void ahrs_realign_heading(float heading) { FLOAT_ANGLE_NORMALIZE(heading); /* quaternion representing only the heading rotation from ltp to body */ struct FloatQuat q_h_new; q_h_new.qx = 0.0; q_h_new.qy = 0.0; q_h_new.qz = sinf(heading/2.0); q_h_new.qi = cosf(heading/2.0); struct FloatQuat* ltp_to_body_quat = stateGetNedToBodyQuat_f(); /* quaternion representing current heading only */ struct FloatQuat q_h; QUAT_COPY(q_h, *ltp_to_body_quat); q_h.qx = 0.; q_h.qy = 0.; FLOAT_QUAT_NORMALIZE(q_h); /* quaternion representing rotation from current to new heading */ struct FloatQuat q_c; FLOAT_QUAT_INV_COMP_NORM_SHORTEST(q_c, q_h, q_h_new); /* correct current heading in body frame */ struct FloatQuat q; FLOAT_QUAT_COMP_NORM_SHORTEST(q, q_c, *ltp_to_body_quat); /* compute ltp to imu rotation quaternion and matrix */ FLOAT_QUAT_COMP(ahrs_impl.ltp_to_imu_quat, q, ahrs_impl.body_to_imu_quat); FLOAT_RMAT_OF_QUAT(ahrs_impl.ltp_to_imu_rmat, ahrs_impl.ltp_to_imu_quat); /* set state */ stateSetNedToBodyQuat_f(&q); ahrs_impl.heading_aligned = TRUE; }
/** * Incorporate errors to reference and zeros state */ static inline void reset_state(void) { ahrs_impl.gibbs_cor.qi = 2.; struct FloatQuat q_tmp; FLOAT_QUAT_COMP(q_tmp, ahrs_impl.ltp_to_imu_quat, ahrs_impl.gibbs_cor); FLOAT_QUAT_NORMALIZE(q_tmp); memcpy(&ahrs_impl.ltp_to_imu_quat, &q_tmp, sizeof(ahrs_impl.ltp_to_imu_quat)); FLOAT_QUAT_ZERO(ahrs_impl.gibbs_cor); }
void stabilization_attitude_read_rc_setpoint_quat_f(struct FloatQuat* q_sp, bool_t in_flight) { // FIXME: remove me, do in quaternion directly // is currently still needed, since the yaw setpoint integration is done in eulers #if defined STABILIZATION_ATTITUDE_TYPE_INT stabilization_attitude_read_rc_setpoint_eulers(&stab_att_sp_euler, in_flight); #else stabilization_attitude_read_rc_setpoint_eulers_f(&stab_att_sp_euler, in_flight); #endif struct FloatQuat q_rp_cmd; #if USE_EARTH_BOUND_RC_SETPOINT stabilization_attitude_read_rc_roll_pitch_earth_quat_f(&q_rp_cmd); #else stabilization_attitude_read_rc_roll_pitch_quat_f(&q_rp_cmd); #endif /* get current heading */ const struct FloatVect3 zaxis = {0., 0., 1.}; struct FloatQuat q_yaw; //Care Free mode if (guidance_h_mode == GUIDANCE_H_MODE_CARE_FREE) { //care_free_heading has been set to current psi when entering care free mode. FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw, zaxis, care_free_heading); } else { FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw, zaxis, stateGetNedToBodyEulers_f()->psi); } /* roll/pitch commands applied to to current heading */ struct FloatQuat q_rp_sp; FLOAT_QUAT_COMP(q_rp_sp, q_yaw, q_rp_cmd); FLOAT_QUAT_NORMALIZE(q_rp_sp); if (in_flight) { /* get current heading setpoint */ struct FloatQuat q_yaw_sp; #if defined STABILIZATION_ATTITUDE_TYPE_INT FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw_sp, zaxis, ANGLE_FLOAT_OF_BFP(stab_att_sp_euler.psi)); #else FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw_sp, zaxis, stab_att_sp_euler.psi); #endif /* rotation between current yaw and yaw setpoint */ struct FloatQuat q_yaw_diff; FLOAT_QUAT_COMP_INV(q_yaw_diff, q_yaw_sp, q_yaw); /* compute final setpoint with yaw */ FLOAT_QUAT_COMP_NORM_SHORTEST(*q_sp, q_rp_sp, q_yaw_diff); } else { QUAT_COPY(*q_sp, q_rp_sp); } }
float test_quat(void) { struct FloatVect3 u = { 1., 2., 3.}; FLOAT_VECT3_NORMALIZE(u); float angle = RadOfDeg(30.); struct FloatQuat q; FLOAT_QUAT_OF_AXIS_ANGLE(q, u, angle); DISPLAY_FLOAT_QUAT("q ", q); struct FloatQuat iq; FLOAT_QUAT_INVERT(iq, q); DISPLAY_FLOAT_QUAT("iq", iq); struct FloatQuat q1; FLOAT_QUAT_COMP(q1, q, iq); DISPLAY_FLOAT_QUAT("q1", q1); struct FloatQuat q2; FLOAT_QUAT_COMP(q2, q, iq); DISPLAY_FLOAT_QUAT("q2", q2); struct FloatQuat qe; QUAT_EXPLEMENTARY(qe, q); DISPLAY_FLOAT_QUAT("qe", qe); struct FloatVect3 a = { 2., 1., 3.}; DISPLAY_FLOAT_VECT3("a ", a); struct FloatVect3 a1; FLOAT_QUAT_VMULT(a1, q, a); DISPLAY_FLOAT_VECT3("a1", a1); struct FloatVect3 a2; FLOAT_QUAT_VMULT(a2, qe, a); DISPLAY_FLOAT_VECT3("a2", a2); return 0.; }
void stabilization_attitude_run(bool_t enable_integrator) { /* * Update reference */ stabilization_attitude_ref_update(); /* * Compute errors for feedback */ /* attitude error */ struct FloatQuat att_err; FLOAT_QUAT_INV_COMP(att_err, ahrs_float.ltp_to_body_quat, stab_att_ref_quat); /* wrap it in the shortest direction */ FLOAT_QUAT_WRAP_SHORTEST(att_err); /* rate error */ struct FloatRates rate_err; RATES_DIFF(rate_err, stab_att_ref_rate, ahrs_float.body_rate); /* integrated error */ if (enable_integrator) { struct FloatQuat new_sum_err, scaled_att_err; /* update accumulator */ scaled_att_err.qi = att_err.qi; scaled_att_err.qx = att_err.qx / IERROR_SCALE; scaled_att_err.qy = att_err.qy / IERROR_SCALE; scaled_att_err.qz = att_err.qz / IERROR_SCALE; FLOAT_QUAT_COMP(new_sum_err, stabilization_att_sum_err_quat, scaled_att_err); FLOAT_QUAT_NORMALIZE(new_sum_err); FLOAT_QUAT_COPY(stabilization_att_sum_err_quat, new_sum_err); FLOAT_EULERS_OF_QUAT(stabilization_att_sum_err_eulers, stabilization_att_sum_err_quat); } else { /* reset accumulator */ FLOAT_QUAT_ZERO( stabilization_att_sum_err_quat ); FLOAT_EULERS_ZERO( stabilization_att_sum_err_eulers ); } attitude_run_ff(stabilization_att_ff_cmd, &stabilization_gains[gain_idx], &stab_att_ref_accel); attitude_run_fb(stabilization_att_fb_cmd, &stabilization_gains[gain_idx], &att_err, &rate_err, &ahrs_float.body_rate_d, &stabilization_att_sum_err_quat); // FIXME: this is very dangerous! only works if this really includes all commands for (int i = COMMAND_ROLL; i <= COMMAND_YAW_SURFACE; i++) { stabilization_cmd[i] = stabilization_att_fb_cmd[i]+stabilization_att_ff_cmd[i]; } /* bound the result */ BoundAbs(stabilization_cmd[COMMAND_ROLL], MAX_PPRZ); BoundAbs(stabilization_cmd[COMMAND_PITCH], MAX_PPRZ); BoundAbs(stabilization_cmd[COMMAND_YAW], MAX_PPRZ); }
float test_quat2(void) { struct FloatEulers eula2b; EULERS_ASSIGN(eula2b, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.)); // DISPLAY_FLOAT_EULERS_DEG("eula2b", eula2b); struct FloatQuat qa2b; FLOAT_QUAT_OF_EULERS(qa2b, eula2b); DISPLAY_FLOAT_QUAT("qa2b", qa2b); struct DoubleEulers eula2b_d; EULERS_ASSIGN(eula2b_d, RadOfDeg(70.), RadOfDeg(0.), RadOfDeg(0.)); struct DoubleQuat qa2b_d; DOUBLE_QUAT_OF_EULERS(qa2b_d, eula2b_d); DISPLAY_FLOAT_QUAT("qa2b_d", qa2b_d); struct FloatVect3 u = { 1., 0., 0.}; float angle = RadOfDeg(70.); struct FloatQuat q; FLOAT_QUAT_OF_AXIS_ANGLE(q, u, angle); DISPLAY_FLOAT_QUAT("q ", q); struct FloatEulers eula2c; EULERS_ASSIGN(eula2c, RadOfDeg(80.), RadOfDeg(0.), RadOfDeg(0.)); // DISPLAY_FLOAT_EULERS_DEG("eula2c", eula2c); struct FloatQuat qa2c; FLOAT_QUAT_OF_EULERS(qa2c, eula2c); DISPLAY_FLOAT_QUAT("qa2c", qa2c); struct FloatQuat qb2a; FLOAT_QUAT_INVERT(qb2a, qa2b); DISPLAY_FLOAT_QUAT("qb2a", qb2a); struct FloatQuat qb2c1; FLOAT_QUAT_COMP(qb2c1, qb2a, qa2c); DISPLAY_FLOAT_QUAT("qb2c1", qb2c1); struct FloatQuat qb2c2; FLOAT_QUAT_INV_COMP(qb2c2, qa2b, qa2c); DISPLAY_FLOAT_QUAT("qb2c2", qb2c2); return 0.; }
//Function that reads the rc setpoint in an earth bound frame void stabilization_attitude_read_rc_setpoint_quat_earth_bound_f(struct FloatQuat* q_sp, bool_t in_flight, bool_t in_carefree, bool_t coordinated_turn) { // FIXME: remove me, do in quaternion directly // is currently still needed, since the yaw setpoint integration is done in eulers #if defined STABILIZATION_ATTITUDE_TYPE_INT stabilization_attitude_read_rc_setpoint_eulers(&stab_att_sp_euler, in_flight, in_carefree, coordinated_turn); #else stabilization_attitude_read_rc_setpoint_eulers_f(&stab_att_sp_euler, in_flight, in_carefree, coordinated_turn); #endif const struct FloatVect3 zaxis = {0., 0., 1.}; struct FloatQuat q_rp_cmd; stabilization_attitude_read_rc_roll_pitch_earth_quat_f(&q_rp_cmd); if (in_flight) { /* get current heading setpoint */ struct FloatQuat q_yaw_sp; #if defined STABILIZATION_ATTITUDE_TYPE_INT FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw_sp, zaxis, ANGLE_FLOAT_OF_BFP(stab_att_sp_euler.psi)); #else FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw_sp, zaxis, stab_att_sp_euler.psi); #endif FLOAT_QUAT_COMP(*q_sp, q_yaw_sp, q_rp_cmd); } else { struct FloatQuat q_yaw; FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw, zaxis, stateGetNedToBodyEulers_f()->psi); /* roll/pitch commands applied to to current heading */ struct FloatQuat q_rp_sp; FLOAT_QUAT_COMP(q_rp_sp, q_yaw, q_rp_cmd); FLOAT_QUAT_NORMALIZE(q_rp_sp); QUAT_COPY(*q_sp, q_rp_sp); } }
void stabilization_attitude_ref_update(void) { /* integrate reference attitude */ #if STABILIZATION_ATTITUDE_REF_QUAT_INFINITESIMAL_STEP struct FloatQuat qdot; FLOAT_QUAT_DERIVATIVE(qdot, stab_att_ref_rate, stab_att_ref_quat); QUAT_SMUL(qdot, qdot, DT_UPDATE); QUAT_ADD(stab_att_ref_quat, qdot); #else // use finite step (involves trig) struct FloatQuat delta_q; FLOAT_QUAT_DIFFERENTIAL(delta_q, stab_att_ref_rate, DT_UPDATE); /* compose new ref_quat by quaternion multiplication of delta rotation and current ref_quat */ struct FloatQuat new_ref_quat; FLOAT_QUAT_COMP(new_ref_quat, delta_q, stab_att_ref_quat); QUAT_COPY(stab_att_ref_quat, new_ref_quat); #endif FLOAT_QUAT_NORMALIZE(stab_att_ref_quat); /* integrate reference rotational speeds */ struct FloatRates delta_rate; RATES_SMUL(delta_rate, stab_att_ref_accel, DT_UPDATE); RATES_ADD(stab_att_ref_rate, delta_rate); /* compute reference angular accelerations */ struct FloatQuat err; /* compute reference attitude error */ FLOAT_QUAT_INV_COMP(err, stab_att_sp_quat, stab_att_ref_quat); /* wrap it in the shortest direction */ FLOAT_QUAT_WRAP_SHORTEST(err); /* propagate the 2nd order linear model */ stab_att_ref_accel.p = -2.*stab_att_ref_model[ref_idx].zeta.p*stab_att_ref_model[ref_idx].omega.p*stab_att_ref_rate.p - stab_att_ref_model[ref_idx].omega.p*stab_att_ref_model[ref_idx].omega.p*err.qx; stab_att_ref_accel.q = -2.*stab_att_ref_model[ref_idx].zeta.q*stab_att_ref_model[ref_idx].omega.q*stab_att_ref_rate.q - stab_att_ref_model[ref_idx].omega.q*stab_att_ref_model[ref_idx].omega.q*err.qy; stab_att_ref_accel.r = -2.*stab_att_ref_model[ref_idx].zeta.r*stab_att_ref_model[ref_idx].omega.r*stab_att_ref_rate.r - stab_att_ref_model[ref_idx].omega.r*stab_att_ref_model[ref_idx].omega.r*err.qz; /* saturate acceleration */ const struct FloatRates MIN_ACCEL = { -REF_ACCEL_MAX_P, -REF_ACCEL_MAX_Q, -REF_ACCEL_MAX_R }; const struct FloatRates MAX_ACCEL = { REF_ACCEL_MAX_P, REF_ACCEL_MAX_Q, REF_ACCEL_MAX_R }; RATES_BOUND_BOX(stab_att_ref_accel, MIN_ACCEL, MAX_ACCEL); /* saturate angular speed and trim accel accordingly */ SATURATE_SPEED_TRIM_ACCEL(); /* compute ref_euler */ FLOAT_EULERS_OF_QUAT(stab_att_ref_euler, stab_att_ref_quat); }
void stabilization_attitude_read_rc(bool_t in_flight) { #if USE_SETPOINTS_WITH_TRANSITIONS stabilization_attitude_read_rc_absolute(in_flight); #else //FIXME: remove me, do in quaternion directly stabilization_attitude_read_rc_setpoint_eulers(&stab_att_sp_euler, in_flight); struct FloatQuat q_rp_cmd; #if USE_EARTH_BOUND_RC_SETPOINT stabilization_attitude_read_rc_roll_pitch_earth_quat(&q_rp_cmd); #else stabilization_attitude_read_rc_roll_pitch_quat(&q_rp_cmd); #endif /* get current heading */ const struct FloatVect3 zaxis = {0., 0., 1.}; struct FloatQuat q_yaw; FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw, zaxis, ANGLE_FLOAT_OF_BFP(stateGetNedToBodyEulers_i()->psi)); /* apply roll and pitch commands with respect to current heading */ struct FloatQuat q_sp; FLOAT_QUAT_COMP(q_sp, q_yaw, q_rp_cmd); FLOAT_QUAT_NORMALIZE(q_sp); if (in_flight) { /* get current heading setpoint */ struct FloatQuat q_yaw_sp; FLOAT_QUAT_OF_AXIS_ANGLE(q_yaw_sp, zaxis, ANGLE_FLOAT_OF_BFP(stab_att_sp_euler.psi)); /* rotation between current yaw and yaw setpoint */ struct FloatQuat q_yaw_diff; FLOAT_QUAT_COMP_INV(q_yaw_diff, q_yaw_sp, q_yaw); /* temporary copy with roll/pitch command and current heading */ struct FloatQuat q_rp_sp; QUAT_COPY(q_rp_sp, q_sp); /* compute final setpoint with yaw */ FLOAT_QUAT_COMP_NORM_SHORTEST(q_sp, q_rp_sp, q_yaw_diff); } QUAT_BFP_OF_REAL(stab_att_sp_quat, q_sp); #endif }
float test_quat_comp(struct FloatQuat qa2b_f, struct FloatQuat qb2c_f, int display) { struct FloatQuat qa2c_f; FLOAT_QUAT_COMP(qa2c_f, qa2b_f, qb2c_f); struct Int32Quat qa2b_i; QUAT_BFP_OF_REAL(qa2b_i, qa2b_f); struct Int32Quat qb2c_i; QUAT_BFP_OF_REAL(qb2c_i, qb2c_f); struct Int32Quat qa2c_i; INT32_QUAT_COMP(qa2c_i, qa2b_i, qb2c_i); struct FloatQuat err; QUAT_DIFF(err, qa2c_f, qa2c_i); float norm_err = FLOAT_QUAT_NORM(err); if (display) { printf("quat comp\n"); DISPLAY_FLOAT_QUAT_AS_EULERS_DEG("a2cf", qa2c_f); DISPLAY_INT32_QUAT_AS_EULERS_DEG("a2ci", qa2c_i); } return norm_err; }
static void print_estimator_state(double time) { #if FILTER_OUTPUT_IN_NED struct EcefCoor_d pos_ecef, cur_pos_ecef, cur_vel_ecef; struct NedCoor_d pos_ned, vel_ned; struct DoubleQuat q_ecef2body, q_ecef2enu, q_enu2body, q_ned2enu, q_ned2body; VECTOR_AS_VECT3(pos_ecef,pos_0_ecef); VECTOR_AS_VECT3(cur_pos_ecef,ins.avg_state.position); VECTOR_AS_VECT3(cur_vel_ecef,ins.avg_state.velocity); ned_of_ecef_point_d(&pos_ned, ¤t_ltp, &cur_pos_ecef); ned_of_ecef_vect_d(&vel_ned, ¤t_ltp, &cur_vel_ecef); int32_t xdd = 0; int32_t ydd = 0; int32_t zdd = 0; int32_t xd = vel_ned.x/0.0000019073; int32_t yd = vel_ned.y/0.0000019073; int32_t zd = vel_ned.z/0.0000019073; int32_t x = pos_ned.x/0.0039; int32_t y = pos_ned.y/0.0039; int32_t z = pos_ned.z/0.0039; fprintf(ins_logfile, "%f %d BOOZ2_INS2 %d %d %d %d %d %d %d %d %d\n", time, AC_ID, xdd, ydd, zdd, xd, yd, zd, x, y, z); #if 0 QUAT_ASSIGN(q_ecef2body, ins.avg_state.orientation.w(), -ins.avg_state.orientation.x(), -ins.avg_state.orientation.y(), -ins.avg_state.orientation.z()); QUAT_ASSIGN(q_ned2enu, 0, M_SQRT1_2, M_SQRT1_2, 0); FLOAT_QUAT_OF_RMAT(q_ecef2enu, current_ltp.ltp_of_ecef); FLOAT_QUAT_INV_COMP(q_enu2body, q_ecef2enu, q_ecef2body); // q_enu2body = q_ecef2body * (q_ecef2enu)^* FLOAT_QUAT_COMP(q_ned2body, q_ned2enu, q_enu2body); // q_ned2body = q_enu2body * q_ned2enu #else /* if 0 */ QUATERNIOND_AS_DOUBLEQUAT(q_ecef2body, ins.avg_state.orientation); DOUBLE_QUAT_OF_RMAT(q_ecef2enu, current_ltp.ltp_of_ecef); FLOAT_QUAT_INV_COMP(q_enu2body, q_ecef2enu, q_ecef2body); QUAT_ENU_FROM_TO_NED(q_enu2body, q_ned2body); #endif /* if 0 */ struct FloatEulers e; FLOAT_EULERS_OF_QUAT(e, q_ned2body); #if PRINT_EULER_NED printf("EULER % 6.1f % 6.1f % 6.1f\n", e.phi*180*M_1_PI, e.theta*180*M_1_PI, e.psi*180*M_1_PI); #endif /* PRINT_EULER_NED */ fprintf(ins_logfile, "%f %d AHRS_EULER %f %f %f\n", time, AC_ID, e.phi, e.theta, e.psi); fprintf(ins_logfile, "%f %d DEBUG_COVARIANCE %f %f %f %f %f %f %f %f %f %f %f %f\n", time, AC_ID, sqrt(ins.cov( 0, 0)), sqrt(ins.cov( 1, 1)), sqrt(ins.cov( 2, 2)), sqrt(ins.cov( 3, 3)), sqrt(ins.cov( 4, 4)), sqrt(ins.cov( 5, 5)), sqrt(ins.cov( 6, 6)), sqrt(ins.cov( 7, 7)), sqrt(ins.cov( 8, 8)), sqrt(ins.cov( 9, 9)), sqrt(ins.cov(10,10)), sqrt(ins.cov(11,11))); fprintf(ins_logfile, "%f %d BOOZ_SIM_GYRO_BIAS %f %f %f\n", time, AC_ID, ins.avg_state.gyro_bias(0), ins.avg_state.gyro_bias(1), ins.avg_state.gyro_bias(2)); #else /* FILTER_OUTPUT_IN_ECEF */ int32_t xdd = 0; int32_t ydd = 0; int32_t zdd = 0; int32_t xd = ins.avg_state.velocity(0)/0.0000019073; int32_t yd = ins.avg_state.velocity(1)/0.0000019073; int32_t zd = ins.avg_state.velocity(2)/0.0000019073; int32_t x = ins.avg_state.position(0)/0.0039; int32_t y = ins.avg_state.position(1)/0.0039; int32_t z = ins.avg_state.position(2)/0.0039; fprintf(ins_logfile, "%f %d BOOZ2_INS2 %d %d %d %d %d %d %d %d %d\n", time, AC_ID, xdd, ydd, zdd, xd, yd, zd, x, y, z); struct FloatQuat q_ecef2body; QUAT_ASSIGN(q_ecef2body, ins.avg_state.orientation.w(), ins.avg_state.orientation.x(), ins.avg_state.orientation.y(), ins.avg_state.orientation.z()); struct FloatEulers e_ecef2body; FLOAT_EULERS_OF_QUAT(e_ecef2body, q_ecef2body); fprintf(ins_logfile, "%f %d AHRS_EULER %f %f %f\n", time, AC_ID, e_ecef2body.phi, e_ecef2body.theta, e_ecef2body.psi); fprintf(ins_logfile, "%f %d DEBUG_COVARIANCE %f %f %f %f %f %f %f %f %f %f %f %f\n", time, AC_ID, sqrt(ins.cov( 0, 0)), sqrt(ins.cov( 1, 1)), sqrt(ins.cov( 2, 2)), sqrt(ins.cov( 3, 3)), sqrt(ins.cov( 4, 4)), sqrt(ins.cov( 5, 5)), sqrt(ins.cov( 6, 6)), sqrt(ins.cov( 7, 7)), sqrt(ins.cov( 8, 8)), sqrt(ins.cov( 9, 9)), sqrt(ins.cov(10,10)), sqrt(ins.cov(11,11))); fprintf(ins_logfile, "%f %d BOOZ_SIM_GYRO_BIAS %f %f %f\n", time, AC_ID, ins.avg_state.gyro_bias(0), ins.avg_state.gyro_bias(1), ins.avg_state.gyro_bias(2)); #endif /* FILTER_OUTPUT_IN_NED / ECEF */ }
static void ahrs_do_update_mag(void) { int i, j, k; #ifdef BAFL_DEBUG2 printf("Mag update.\n"); #endif MAGS_FLOAT_OF_BFP(bafl_mag, imu.mag); /* P_prio = P */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_Pprio[i][j] = bafl_P[i][j]; } } /* * set up measurement matrix * * h = [236.; -2.; 396.]; * hx = [ h(2); -h(1); 0]; //only psi (phi and theta = 0) * Hm = Cnb * hx; * H = [ 0 0 0 0 0 * 0 0 Cnb*hx 0 0 0 * 0 0 0 0 0 ]; * */ /*bafl_H[0][2] = RMAT_ELMT(bafl_dcm, 0, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 0, 1) * bafl_h.x; bafl_H[1][2] = RMAT_ELMT(bafl_dcm, 1, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 1, 1) * bafl_h.x; bafl_H[2][2] = RMAT_ELMT(bafl_dcm, 2, 0) * bafl_h.y - RMAT_ELMT(bafl_dcm, 2, 1) * bafl_h.x;*/ bafl_H[0][2] = -RMAT_ELMT(bafl_dcm, 0, 1); bafl_H[1][2] = -RMAT_ELMT(bafl_dcm, 1, 1); bafl_H[2][2] = -RMAT_ELMT(bafl_dcm, 2, 1); //rest is zero /********************************************** * compute Kalman gain K * * K = P_prio * H_T * inv(S) * S = H * P_prio * HT + R * * K = P_prio * HT * inv(H * P_prio * HT + R) * **********************************************/ /* covariance residual S = H * P_prio * HT + R */ /* temp_S(3x6) = H(3x6) * P_prio(6x6) * * only third column of H is non-zero */ for (i = 0; i < 3; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_tempS[i][j] = bafl_H[i][2] * bafl_Pprio[2][j]; } } /* S(3x3) = temp_S(3x6) * HT(6x3) + R(3x3) * * only third row of HT is non-zero */ for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { bafl_S[i][j] = bafl_tempS[i][2] * bafl_H[j][2]; /* H[j][2] = HT[2][j] */ } bafl_S[i][i] += bafl_R_mag; } /* invert S */ FLOAT_MAT33_INVERT(bafl_invS, bafl_S); /* temp_K(6x3) = P_prio(6x6) * HT(6x3) * * only third row of HT is non-zero */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < 3; j++) { /* not computing zero elements */ bafl_tempK[i][j] = bafl_Pprio[i][2] * bafl_H[j][2]; /* H[j][2] = HT[2][j] */ } } /* K(6x3) = temp_K(6x3) * invS(3x3) */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < 3; j++) { bafl_K[i][j] = bafl_tempK[i][0] * bafl_invS[0][j]; bafl_K[i][j] += bafl_tempK[i][1] * bafl_invS[1][j]; bafl_K[i][j] += bafl_tempK[i][2] * bafl_invS[2][j]; } } /********************************************** * Update filter state. * * The a priori filter state is zero since the errors are corrected after each update. * * X = X_prio + K (y - H * X_prio) * X = K * y **********************************************/ /* innovation * y = Cnb * [hx; hy; hz] - mag */ FLOAT_RMAT_VECT3_MUL(bafl_ym, bafl_dcm, bafl_h); //can be optimized FLOAT_VECT3_SUB(bafl_ym, bafl_mag); /* X(6) = K(6x3) * y(3) */ for (i = 0; i < BAFL_SSIZE; i++) { bafl_X[i] = bafl_K[i][0] * bafl_ym.x; bafl_X[i] += bafl_K[i][1] * bafl_ym.y; bafl_X[i] += bafl_K[i][2] * bafl_ym.z; } /********************************************** * Update the filter covariance. * * P = P_prio - K * H * P_prio * P = ( I - K * H ) * P_prio * **********************************************/ /* temp(6x6) = I(6x6) - K(6x3)*H(3x6) * * last 3 columns of H are zero */ for (i = 0; i < 6; i++) { for (j = 0; j < 6; j++) { if (i == j) { bafl_tempP[i][j] = 1.; } else { bafl_tempP[i][j] = 0.; } if (j == 2) { /* omit the parts where H is zero */ for (k = 0; k < 3; k++) { bafl_tempP[i][j] -= bafl_K[i][k] * bafl_H[k][j]; } } } } /* P(6x6) = temp(6x6) * P_prio(6x6) */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_P[i][j] = bafl_tempP[i][0] * bafl_Pprio[0][j]; for (k = 1; k < BAFL_SSIZE; k++) { bafl_P[i][j] += bafl_tempP[i][k] * bafl_Pprio[k][j]; } } } #ifdef LKF_PRINT_P printf("Pum="); for (i = 0; i < 6; i++) { printf("["); for (j = 0; j < 6; j++) { printf("%f\t", bafl_P[i][j]); } printf("]\n "); } printf("\n"); #endif /********************************************** * Correct errors. * * **********************************************/ /* Error quaternion. */ QUAT_ASSIGN(bafl_q_m_err, 1.0, bafl_X[0]/2, bafl_X[1]/2, bafl_X[2]/2); FLOAT_QUAT_INVERT(bafl_q_m_err, bafl_q_m_err); /* normalize */ float q_sq; q_sq = bafl_q_m_err.qx * bafl_q_m_err.qx + bafl_q_m_err.qy * bafl_q_m_err.qy + bafl_q_m_err.qz * bafl_q_m_err.qz; if (q_sq > 1) { /* this should actually never happen */ FLOAT_QUAT_SMUL(bafl_q_m_err, bafl_q_m_err, 1 / sqrtf(1 + q_sq)); printf("mag error quaternion q_sq > 1!!\n"); } else { bafl_q_m_err.qi = sqrtf(1 - q_sq); } /* correct attitude */ FLOAT_QUAT_COMP(bafl_qtemp, bafl_q_m_err, bafl_quat); FLOAT_QUAT_COPY(bafl_quat, bafl_qtemp); /* correct gyro bias */ RATES_ASSIGN(bafl_b_m_err, bafl_X[3], bafl_X[4], bafl_X[5]); RATES_SUB(bafl_bias, bafl_b_m_err); /* * compute all representations */ /* maintain rotation matrix representation */ FLOAT_RMAT_OF_QUAT(bafl_dcm, bafl_quat); /* maintain euler representation */ FLOAT_EULERS_OF_RMAT(bafl_eulers, bafl_dcm); AHRS_TO_BFP(); AHRS_LTP_TO_BODY(); }
static void ahrs_do_update_accel(void) { int i, j, k; #ifdef BAFL_DEBUG2 printf("Accel update.\n"); #endif /* P_prio = P */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_Pprio[i][j] = bafl_P[i][j]; } } /* * set up measurement matrix * * g = 9.81 * gx = [ 0 -g 0 * g 0 0 * 0 0 0 ] * H = [ 0 0 0 ] * [ -Cnb*gx 0 0 0 ] * [ 0 0 0 ] * * */ bafl_H[0][0] = -RMAT_ELMT(bafl_dcm, 0, 1) * BAFL_g; bafl_H[0][1] = RMAT_ELMT(bafl_dcm, 0, 0) * BAFL_g; bafl_H[1][0] = -RMAT_ELMT(bafl_dcm, 1, 1) * BAFL_g; bafl_H[1][1] = RMAT_ELMT(bafl_dcm, 1, 0) * BAFL_g; bafl_H[2][0] = -RMAT_ELMT(bafl_dcm, 2, 1) * BAFL_g; bafl_H[2][1] = RMAT_ELMT(bafl_dcm, 2, 0) * BAFL_g; /* rest is zero bafl_H[0][2] = 0.; bafl_H[1][2] = 0.; bafl_H[2][2] = 0.;*/ /********************************************** * compute Kalman gain K * * K = P_prio * H_T * inv(S) * S = H * P_prio * HT + R * * K = P_prio * HT * inv(H * P_prio * HT + R) * **********************************************/ /* covariance residual S = H * P_prio * HT + R */ /* temp_S(3x6) = H(3x6) * P_prio(6x6) * last 4 columns of H are zero */ for (i = 0; i < 3; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_tempS[i][j] = bafl_H[i][0] * bafl_Pprio[0][j]; bafl_tempS[i][j] += bafl_H[i][1] * bafl_Pprio[1][j]; } } /* S(3x3) = temp_S(3x6) * HT(6x3) + R(3x3) * * bottom 4 rows of HT are zero */ for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { bafl_S[i][j] = bafl_tempS[i][0] * bafl_H[j][0]; /* H[j][0] = HT[0][j] */ bafl_S[i][j] += bafl_tempS[i][1] * bafl_H[j][1]; /* H[j][0] = HT[0][j] */ } bafl_S[i][i] += bafl_R_accel; } /* invert S */ FLOAT_MAT33_INVERT(bafl_invS, bafl_S); /* temp_K(6x3) = P_prio(6x6) * HT(6x3) * * bottom 4 rows of HT are zero */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < 3; j++) { /* not computing zero elements */ bafl_tempK[i][j] = bafl_Pprio[i][0] * bafl_H[j][0]; /* H[j][0] = HT[0][j] */ bafl_tempK[i][j] += bafl_Pprio[i][1] * bafl_H[j][1]; /* H[j][1] = HT[1][j] */ } } /* K(6x3) = temp_K(6x3) * invS(3x3) */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < 3; j++) { bafl_K[i][j] = bafl_tempK[i][0] * bafl_invS[0][j]; bafl_K[i][j] += bafl_tempK[i][1] * bafl_invS[1][j]; bafl_K[i][j] += bafl_tempK[i][2] * bafl_invS[2][j]; } } /********************************************** * Update filter state. * * The a priori filter state is zero since the errors are corrected after each update. * * X = X_prio + K (y - H * X_prio) * X = K * y **********************************************/ /*printf("R = "); for (i = 0; i < 3; i++) { printf("["); for (j = 0; j < 3; j++) { printf("%f\t", RMAT_ELMT(bafl_dcm, i, j)); } printf("]\n "); } printf("\n");*/ /* innovation * y = Cnb * -[0; 0; g] - accel */ bafl_ya.x = -RMAT_ELMT(bafl_dcm, 0, 2) * BAFL_g - bafl_accel_measure.x; bafl_ya.y = -RMAT_ELMT(bafl_dcm, 1, 2) * BAFL_g - bafl_accel_measure.y; bafl_ya.z = -RMAT_ELMT(bafl_dcm, 2, 2) * BAFL_g - bafl_accel_measure.z; /* X(6) = K(6x3) * y(3) */ for (i = 0; i < BAFL_SSIZE; i++) { bafl_X[i] = bafl_K[i][0] * bafl_ya.x; bafl_X[i] += bafl_K[i][1] * bafl_ya.y; bafl_X[i] += bafl_K[i][2] * bafl_ya.z; } /********************************************** * Update the filter covariance. * * P = P_prio - K * H * P_prio * P = ( I - K * H ) * P_prio * **********************************************/ /* temp(6x6) = I(6x6) - K(6x3)*H(3x6) * * last 4 columns of H are zero */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { if (i == j) { bafl_tempP[i][j] = 1.; } else { bafl_tempP[i][j] = 0.; } if (j < 2) { /* omit the parts where H is zero */ for (k = 0; k < 3; k++) { bafl_tempP[i][j] -= bafl_K[i][k] * bafl_H[k][j]; } } } } /* P(6x6) = temp(6x6) * P_prio(6x6) */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_P[i][j] = bafl_tempP[i][0] * bafl_Pprio[0][j]; for (k = 1; k < BAFL_SSIZE; k++) { bafl_P[i][j] += bafl_tempP[i][k] * bafl_Pprio[k][j]; } } } #ifdef LKF_PRINT_P printf("Pua="); for (i = 0; i < 6; i++) { printf("["); for (j = 0; j < 6; j++) { printf("%f\t", bafl_P[i][j]); } printf("]\n "); } printf("\n"); #endif /********************************************** * Correct errors. * * **********************************************/ /* Error quaternion. */ QUAT_ASSIGN(bafl_q_a_err, 1.0, bafl_X[0]/2, bafl_X[1]/2, bafl_X[2]/2); FLOAT_QUAT_INVERT(bafl_q_a_err, bafl_q_a_err); /* normalize * Is this needed? Or is the approximation good enough?*/ float q_sq; q_sq = bafl_q_a_err.qx * bafl_q_a_err.qx + bafl_q_a_err.qy * bafl_q_a_err.qy + bafl_q_a_err.qz * bafl_q_a_err.qz; if (q_sq > 1) { /* this should actually never happen */ FLOAT_QUAT_SMUL(bafl_q_a_err, bafl_q_a_err, 1 / sqrtf(1 + q_sq)); printf("Accel error quaternion q_sq > 1!!\n"); } else { bafl_q_a_err.qi = sqrtf(1 - q_sq); } /* correct attitude */ FLOAT_QUAT_COMP(bafl_qtemp, bafl_q_a_err, bafl_quat); FLOAT_QUAT_COPY(bafl_quat, bafl_qtemp); /* correct gyro bias */ RATES_ASSIGN(bafl_b_a_err, bafl_X[3], bafl_X[4], bafl_X[5]); RATES_SUB(bafl_bias, bafl_b_a_err); /* * compute all representations */ /* maintain rotation matrix representation */ FLOAT_RMAT_OF_QUAT(bafl_dcm, bafl_quat); /* maintain euler representation */ FLOAT_EULERS_OF_RMAT(bafl_eulers, bafl_dcm); AHRS_TO_BFP(); AHRS_LTP_TO_BODY(); }
/* * Propagate our dynamic system in time * * Run the strapdown computation and the predict step of the filter * * * quat_dot = Wxq(pqr) * quat * bias_dot = 0 * * Wxq is the quaternion omega matrix: * * [ 0, -p, -q, -r ] * 1/2 * [ p, 0, r, -q ] * [ q, -r, 0, p ] * [ r, q, -p, 0 ] * */ void ahrs_propagate(void) { int i, j, k; ahrs_lowpass_accel(); /* compute unbiased rates */ RATES_FLOAT_OF_BFP(bafl_rates, imu.gyro); RATES_SUB(bafl_rates, bafl_bias); /* run strapdown computation * */ /* multiplicative quaternion update */ /* compute correction quaternion */ QUAT_ASSIGN(bafl_qr, 1., bafl_rates.p * BAFL_DT / 2, bafl_rates.q * BAFL_DT / 2, bafl_rates.r * BAFL_DT / 2); /* normalize it. maybe not necessary?? */ float q_sq; q_sq = (bafl_qr.qx * bafl_qr.qx +bafl_qr.qy * bafl_qr.qy + bafl_qr.qz * bafl_qr.qz) / 4; if (q_sq > 1) { /* this should actually never happen */ FLOAT_QUAT_SMUL(bafl_qr, bafl_qr, 1 / sqrtf(1 + q_sq)); } else { bafl_qr.qi = sqrtf(1 - q_sq); } /* propagate correction quaternion */ FLOAT_QUAT_COMP(bafl_qtemp, bafl_quat, bafl_qr); FLOAT_QUAT_COPY(bafl_quat, bafl_qtemp); bafl_qnorm = FLOAT_QUAT_NORM(bafl_quat); //TODO check if broot force normalization is good, use lagrange normalization? FLOAT_QUAT_NORMALISE(bafl_quat); /* * compute all representations */ /* maintain rotation matrix representation */ FLOAT_RMAT_OF_QUAT(bafl_dcm, bafl_quat); /* maintain euler representation */ FLOAT_EULERS_OF_RMAT(bafl_eulers, bafl_dcm); AHRS_TO_BFP(); AHRS_LTP_TO_BODY(); /* error KF-Filter * propagate only the error covariance matrix since error is corrected after each measurement * * F = [ 0 0 0 ] * [ 0 0 0 -Cbn ] * [ 0 0 0 ] * [ 0 0 0 0 0 0 ] * [ 0 0 0 0 0 0 ] * [ 0 0 0 0 0 0 ] * * T = e^(dt * F) * * T = [ 1 0 0 ] * [ 0 1 0 -Cbn*dt ] * [ 0 0 1 ] * [ 0 0 0 1 0 0 ] * [ 0 0 0 0 1 0 ] * [ 0 0 0 0 0 1 ] * * P_prio = T * P * T_T + Q * */ /* * compute state transition matrix T * * diagonal elements of T are always one */ for (i = 0; i < 3; i++) { for (j = 0; j < 3; j++) { bafl_T[i][j + 3] = -RMAT_ELMT(bafl_dcm, j, i); /* inverted bafl_dcm */ } } /* * estimate the a priori error covariance matrix P_k = T * P_k-1 * T_T + Q */ /* Temporary multiplication temp(6x6) = T(6x6) * P(6x6) */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_tempP[i][j] = 0.; for (k = 0; k < BAFL_SSIZE; k++) { bafl_tempP[i][j] += bafl_T[i][k] * bafl_P[k][j]; } } } /* P_k(6x6) = temp(6x6) * T_T(6x6) + Q */ for (i = 0; i < BAFL_SSIZE; i++) { for (j = 0; j < BAFL_SSIZE; j++) { bafl_P[i][j] = 0.; for (k = 0; k < BAFL_SSIZE; k++) { bafl_P[i][j] += bafl_tempP[i][k] * bafl_T[j][k]; //T[j][k] = T_T[k][j] } } if (i<3) { bafl_P[i][i] += bafl_Q_att; } else { bafl_P[i][i] += bafl_Q_gyro; } } #ifdef LKF_PRINT_P printf("Pp ="); for (i = 0; i < 6; i++) { printf("["); for (j = 0; j < 6; j++) { printf("%f\t", bafl_P[i][j]); } printf("]\n "); } printf("\n"); #endif }
void quat_from_earth_cmd_f(struct FloatQuat *quat, struct FloatVect2 *cmd, float heading) { /* cmd_x is positive to north = negative pitch * cmd_y is positive to east = positive roll * * orientation vector describing simultaneous rotation of roll/pitch */ const struct FloatVect3 ov = {cmd->y, -cmd->x, 0.0}; /* quaternion from that orientation vector */ struct FloatQuat q_rp; FLOAT_QUAT_OF_ORIENTATION_VECT(q_rp, ov); /* as rotation matrix */ struct FloatRMat R_rp; FLOAT_RMAT_OF_QUAT(R_rp, q_rp); /* body x-axis (before heading command) is first column */ struct FloatVect3 b_x; VECT3_ASSIGN(b_x, R_rp.m[0], R_rp.m[3], R_rp.m[6]); /* body z-axis (thrust vect) is last column */ struct FloatVect3 thrust_vect; VECT3_ASSIGN(thrust_vect, R_rp.m[2], R_rp.m[5], R_rp.m[8]); /// @todo optimize yaw angle calculation /* * Instead of using the psi setpoint angle to rotate around the body z-axis, * calculate the real angle needed to align the projection of the body x-axis * onto the horizontal plane with the psi setpoint. * * angle between two vectors a and b: * angle = atan2(norm(cross(a,b)), dot(a,b)) * sign(dot(cross(a,b), n)) * where the normal n is the thrust vector (i.e. both a and b lie in that plane) */ // desired heading vect in earth x-y plane const struct FloatVect3 psi_vect = {cosf(heading), sinf(heading), 0.0}; /* projection of desired heading onto body x-y plane * b = v - dot(v,n)*n */ float dot = FLOAT_VECT3_DOT_PRODUCT(psi_vect, thrust_vect); struct FloatVect3 dotn; FLOAT_VECT3_SMUL(dotn, thrust_vect, dot); // b = v - dot(v,n)*n struct FloatVect3 b; FLOAT_VECT3_DIFF(b, psi_vect, dotn); dot = FLOAT_VECT3_DOT_PRODUCT(b_x, b); struct FloatVect3 cross; VECT3_CROSS_PRODUCT(cross, b_x, b); // norm of the cross product float nc = FLOAT_VECT3_NORM(cross); // angle = atan2(norm(cross(a,b)), dot(a,b)) float yaw2 = atan2(nc, dot) / 2.0; // negative angle if needed // sign(dot(cross(a,b), n) float dot_cross_ab = FLOAT_VECT3_DOT_PRODUCT(cross, thrust_vect); if (dot_cross_ab < 0) { yaw2 = -yaw2; } /* quaternion with yaw command */ struct FloatQuat q_yaw; QUAT_ASSIGN(q_yaw, cosf(yaw2), 0.0, 0.0, sinf(yaw2)); /* final setpoint: apply roll/pitch, then yaw around resulting body z-axis */ FLOAT_QUAT_COMP(*quat, q_rp, q_yaw); FLOAT_QUAT_NORMALIZE(*quat); FLOAT_QUAT_WRAP_SHORTEST(*quat); }
void stabilization_attitude_run(bool_t enable_integrator) { /* * Update reference */ stabilization_attitude_ref_update(); /* * Compute errors for feedback */ /* attitude error */ struct FloatQuat att_err; struct FloatQuat* att_quat = stateGetNedToBodyQuat_f(); FLOAT_QUAT_INV_COMP(att_err, *att_quat, stab_att_ref_quat); /* wrap it in the shortest direction */ FLOAT_QUAT_WRAP_SHORTEST(att_err); /* rate error */ struct FloatRates rate_err; struct FloatRates* body_rate = stateGetBodyRates_f(); RATES_DIFF(rate_err, stab_att_ref_rate, *body_rate); /* rate_d error */ struct FloatRates body_rate_d; RATES_DIFF(body_rate_d, *body_rate, last_body_rate); RATES_COPY(last_body_rate, *body_rate); /* integrated error */ if (enable_integrator) { struct FloatQuat new_sum_err, scaled_att_err; /* update accumulator */ scaled_att_err.qi = att_err.qi; scaled_att_err.qx = att_err.qx / IERROR_SCALE; scaled_att_err.qy = att_err.qy / IERROR_SCALE; scaled_att_err.qz = att_err.qz / IERROR_SCALE; FLOAT_QUAT_COMP(new_sum_err, stabilization_att_sum_err_quat, scaled_att_err); FLOAT_QUAT_NORMALIZE(new_sum_err); FLOAT_QUAT_COPY(stabilization_att_sum_err_quat, new_sum_err); FLOAT_EULERS_OF_QUAT(stabilization_att_sum_err_eulers, stabilization_att_sum_err_quat); } else { /* reset accumulator */ FLOAT_QUAT_ZERO( stabilization_att_sum_err_quat ); FLOAT_EULERS_ZERO( stabilization_att_sum_err_eulers ); } attitude_run_ff(stabilization_att_ff_cmd, &stabilization_gains[gain_idx], &stab_att_ref_accel); attitude_run_fb(stabilization_att_fb_cmd, &stabilization_gains[gain_idx], &att_err, &rate_err, &body_rate_d, &stabilization_att_sum_err_quat); stabilization_cmd[COMMAND_ROLL] = stabilization_att_fb_cmd[COMMAND_ROLL] + stabilization_att_ff_cmd[COMMAND_ROLL]; stabilization_cmd[COMMAND_PITCH] = stabilization_att_fb_cmd[COMMAND_PITCH] + stabilization_att_ff_cmd[COMMAND_PITCH]; stabilization_cmd[COMMAND_YAW] = stabilization_att_fb_cmd[COMMAND_YAW] + stabilization_att_ff_cmd[COMMAND_YAW]; #ifdef HAS_SURFACE_COMMANDS stabilization_cmd[COMMAND_ROLL_SURFACE] = stabilization_att_fb_cmd[COMMAND_ROLL_SURFACE] + stabilization_att_ff_cmd[COMMAND_ROLL_SURFACE]; stabilization_cmd[COMMAND_PITCH_SURFACE] = stabilization_att_fb_cmd[COMMAND_PITCH_SURFACE] + stabilization_att_ff_cmd[COMMAND_PITCH_SURFACE]; stabilization_cmd[COMMAND_YAW_SURFACE] = stabilization_att_fb_cmd[COMMAND_YAW_SURFACE] + stabilization_att_ff_cmd[COMMAND_YAW_SURFACE]; #endif /* bound the result */ BoundAbs(stabilization_cmd[COMMAND_ROLL], MAX_PPRZ); BoundAbs(stabilization_cmd[COMMAND_PITCH], MAX_PPRZ); BoundAbs(stabilization_cmd[COMMAND_YAW], MAX_PPRZ); }