stabilization_indi.c

Go to the documentation of this file.

/*
 * Copyright (C) Ewoud Smeur <ewoud_smeur@msn.com>
 * MAVLab Delft University of Technology
 *
 * This file is part of paparazzi.
 *
 * paparazzi 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 2, or (at your option)
 * any later version.
 *
 * paparazzi 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 paparazzi; see the file COPYING.  If not, write to
 * the Free Software Foundation, 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

#include "firmwares/rotorcraft/stabilization/stabilization_indi.h"
#include "firmwares/rotorcraft/stabilization/stabilization_attitude.h"
#include "firmwares/rotorcraft/stabilization/stabilization_attitude_rc_setpoint.h"
#include "firmwares/rotorcraft/stabilization/stabilization_attitude_quat_transformations.h"

#include "math/pprz_algebra_float.h"
#include "state.h"
#include "generated/airframe.h"
#include "modules/radio_control/radio_control.h"
#include "modules/actuators/actuators.h"
#include "modules/core/abi.h"
#include "filters/low_pass_filter.h"
#include "wls/wls_alloc.h"
#include <stdio.h>

// Factor that the estimated G matrix is allowed to deviate from initial one
#define INDI_ALLOWED_G_FACTOR 2.0

#ifdef STABILIZATION_INDI_FILT_CUTOFF_P
#define STABILIZATION_INDI_FILTER_ROLL_RATE TRUE
#else
#define STABILIZATION_INDI_FILT_CUTOFF_P 20.0
#endif

#ifdef STABILIZATION_INDI_FILT_CUTOFF_Q
#define STABILIZATION_INDI_FILTER_PITCH_RATE TRUE
#else
#define STABILIZATION_INDI_FILT_CUTOFF_Q 20.0
#endif

#ifdef STABILIZATION_INDI_FILT_CUTOFF_R
#define STABILIZATION_INDI_FILTER_YAW_RATE TRUE
#else
#define STABILIZATION_INDI_FILT_CUTOFF_R 20.0
#endif

float du_min[INDI_NUM_ACT];
float du_max[INDI_NUM_ACT];
float du_pref[INDI_NUM_ACT];
float indi_v[INDI_OUTPUTS];
float *Bwls[INDI_OUTPUTS];
int num_iter = 0;

static void lms_estimation(void);
static void get_actuator_state(void);
static void calc_g1_element(float dx_error, int8_t i, int8_t j, float mu_extra);
static void calc_g2_element(float dx_error, int8_t j, float mu_extra);
static void calc_g1g2_pseudo_inv(void);
static void bound_g_mat(void);

int32_t stabilization_att_indi_cmd[COMMANDS_NB];
struct Indi_gains indi_gains = {
  .att = {
    STABILIZATION_INDI_REF_ERR_P,
    STABILIZATION_INDI_REF_ERR_Q,
    STABILIZATION_INDI_REF_ERR_R
  },
  .rate = {
    STABILIZATION_INDI_REF_RATE_P,
    STABILIZATION_INDI_REF_RATE_Q,
    STABILIZATION_INDI_REF_RATE_R
  },
};

#if STABILIZATION_INDI_USE_ADAPTIVE
bool indi_use_adaptive = true;
#else
bool indi_use_adaptive = false;
#endif

#ifdef STABILIZATION_INDI_ACT_RATE_LIMIT
float act_rate_limit[INDI_NUM_ACT] = STABILIZATION_INDI_ACT_RATE_LIMIT;
#endif

#ifdef STABILIZATION_INDI_ACT_IS_SERVO
bool act_is_servo[INDI_NUM_ACT] = STABILIZATION_INDI_ACT_IS_SERVO;
#else
bool act_is_servo[INDI_NUM_ACT] = {0};
#endif

#ifdef STABILIZATION_INDI_ACT_PREF
// Preferred (neutral, least energy) actuator value
float act_pref[INDI_NUM_ACT] = STABILIZATION_INDI_ACT_PREF;
#else
// Assume 0 is neutral
float act_pref[INDI_NUM_ACT] = {0.0};
#endif

float act_dyn[INDI_NUM_ACT] = STABILIZATION_INDI_ACT_DYN;

#ifdef STABILIZATION_INDI_WLS_PRIORITIES
static float Wv[INDI_OUTPUTS] = STABILIZATION_INDI_WLS_PRIORITIES;
#else
//State prioritization {W Roll, W pitch, W yaw, TOTAL THRUST}
static float Wv[INDI_OUTPUTS] = {1000, 1000, 1, 100};
#endif

// variables needed for control
float actuator_state_filt_vect[INDI_NUM_ACT];
struct FloatRates angular_accel_ref = {0., 0., 0.};
float angular_acceleration[3] = {0., 0., 0.};
float actuator_state[INDI_NUM_ACT];
float indi_u[INDI_NUM_ACT];
float indi_du[INDI_NUM_ACT];
float g2_times_du;

float q_filt = 0.0;
float r_filt = 0.0;

// variables needed for estimation
float g1g2_trans_mult[INDI_OUTPUTS][INDI_OUTPUTS];
float g1g2inv[INDI_OUTPUTS][INDI_OUTPUTS];
float actuator_state_filt_vectd[INDI_NUM_ACT];
float actuator_state_filt_vectdd[INDI_NUM_ACT];
float estimation_rate_d[INDI_NUM_ACT];
float estimation_rate_dd[INDI_NUM_ACT];
float du_estimation[INDI_NUM_ACT];
float ddu_estimation[INDI_NUM_ACT];

// The learning rate per axis (roll, pitch, yaw, thrust)
float mu1[INDI_OUTPUTS] = {0.00001, 0.00001, 0.000003, 0.000002};
// The learning rate for the propeller inertia (scaled by 512 wrt mu1)
float mu2 = 0.002;

// other variables
float act_obs[INDI_NUM_ACT];

// Number of actuators used to provide thrust
int32_t num_thrusters;

struct Int32Eulers stab_att_sp_euler;
struct Int32Quat   stab_att_sp_quat;

abi_event rpm_ev;
static void rpm_cb(uint8_t sender_id, uint16_t *rpm, uint8_t num_act);

abi_event thrust_ev;
static void thrust_cb(uint8_t sender_id, float thrust_increment);
float indi_thrust_increment;
bool indi_thrust_increment_set = false;

float g1g2_pseudo_inv[INDI_NUM_ACT][INDI_OUTPUTS];
float g2[INDI_NUM_ACT] = STABILIZATION_INDI_G2; //scaled by INDI_G_SCALING
float g1[INDI_OUTPUTS][INDI_NUM_ACT] = {STABILIZATION_INDI_G1_ROLL,
                                        STABILIZATION_INDI_G1_PITCH, STABILIZATION_INDI_G1_YAW, STABILIZATION_INDI_G1_THRUST
                                       };
float g1g2[INDI_OUTPUTS][INDI_NUM_ACT];
float g1_est[INDI_OUTPUTS][INDI_NUM_ACT];
float g2_est[INDI_NUM_ACT];
float g1_init[INDI_OUTPUTS][INDI_NUM_ACT];
float g2_init[INDI_NUM_ACT];

Butterworth2LowPass actuator_lowpass_filters[INDI_NUM_ACT];
Butterworth2LowPass estimation_input_lowpass_filters[INDI_NUM_ACT];
Butterworth2LowPass measurement_lowpass_filters[3];
Butterworth2LowPass estimation_output_lowpass_filters[3];
Butterworth2LowPass acceleration_lowpass_filter;
static struct FirstOrderLowPass rates_filt_fo[3];

struct FloatVect3 body_accel_f;

void init_filters(void);

#if PERIODIC_TELEMETRY
#include "modules/datalink/telemetry.h"
static void send_indi_g(struct transport_tx *trans, struct link_device *dev)
{
  pprz_msg_send_INDI_G(trans, dev, AC_ID, INDI_NUM_ACT, g1_est[0],
                       INDI_NUM_ACT, g1_est[1],
                       INDI_NUM_ACT, g1_est[2],
                       INDI_NUM_ACT, g1_est[3],
                       INDI_NUM_ACT, g2_est);
}

static void send_ahrs_ref_quat(struct transport_tx *trans, struct link_device *dev)
{
  struct Int32Quat *quat = stateGetNedToBodyQuat_i();
  pprz_msg_send_AHRS_REF_QUAT(trans, dev, AC_ID,
                              &stab_att_sp_quat.qi,
                              &stab_att_sp_quat.qx,
                              &stab_att_sp_quat.qy,
                              &stab_att_sp_quat.qz,
                              &(quat->qi),
                              &(quat->qx),
                              &(quat->qy),
                              &(quat->qz));
}
#endif

void stabilization_indi_init(void)
{
  // Initialize filters
  init_filters();

  AbiBindMsgRPM(RPM_SENSOR_ID, &rpm_ev, rpm_cb);
  AbiBindMsgTHRUST(THRUST_INCREMENT_ID, &thrust_ev, thrust_cb);

  float_vect_zero(actuator_state_filt_vectd, INDI_NUM_ACT);
  float_vect_zero(actuator_state_filt_vectdd, INDI_NUM_ACT);
  float_vect_zero(estimation_rate_d, INDI_NUM_ACT);
  float_vect_zero(estimation_rate_dd, INDI_NUM_ACT);
  float_vect_zero(actuator_state_filt_vect, INDI_NUM_ACT);

  //Calculate G1G2_PSEUDO_INVERSE
  calc_g1g2_pseudo_inv();

  // Initialize the array of pointers to the rows of g1g2
  uint8_t i;
  for (i = 0; i < INDI_OUTPUTS; i++) {
    Bwls[i] = g1g2[i];
  }

  // Initialize the estimator matrices
  float_vect_copy(g1_est[0], g1[0], INDI_OUTPUTS * INDI_NUM_ACT);
  float_vect_copy(g2_est, g2, INDI_NUM_ACT);
  // Remember the initial matrices
  float_vect_copy(g1_init[0], g1[0], INDI_OUTPUTS * INDI_NUM_ACT);
  float_vect_copy(g2_init, g2, INDI_NUM_ACT);

  // Assume all non-servos are delivering thrust
  num_thrusters = INDI_NUM_ACT;
  for (i = 0; i < INDI_NUM_ACT; i++) {
    num_thrusters -= act_is_servo[i];
  }

#if PERIODIC_TELEMETRY
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_INDI_G, send_indi_g);
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_AHRS_REF_QUAT, send_ahrs_ref_quat);
#endif
}

void stabilization_indi_enter(void)
{
  /* reset psi setpoint to current psi angle */
  stab_att_sp_euler.psi = stabilization_attitude_get_heading_i();

  float_vect_zero(du_estimation, INDI_NUM_ACT);
  float_vect_zero(ddu_estimation, INDI_NUM_ACT);
}

void init_filters(void)
{
  // tau = 1/(2*pi*Fc)
  float tau = 1.0 / (2.0 * M_PI * STABILIZATION_INDI_FILT_CUTOFF);
  float tau_est = 1.0 / (2.0 * M_PI * STABILIZATION_INDI_ESTIMATION_FILT_CUTOFF);
  float sample_time = 1.0 / PERIODIC_FREQUENCY;
  // Filtering of the gyroscope
  int8_t i;
  for (i = 0; i < 3; i++) {
    init_butterworth_2_low_pass(&measurement_lowpass_filters[i], tau, sample_time, 0.0);
    init_butterworth_2_low_pass(&estimation_output_lowpass_filters[i], tau_est, sample_time, 0.0);
  }

  // Filtering of the actuators
  for (i = 0; i < INDI_NUM_ACT; i++) {
    init_butterworth_2_low_pass(&actuator_lowpass_filters[i], tau, sample_time, 0.0);
    init_butterworth_2_low_pass(&estimation_input_lowpass_filters[i], tau_est, sample_time, 0.0);
  }

  // Filtering of the accel body z
  init_butterworth_2_low_pass(&acceleration_lowpass_filter, tau_est, sample_time, 0.0);

  // Init rate filter for feedback
  float time_constants[3] = {1.0/(2 * M_PI * STABILIZATION_INDI_FILT_CUTOFF_P), 1.0/(2 * M_PI * STABILIZATION_INDI_FILT_CUTOFF_Q), 1.0/(2 * M_PI * STABILIZATION_INDI_FILT_CUTOFF_R)};

  init_first_order_low_pass(&rates_filt_fo[0], time_constants[0], sample_time, stateGetBodyRates_f()->p);
  init_first_order_low_pass(&rates_filt_fo[1], time_constants[1], sample_time, stateGetBodyRates_f()->q);
  init_first_order_low_pass(&rates_filt_fo[2], time_constants[2], sample_time, stateGetBodyRates_f()->r);
}

void stabilization_indi_set_failsafe_setpoint(void)
{
  /* set failsafe to zero roll/pitch and current heading */
  int32_t heading2 = stabilization_attitude_get_heading_i() / 2;
  PPRZ_ITRIG_COS(stab_att_sp_quat.qi, heading2);
  stab_att_sp_quat.qx = 0;
  stab_att_sp_quat.qy = 0;
  PPRZ_ITRIG_SIN(stab_att_sp_quat.qz, heading2);
}

void stabilization_indi_set_rpy_setpoint_i(struct Int32Eulers *rpy)
{
  // stab_att_sp_euler.psi still used in ref..
  stab_att_sp_euler = *rpy;

  int32_quat_of_eulers(&stab_att_sp_quat, &stab_att_sp_euler);
}

void stabilization_indi_set_earth_cmd_i(struct Int32Vect2 *cmd, int32_t heading)
{
  // stab_att_sp_euler.psi still used in ref..
  stab_att_sp_euler.psi = heading;

  // compute sp_euler phi/theta for debugging/telemetry
  /* Rotate horizontal commands to body frame by psi */
  int32_t psi = stateGetNedToBodyEulers_i()->psi;
  int32_t s_psi, c_psi;
  PPRZ_ITRIG_SIN(s_psi, psi);
  PPRZ_ITRIG_COS(c_psi, psi);
  stab_att_sp_euler.phi = (-s_psi * cmd->x + c_psi * cmd->y) >> INT32_TRIG_FRAC;
  stab_att_sp_euler.theta = -(c_psi * cmd->x + s_psi * cmd->y) >> INT32_TRIG_FRAC;

  quat_from_earth_cmd_i(&stab_att_sp_quat, cmd, heading);
}

void stabilization_indi_rate_run(struct FloatRates rate_sp, bool in_flight)
{
  /* Propagate the filter on the gyroscopes */
  struct FloatRates *body_rates = stateGetBodyRates_f();
  float rate_vect[3] = {body_rates->p, body_rates->q, body_rates->r};
  int8_t i;
  for (i = 0; i < 3; i++) {
    update_butterworth_2_low_pass(&measurement_lowpass_filters[i], rate_vect[i]);
    update_butterworth_2_low_pass(&estimation_output_lowpass_filters[i], rate_vect[i]);

    //Calculate the angular acceleration via finite difference
    angular_acceleration[i] = (measurement_lowpass_filters[i].o[0]
                               - measurement_lowpass_filters[i].o[1]) * PERIODIC_FREQUENCY;

    // Calculate derivatives for estimation
    float estimation_rate_d_prev = estimation_rate_d[i];
    estimation_rate_d[i] = (estimation_output_lowpass_filters[i].o[0] - estimation_output_lowpass_filters[i].o[1]) * PERIODIC_FREQUENCY;
    estimation_rate_dd[i] = (estimation_rate_d[i] - estimation_rate_d_prev) * PERIODIC_FREQUENCY;
  }

  //The rates used for feedback are by default the measured rates.
  //If there is a lot of noise on the gyroscope, it might be good to use the filtered value for feedback.
  //Note that due to the delay, the PD controller may need relaxed gains.
  struct FloatRates rates_filt;
#if STABILIZATION_INDI_FILTER_ROLL_RATE
  rates_filt.p = update_first_order_low_pass(&rates_filt_fo[0], body_rates->p);
#else
  rates_filt.p = body_rates->p;
#endif
#if STABILIZATION_INDI_FILTER_PITCH_RATE
  rates_filt.q = update_first_order_low_pass(&rates_filt_fo[1], body_rates->q);
#else
  rates_filt.q = body_rates->q;
#endif
#if STABILIZATION_INDI_FILTER_YAW_RATE
  rates_filt.r = update_first_order_low_pass(&rates_filt_fo[2], body_rates->r);
#else
  rates_filt.r = body_rates->r;
#endif

  //calculate the virtual control (reference acceleration) based on a PD controller
  angular_accel_ref.p = (rate_sp.p - rates_filt.p) * indi_gains.rate.p;
  angular_accel_ref.q = (rate_sp.q - rates_filt.q) * indi_gains.rate.q;
  angular_accel_ref.r = (rate_sp.r - rates_filt.r) * indi_gains.rate.r;

  g2_times_du = 0.0;
  for (i = 0; i < INDI_NUM_ACT; i++) {
    g2_times_du += g2[i] * indi_du[i];
  }
  //G2 is scaled by INDI_G_SCALING to make it readable
  g2_times_du = g2_times_du / INDI_G_SCALING;

  float v_thrust = 0.0;
  if (indi_thrust_increment_set && in_flight) {
    v_thrust = indi_thrust_increment;

    //update thrust command such that the current is correctly estimated
    stabilization_cmd[COMMAND_THRUST] = 0;
    for (i = 0; i < INDI_NUM_ACT; i++) {
      stabilization_cmd[COMMAND_THRUST] += actuator_state[i] * -((int32_t) act_is_servo[i] - 1);
    }
    stabilization_cmd[COMMAND_THRUST] /= num_thrusters;

  } else {
    // incremental thrust
    for (i = 0; i < INDI_NUM_ACT; i++) {
      v_thrust +=
        (stabilization_cmd[COMMAND_THRUST] - actuator_state_filt_vect[i]) * Bwls[3][i];
    }
  }

  // The control objective in array format
  indi_v[0] = (angular_accel_ref.p - angular_acceleration[0]);
  indi_v[1] = (angular_accel_ref.q - angular_acceleration[1]);
  indi_v[2] = (angular_accel_ref.r - angular_acceleration[2] + g2_times_du);
  indi_v[3] = v_thrust;

#if STABILIZATION_INDI_ALLOCATION_PSEUDO_INVERSE
  // Calculate the increment for each actuator
  for (i = 0; i < INDI_NUM_ACT; i++) {
    indi_du[i] = (g1g2_pseudo_inv[i][0] * indi_v[0])
                 + (g1g2_pseudo_inv[i][1] * indi_v[1])
                 + (g1g2_pseudo_inv[i][2] * indi_v[2])
                 + (g1g2_pseudo_inv[i][3] * indi_v[3]);
  }
#else
  // Calculate the min and max increments
  for (i = 0; i < INDI_NUM_ACT; i++) {
    du_min[i] = -MAX_PPRZ * act_is_servo[i] - actuator_state_filt_vect[i];
    du_max[i] = MAX_PPRZ - actuator_state_filt_vect[i];
    du_pref[i] = act_pref[i] - actuator_state_filt_vect[i];

#ifdef GUIDANCE_INDI_MIN_THROTTLE
    float airspeed = stateGetAirspeed_f();
    //limit minimum thrust ap can give
    if(!act_is_servo[i]) {
      if((guidance_h.mode == GUIDANCE_H_MODE_HOVER) || (guidance_h.mode == GUIDANCE_H_MODE_NAV)) {
        if(airspeed < 8.0) {
          du_min[i] = GUIDANCE_INDI_MIN_THROTTLE - actuator_state_filt_vect[i];
        } else {
          du_min[i] = GUIDANCE_INDI_MIN_THROTTLE_FWD - actuator_state_filt_vect[i];
        }
      }
    }
#endif
  }

  // WLS Control Allocator
  num_iter =
    wls_alloc(indi_du, indi_v, du_min, du_max, Bwls, 0, 0, Wv, 0, du_pref, 10000, 10);
#endif

  // Add the increments to the actuators
  float_vect_sum(indi_u, actuator_state_filt_vect, indi_du, INDI_NUM_ACT);

  // Bound the inputs to the actuators
  for (i = 0; i < INDI_NUM_ACT; i++) {
    if (act_is_servo[i]) {
      BoundAbs(indi_u[i], MAX_PPRZ);
    } else {
      Bound(indi_u[i], 0, MAX_PPRZ);
    }
  }

  //Don't increment if not flying (not armed)
  if (!in_flight) {
    float_vect_zero(indi_u, INDI_NUM_ACT);
    float_vect_zero(indi_du, INDI_NUM_ACT);
  }

  // Propagate actuator filters
  get_actuator_state();
  for (i = 0; i < INDI_NUM_ACT; i++) {
    update_butterworth_2_low_pass(&actuator_lowpass_filters[i], actuator_state[i]);
    update_butterworth_2_low_pass(&estimation_input_lowpass_filters[i], actuator_state[i]);
    actuator_state_filt_vect[i] = actuator_lowpass_filters[i].o[0];

    // calculate derivatives for estimation
    float actuator_state_filt_vectd_prev = actuator_state_filt_vectd[i];
    actuator_state_filt_vectd[i] = (estimation_input_lowpass_filters[i].o[0] - estimation_input_lowpass_filters[i].o[1]) * PERIODIC_FREQUENCY;
    actuator_state_filt_vectdd[i] = (actuator_state_filt_vectd[i] - actuator_state_filt_vectd_prev) * PERIODIC_FREQUENCY;
  }

  // Use online effectiveness estimation only when flying
  if (in_flight && indi_use_adaptive) {
    lms_estimation();
  }

  /*Commit the actuator command*/
  for (i = 0; i < INDI_NUM_ACT; i++) {
    actuators_pprz[i] = (int16_t) indi_u[i];
  }

  // Set the stab_cmd to 42 to indicate that it is not used
  stabilization_cmd[COMMAND_ROLL] = 42;
  stabilization_cmd[COMMAND_PITCH] = 42;
  stabilization_cmd[COMMAND_YAW] = 42;
}

void stabilization_indi_attitude_run(struct Int32Quat quat_sp, bool in_flight)
{
  /* attitude error                          */
  struct FloatQuat att_err;
  struct FloatQuat *att_quat = stateGetNedToBodyQuat_f();
  struct FloatQuat quat_sp_f;

  QUAT_FLOAT_OF_BFP(quat_sp_f, quat_sp);
  float_quat_inv_comp_norm_shortest(&att_err, att_quat, &quat_sp_f);

  struct FloatVect3 att_fb;

#if TILT_TWIST_CTRL
  struct FloatQuat tilt;
  struct FloatQuat twist;
  float_quat_tilt_twist(&tilt, &twist, &att_err);
  att_fb.x = tilt.qx;
  att_fb.y = tilt.qy;
  att_fb.z = twist.qz;
#else
  att_fb.x = att_err.qx;
  att_fb.y = att_err.qy;
  att_fb.z = att_err.qz;
#endif

  // local variable to compute rate setpoints based on attitude error
  struct FloatRates rate_sp;

  // calculate the virtual control (reference acceleration) based on a PD controller
  rate_sp.p = indi_gains.att.p * att_fb.x / indi_gains.rate.p;
  rate_sp.q = indi_gains.att.q * att_fb.y / indi_gains.rate.q;
  rate_sp.r = indi_gains.att.r * att_fb.z / indi_gains.rate.r;

  // Possibly we can use some bounding here
  /*BoundAbs(rate_sp.r, 5.0);*/

  /* compute the INDI command */
  stabilization_indi_rate_run(rate_sp, in_flight);

  // Reset thrust increment boolean
  indi_thrust_increment_set = false;
}

// This function reads rc commands
void stabilization_indi_read_rc(bool in_flight, bool in_carefree, bool coordinated_turn)
{
  struct FloatQuat q_sp;
#if USE_EARTH_BOUND_RC_SETPOINT
  stabilization_attitude_read_rc_setpoint_quat_earth_bound_f(&q_sp, in_flight, in_carefree, coordinated_turn);
#else
  stabilization_attitude_read_rc_setpoint_quat_f(&q_sp, in_flight, in_carefree, coordinated_turn);
#endif

  QUAT_BFP_OF_REAL(stab_att_sp_quat, q_sp);
}

void get_actuator_state(void)
{
#if INDI_RPM_FEEDBACK
  float_vect_copy(actuator_state, act_obs, INDI_NUM_ACT);
#else
  //actuator dynamics
  int8_t i;
  float UNUSED prev_actuator_state;
  for (i = 0; i < INDI_NUM_ACT; i++) {
    prev_actuator_state = actuator_state[i];

    actuator_state[i] = actuator_state[i]
                        + act_dyn[i] * (indi_u[i] - actuator_state[i]);

#ifdef STABILIZATION_INDI_ACT_RATE_LIMIT
    if ((actuator_state[i] - prev_actuator_state) > act_rate_limit[i]) {
      actuator_state[i] = prev_actuator_state + act_rate_limit[i];
    } else if ((actuator_state[i] - prev_actuator_state) < -act_rate_limit[i]) {
      actuator_state[i] = prev_actuator_state - act_rate_limit[i];
    }
#endif
  }

#endif
}

void calc_g1_element(float ddx_error, int8_t i, int8_t j, float mu)
{
  g1_est[i][j] = g1_est[i][j] - du_estimation[j] * mu * ddx_error;
}

void calc_g2_element(float ddx_error, int8_t j, float mu)
{
  g2_est[j] = g2_est[j] - ddu_estimation[j] * mu * ddx_error;
}

void lms_estimation(void)
{

  // Get the acceleration in body axes
  struct Int32Vect3 *body_accel_i;
  body_accel_i = stateGetAccelBody_i();
  ACCELS_FLOAT_OF_BFP(body_accel_f, *body_accel_i);

  // Filter the acceleration in z axis
  update_butterworth_2_low_pass(&acceleration_lowpass_filter, body_accel_f.z);

  // Calculate the derivative of the acceleration via finite difference
  float indi_accel_d = (acceleration_lowpass_filter.o[0]
                        - acceleration_lowpass_filter.o[1]) * PERIODIC_FREQUENCY;

  // scale the inputs to avoid numerical errors
  float_vect_smul(du_estimation, actuator_state_filt_vectd, 0.001, INDI_NUM_ACT);
  float_vect_smul(ddu_estimation, actuator_state_filt_vectdd, 0.001 / PERIODIC_FREQUENCY, INDI_NUM_ACT);

  float ddx_estimation[INDI_OUTPUTS] = {estimation_rate_dd[0], estimation_rate_dd[1], estimation_rate_dd[2], indi_accel_d};

  //Estimation of G
  // TODO: only estimate when du_norm2 is large enough (enough input)
  /*float du_norm2 = du_estimation[0]*du_estimation[0] + du_estimation[1]*du_estimation[1] +du_estimation[2]*du_estimation[2] + du_estimation[3]*du_estimation[3];*/
  int8_t i;
  for (i = 0; i < INDI_OUTPUTS; i++) {
    // Calculate the error between prediction and measurement
    float ddx_error = - ddx_estimation[i];
    int8_t j;
    for (j = 0; j < INDI_NUM_ACT; j++) {
      ddx_error += g1_est[i][j] * du_estimation[j];
      if (i == 2) {
        // Changing the momentum of the rotors gives a counter torque
        ddx_error += g2_est[j] * ddu_estimation[j];
      }
    }

    // when doing the yaw axis, also use G2
    if (i == 2) {
      for (j = 0; j < INDI_NUM_ACT; j++) {
        calc_g2_element(ddx_error, j, mu2);
      }
    } else if (i == 3) {
      // If the acceleration change is very large (rough landing), don't adapt
      if (fabs(indi_accel_d) > 60.0) {
        ddx_error = 0.0;
      }
    }

    // Calculate the row of the G1 matrix corresponding to this axis
    for (j = 0; j < INDI_NUM_ACT; j++) {
      calc_g1_element(ddx_error, i, j, mu1[i]);
    }
  }

  bound_g_mat();

  // Save the calculated matrix to G1 and G2
  // until thrust is included, first part of the array
  float_vect_copy(g1[0], g1_est[0], INDI_OUTPUTS * INDI_NUM_ACT);
  float_vect_copy(g2, g2_est, INDI_NUM_ACT);

#if STABILIZATION_INDI_ALLOCATION_PSEUDO_INVERSE
  // Calculate the inverse of (G1+G2)
  calc_g1g2_pseudo_inv();
#endif
}

void calc_g1g2_pseudo_inv(void)
{

  //sum of G1 and G2
  int8_t i;
  int8_t j;
  for (i = 0; i < INDI_OUTPUTS; i++) {
    for (j = 0; j < INDI_NUM_ACT; j++) {
      if (i != 2) {
        g1g2[i][j] = g1[i][j] / INDI_G_SCALING;
      } else {
        g1g2[i][j] = (g1[i][j] + g2[j]) / INDI_G_SCALING;
      }
    }
  }

  //G1G2*transpose(G1G2)
  //calculate matrix multiplication of its transpose INDI_OUTPUTSxnum_act x num_actxINDI_OUTPUTS
  float element = 0;
  int8_t row;
  int8_t col;
  for (row = 0; row < INDI_OUTPUTS; row++) {
    for (col = 0; col < INDI_OUTPUTS; col++) {
      element = 0;
      for (i = 0; i < INDI_NUM_ACT; i++) {
        element = element + g1g2[row][i] * g1g2[col][i];
      }
      g1g2_trans_mult[row][col] = element;
    }
  }

  //there are numerical errors if the scaling is not right.
  float_vect_scale(g1g2_trans_mult[0], 100.0, INDI_OUTPUTS * INDI_OUTPUTS);

  //inverse of 4x4 matrix
  float_mat_inv_4d(g1g2inv[0], g1g2_trans_mult[0]);

  //scale back
  float_vect_scale(g1g2inv[0], 100.0, INDI_OUTPUTS * INDI_OUTPUTS);

  //G1G2'*G1G2inv
  //calculate matrix multiplication INDI_NUM_ACTxINDI_OUTPUTS x INDI_OUTPUTSxINDI_OUTPUTS
  for (row = 0; row < INDI_NUM_ACT; row++) {
    for (col = 0; col < INDI_OUTPUTS; col++) {
      element = 0;
      for (i = 0; i < INDI_OUTPUTS; i++) {
        element = element + g1g2[i][row] * g1g2inv[col][i];
      }
      g1g2_pseudo_inv[row][col] = element;
    }
  }
}

static void rpm_cb(uint8_t __attribute__((unused)) sender_id, uint16_t UNUSED *rpm, uint8_t UNUSED num_act)
{
#if INDI_RPM_FEEDBACK
  int8_t i;
  for (i = 0; i < num_act; i++) {
    act_obs[i] = (rpm[i] - get_servo_min(i));
    act_obs[i] *= (MAX_PPRZ / (float)(get_servo_max(i) - get_servo_min(i)));
    Bound(act_obs[i], 0, MAX_PPRZ);
  }
#endif
}

static void thrust_cb(uint8_t UNUSED sender_id, float thrust_increment)
{
  indi_thrust_increment = thrust_increment;
  indi_thrust_increment_set = true;
}

static void bound_g_mat(void)
{
  int8_t i;
  int8_t j;
  for (j = 0; j < INDI_NUM_ACT; j++) {
    float max_limit;
    float min_limit;

    // Limit the values of the estimated G1 matrix
    for (i = 0; i < INDI_OUTPUTS; i++) {
      if (g1_init[i][j] > 0.0) {
        max_limit = g1_init[i][j] * INDI_ALLOWED_G_FACTOR;
        min_limit = g1_init[i][j] / INDI_ALLOWED_G_FACTOR;
      } else {
        max_limit = g1_init[i][j] / INDI_ALLOWED_G_FACTOR;
        min_limit = g1_init[i][j] * INDI_ALLOWED_G_FACTOR;
      }

      if (g1_est[i][j] > max_limit) {
        g1_est[i][j] = max_limit;
      }
      if (g1_est[i][j] < min_limit) {
        g1_est[i][j] = min_limit;
      }
    }

    // Do the same for the G2 matrix
    if (g2_init[j] > 0.0) {
      max_limit = g2_init[j] * INDI_ALLOWED_G_FACTOR;
      min_limit = g2_init[j] / INDI_ALLOWED_G_FACTOR;
    } else {
      max_limit = g2_init[j] / INDI_ALLOWED_G_FACTOR;
      min_limit = g2_init[j] * INDI_ALLOWED_G_FACTOR;
    }

    if (g2_est[j] > max_limit) {
      g2_est[j] = max_limit;
    }
    if (g2_est[j] < min_limit) {
      g2_est[j] = min_limit;
    }
  }
}