deltat; } _error_yaw_sum += fabsf(yaw_error); _error_yaw_count++; } // 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 drift correction implementation is based on a paper // by Bill Premerlani from here: // http://gentlenav.googlecode.com/files/RollPitchDriftCompensation.pdf void AP_AHRS_DCM::drift_correction(float deltat) { Matrix3f temp_dcm = _dcm_matrix; Vector3f velocity; uint32_t last_correction_time; // perform yaw drift correction if we have a new yaw reference // vector drift_correction_yaw(); // apply trim temp_dcm.rotateXY(_trim); // rotate accelerometer values into the earth frame _accel_ef = temp_dcm * _accel_vector; // integrate the accel vector in the earth frame between GPS readings _ra_sum += _accel_ef * deltat; // keep a sum of the deltat values, so we know how much time // we have integrated over _ra_deltat += deltat; if (!have_gps() || _gps->status() < GPS::GPS_OK_FIX_3D || _gps->num_sats < _gps_minsats) { // no GPS, or not a good lock. From experience we need at // least 6 satellites to get a really reliable velocity number // from the GPS. // // As a fallback we use the fixed wing acceleration correction // if we have an airspeed estimate (which we only have if // _fly_forward is set), otherwise no correction if (_ra_deltat < 0.2f) { // not enough time has accumulated return; } float airspeed; if (_airspeed && _airspeed->use()) { airspeed = _airspeed->get_airspeed(); } else { airspeed = _last_airspeed; } // use airspeed to estimate our ground velocity in // earth frame by subtracting the wind velocity = _dcm_matrix.colx() * airspeed; // add in wind estimate velocity += _wind; last_correction_time = hal.scheduler->millis(); _have_gps_lock = false; } else { if (_gps->last_fix_time == _ra_sum_start) { // we don't have a new GPS fix - nothing more to do return; } velocity = Vector3f(_gps->velocity_north(), _gps->velocity_east(), _gps->velocity_down()); last_correction_time = _gps->last_fix_time; if (_have_gps_lock == false) { // if we didn't have GPS lock in the last drift // correction interval then set the velocities equal _last_velocity = velocity; } _have_gps_lock = true; // keep last airspeed estimate for dead-reckoning purposes Vector3f airspeed = velocity - _wind; airspeed.z = 0; _last_airspeed = airspeed.length(); } if (have_gps()) { // use GPS for positioning with any fix, even a 2D fix _last_lat = _gps->latitude; _last_lng = _gps->longitude; _position_offset_north = 0; _position_offset_east = 0; // once we have a single GPS lock, we can update using // dead-reckoning from then on _have_position = true; } else { // update dead-reckoning position estimate _position_offset_north += velocity.x * _ra_deltat; _position_offset_east += velocity.y * _ra_deltat; } // see if this is our first time through - in which case we // just setup the start times and return if (_ra_sum_start == 0) { _ra_sum_start = last_correction_time; _last_velocity = velocity; return; } // equation 9: get the corrected acceleration vector in earth frame. Units // are m/s/s Vector3f GA_e; GA_e = Vector3f(0, 0, -1.0f); if (_flags.correct_centrifugal && (_have_gps_lock || _flags.fly_forward)) { float v_scale = gps_gain.get()/(_ra_deltat*GRAVITY_MSS); Vector3f vdelta = (velocity - _last_velocity) * v_scale; // limit vertical acceleration correction to 0.5 gravities. The // barometer sometimes gives crazy acceleration changes. vdelta.z = constrain_float(vdelta.z, -0.5f, 0.5f); GA_e += vdelta; GA_e.normalize(); if (GA_e.is_inf()) { // wait for some non-zero acceleration information return; } } // calculate the error term in earth frame. Vector3f GA_b = _ra_sum / (_ra_deltat * GRAVITY_MSS); float length = GA_b.length(); if (length > 1.0f) { GA_b /= length; if (GA_b.is_inf()) { // wait for some non-zero acceleration information return; } } Vector3f error = GA_b % GA_e; #define YAW_INDEPENDENT_DRIFT_CORRECTION 0 #if YAW_INDEPENDENT_DRIFT_CORRECTION // step 2 calculate earth_error_Z float earth_error_Z = error.z; // equation 10 float tilt = pythagorous2(GA_e.x, GA_e.y); // equation 11 float theta = atan2f(GA_b.y, GA_b.x); // equation 12 Vector3f GA_e2 = Vector3f(cosf(theta)*tilt, sinf(theta)*tilt, GA_e.z); // step 6 error = GA_b % GA_e2; error.z = earth_error_Z; #endif // YAW_INDEPENDENT_DRIFT_CORRECTION // to reduce the impact of two competing yaw controllers, we // reduce the impact of the gps/accelerometers on yaw when we are // flat, but still allow for yaw correction using the // accelerometers at high roll angles as long as we have a GPS if (use_compass()) { if (have_gps() && gps_gain == 1.0f) { error.z *= sinf(fabsf(roll)); } else { error.z = 0; } } // convert the error term to body frame error = _dcm_matrix.mul_transpose(error); if (error.is_nan() || error.is_inf()) { // don't allow bad values check_matrix(); return; } _error_rp_sum += error.length(); _error_rp_count++; // base the P gain on the spin rate float spin_rate = _omega.length(); // 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 * _P_gain(spin_rate) * _kp; if (_flags.fast_ground_gains) { _omega_P *= 8; } if (_flags.fly_forward && _gps && _gps->status() >= GPS::GPS_OK_FIX_2D && _gps->ground_speed_cm < GPS_SPEED_MIN && _accel_vector.x >= 7 && pitch_sensor > -3000 && pitch_sensor < 3000) { // assume we are in a launch acceleration, and reduce the // rp gain by 50% to reduce the impact of GPS lag on // takeoff attitude when using a catapult _omega_P *= 0.5f; } // accumulate some integrator error if (spin_rate < ToRad(SPIN_RATE_LIMIT)) { _omega_I_sum += error * _ki * _ra_deltat; _omega_I_sum_time += _ra_deltat; } if (_omega_I_sum_time >= 5) { // limit the rate of change of omega_I to the hardware // reported maximum gyro drift rate. This ensures that // short term errors don't cause a buildup of omega_I // beyond the physical limits of the device float change_limit = _gyro_drift_limit * _omega_I_sum_time; _omega_I_sum.x = constrain_float(_omega_I_sum.x, -change_limit, change_limit); _omega_I_sum.y = constrain_float(_omega_I_sum.y, -change_limit, change_limit); _omega_I_sum.z = constrain_float(_omega_I_sum.z, -change_limit, change_limit); _omega_I += _omega_I_sum; _omega_I_sum.zero(); _omega_I_sum_time = 0; } // zero our accumulator ready for the next GPS step _ra_sum.zero(); _ra_deltat = 0; _ra_sum_start = last_correction_time; // remember the velocity for next time _last_velocity = velocity; if (_have_gps_lock && _flags.fly_forward) { // update wind estimate estimate_wind(velocity); } } // update our wind speed estimate void AP_AHRS_DCM::estimate_wind(Vector3f &velocity) { if (!_flags.wind_estimation) { return; } // this is based on the wind speed estimation code from MatrixPilot by // Bill Premerlani. Adaption for ArduPilot by Jon Challinger // See http://gentlenav.googlecode.com/files/WindEstimation.pdf Vector3f fuselageDirection = _dcm_matrix.colx(); Vector3f fuselageDirectionDiff = fuselageDirection - _last_fuse; uint32_t now = hal.scheduler->millis(); // scrap our data and start over if we're taking too long to get a direction change if (now - _last_wind_time > 10000) { _last_wind_time = now; _last_fuse = fuselageDirection; _last_vel = velocity; return; } float diff_length = fuselageDirectionDiff.length(); if (diff_length > 0.2f) { // when turning, use the attitude response to estimate // wind speed float V; Vector3f velocityDiff = velocity - _last_vel; // estimate airspeed it using equation 6 V = velocityDiff.length() / diff_length; _last_fuse = fuselageDirection; _last_vel = velocity; Vector3f fuselageDirectionSum = fuselageDirection + _last_fuse; Vector3f velocitySum = velocity + _last_vel; float theta = atan2f(velocityDiff.y, velocityDiff.x) - atan2f(fuselageDirectionDiff.y, fuselageDirectionDiff.x); float sintheta = sinf(theta); float costheta = cosf(theta); Vector3f wind = Vector3f(); wind.x = velocitySum.x - V * (costheta * fuselageDirectionSum.x - sintheta * fuselageDirectionSum.y); wind.y = velocitySum.y - V * (sintheta * fuselageDirectionSum.x + costheta * fuselageDirectionSum.y); wind.z = velocitySum.z - V * fuselageDirectionSum.z; wind *= 0.5f; if (wind.length() < _wind.length() + 20) { _wind = _wind * 0.95f + wind * 0.05f; } _last_wind_time = now; } else if (now - _last_wind_time > 2000 && _airspeed && _airspeed->use()) { // when flying straight use airspeed to get wind estimate if available Vector3f airspeed = _dcm_matrix.colx() * _airspeed->get_airspeed(); Vector3f wind = velocity - (airspeed * get_EAS2TAS()); _wind = _wind * 0.92f + wind * 0.08f; } } // 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); roll_sensor = degrees(roll) * 100; pitch_sensor = degrees(pitch) * 100; yaw_sensor = degrees(yaw) * 100; if (yaw_sensor < 0) yaw_sensor += 36000; } /* 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; } // return our current position estimate using // dead-reckoning or GPS bool AP_AHRS_DCM::get_position(struct Location &loc) { if (!_have_position) { return false; } loc.lat = _last_lat; loc.lng = _last_lng; location_offset(loc, _position_offset_north, _position_offset_east); return true; } // return an airspeed estimate if available bool AP_AHRS_DCM::airspeed_estimate(float *airspeed_ret) { bool ret = false; if (_airspeed && _airspeed->use()) { *airspeed_ret = _airspeed->get_airspeed(); return true; } if (!_flags.wind_estimation) { return false; } // estimate it via GPS speed and wind if (have_gps()) { *airspeed_ret = _last_airspeed; ret = true; } if (ret && _wind_max > 0 && _gps && _gps->status() >= GPS::GPS_OK_FIX_2D) { // constrain the airspeed by the ground speed // and AHRS_WIND_MAX float gnd_speed = _gps->ground_speed_cm*0.01f; float true_airspeed = *airspeed_ret * get_EAS2TAS(); true_airspeed = constrain_float(true_airspeed, gnd_speed - _wind_max, gnd_speed + _wind_max); *airspeed_ret = true_airspeed / get_EAS2TAS(); } return ret; }