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ardupilot/ArduCopter/Attitude.pde

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/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
// get_pilot_desired_angle - transform pilot's roll or pitch input into a desired lean angle
// returns desired angle in centi-degrees
static void get_pilot_desired_lean_angles(int16_t roll_in, int16_t pitch_in, int16_t &roll_out, int16_t &pitch_out)
{
static float _scaler = 1.0;
static int16_t _angle_max = 0;
// range check the input
roll_in = constrain_int16(roll_in, -ROLL_PITCH_INPUT_MAX, ROLL_PITCH_INPUT_MAX);
pitch_in = constrain_int16(pitch_in, -ROLL_PITCH_INPUT_MAX, ROLL_PITCH_INPUT_MAX);
// return immediately if no scaling required
if (g.angle_max == ROLL_PITCH_INPUT_MAX) {
roll_out = roll_in;
pitch_out = pitch_in;
return;
}
// check if angle_max has been updated and redo scaler
if (g.angle_max != _angle_max) {
_angle_max = g.angle_max;
_scaler = (float)g.angle_max/(float)ROLL_PITCH_INPUT_MAX;
}
// convert pilot input to lean angle
roll_out = roll_in * _scaler;
pitch_out = pitch_in * _scaler;
}
static void
get_stabilize_roll(int32_t target_angle)
{
// angle error
target_angle = wrap_180_cd(target_angle - ahrs.roll_sensor);
// convert to desired rate
int32_t target_rate = g.pi_stabilize_roll.kP() * target_angle;
// constrain the target rate
if (!ap.disable_stab_rate_limit) {
target_rate = constrain_int32(target_rate, -g.angle_rate_max, g.angle_rate_max);
}
// set targets for rate controller
set_roll_rate_target(target_rate, EARTH_FRAME);
}
static void
get_stabilize_pitch(int32_t target_angle)
{
// angle error
target_angle = wrap_180_cd(target_angle - ahrs.pitch_sensor);
// convert to desired rate
int32_t target_rate = g.pi_stabilize_pitch.kP() * target_angle;
// constrain the target rate
if (!ap.disable_stab_rate_limit) {
target_rate = constrain_int32(target_rate, -g.angle_rate_max, g.angle_rate_max);
}
// set targets for rate controller
set_pitch_rate_target(target_rate, EARTH_FRAME);
}
static void
get_stabilize_yaw(int32_t target_angle)
{
int32_t target_rate;
int32_t angle_error;
int32_t output = 0;
// angle error
angle_error = wrap_180_cd(target_angle - ahrs.yaw_sensor);
// limit the error we're feeding to the PID
angle_error = constrain_int32(angle_error, -4500, 4500);
// convert angle error to desired Rate:
target_rate = g.pi_stabilize_yaw.kP() * angle_error;
// do not use rate controllers for helicotpers with external gyros
#if FRAME_CONFIG == HELI_FRAME
if(motors.tail_type() == AP_MOTORS_HELI_TAILTYPE_SERVO_EXTGYRO) {
g.rc_4.servo_out = constrain_int32(target_rate, -4500, 4500);
}
#endif
#if LOGGING_ENABLED == ENABLED
// log output if PID logging is on and we are tuning the yaw
if( g.log_bitmask & MASK_LOG_PID && g.radio_tuning == CH6_STABILIZE_YAW_KP ) {
pid_log_counter++;
if( pid_log_counter >= 10 ) { // (update rate / desired output rate) = (100hz / 10hz) = 10
pid_log_counter = 0;
Log_Write_PID(CH6_STABILIZE_YAW_KP, angle_error, target_rate, 0, 0, output, tuning_value);
}
}
#endif
// set targets for rate controller
set_yaw_rate_target(target_rate, EARTH_FRAME);
}
// get_acro_level_rates - calculate earth frame rate corrections to pull the copter back to level while in ACRO mode
static void
get_acro_level_rates()
{
// zero earth frame leveling if trainer is disabled
if (g.acro_trainer == ACRO_TRAINER_DISABLED) {
set_roll_rate_target(0, BODY_EARTH_FRAME);
set_pitch_rate_target(0, BODY_EARTH_FRAME);
set_yaw_rate_target(0, BODY_EARTH_FRAME);
return;
}
// Calculate trainer mode earth frame rate command for roll
int32_t roll_angle = wrap_180_cd(ahrs.roll_sensor);
int32_t target_rate = 0;
if (g.acro_trainer == ACRO_TRAINER_LIMITED) {
if (roll_angle > g.angle_max){
target_rate = g.pi_stabilize_roll.get_p(g.angle_max-roll_angle);
}else if (roll_angle < -g.angle_max) {
target_rate = g.pi_stabilize_roll.get_p(-g.angle_max-roll_angle);
}
}
roll_angle = constrain_int32(roll_angle, -ACRO_LEVEL_MAX_ANGLE, ACRO_LEVEL_MAX_ANGLE);
target_rate -= roll_angle * g.acro_balance_roll;
// add earth frame targets for roll rate controller
set_roll_rate_target(target_rate, BODY_EARTH_FRAME);
// Calculate trainer mode earth frame rate command for pitch
int32_t pitch_angle = wrap_180_cd(ahrs.pitch_sensor);
target_rate = 0;
if (g.acro_trainer == ACRO_TRAINER_LIMITED) {
if (pitch_angle > g.angle_max){
target_rate = g.pi_stabilize_pitch.get_p(g.angle_max-pitch_angle);
}else if (pitch_angle < -g.angle_max) {
target_rate = g.pi_stabilize_pitch.get_p(-g.angle_max-pitch_angle);
}
}
pitch_angle = constrain_int32(pitch_angle, -ACRO_LEVEL_MAX_ANGLE, ACRO_LEVEL_MAX_ANGLE);
target_rate -= pitch_angle * g.acro_balance_pitch;
// add earth frame targets for pitch rate controller
set_pitch_rate_target(target_rate, BODY_EARTH_FRAME);
// add earth frame targets for yaw rate controller
set_yaw_rate_target(0, BODY_EARTH_FRAME);
}
// Roll with rate input and stabilized in the body frame
static void
get_roll_rate_stabilized_bf(int32_t stick_angle)
{
static float angle_error = 0;
// convert the input to the desired body frame roll rate
int32_t rate_request = stick_angle * g.acro_rp_p;
if (g.acro_trainer == ACRO_TRAINER_LIMITED) {
rate_request += acro_roll_rate;
}else{
// Scale pitch leveling by stick input
acro_roll_rate = (float)acro_roll_rate*acro_level_mix;
// Calculate rate limit to prevent change of rate through inverted
int32_t rate_limit = labs(labs(rate_request)-labs(acro_roll_rate));
rate_request += acro_roll_rate;
rate_request = constrain_int32(rate_request, -rate_limit, rate_limit);
}
// add automatic correction
int32_t rate_correction = g.pi_stabilize_roll.get_p(angle_error);
// set body frame targets for rate controller
set_roll_rate_target(rate_request+rate_correction, BODY_FRAME);
// Calculate integrated body frame rate error
angle_error += (rate_request - (omega.x * DEGX100)) * G_Dt;
// don't let angle error grow too large
angle_error = constrain_float(angle_error, -MAX_ROLL_OVERSHOOT, MAX_ROLL_OVERSHOOT);
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
}
// Pitch with rate input and stabilized in the body frame
static void
get_pitch_rate_stabilized_bf(int32_t stick_angle)
{
static float angle_error = 0;
// convert the input to the desired body frame pitch rate
int32_t rate_request = stick_angle * g.acro_rp_p;
if (g.acro_trainer == ACRO_TRAINER_LIMITED) {
rate_request += acro_pitch_rate;
}else{
// Scale pitch leveling by stick input
acro_pitch_rate = (float)acro_pitch_rate*acro_level_mix;
// Calculate rate limit to prevent change of rate through inverted
int32_t rate_limit = labs(labs(rate_request)-labs(acro_pitch_rate));
rate_request += acro_pitch_rate;
rate_request = constrain_int32(rate_request, -rate_limit, rate_limit);
}
// add automatic correction
int32_t rate_correction = g.pi_stabilize_pitch.get_p(angle_error);
// set body frame targets for rate controller
set_pitch_rate_target(rate_request+rate_correction, BODY_FRAME);
// Calculate integrated body frame rate error
angle_error += (rate_request - (omega.y * DEGX100)) * G_Dt;
// don't let angle error grow too large
angle_error = constrain_float(angle_error, -MAX_PITCH_OVERSHOOT, MAX_PITCH_OVERSHOOT);
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
}
// Yaw with rate input and stabilized in the body frame
static void
get_yaw_rate_stabilized_bf(int32_t stick_angle)
{
static float angle_error = 0;
// convert the input to the desired body frame yaw rate
int32_t rate_request = stick_angle * g.acro_yaw_p;
if (g.acro_trainer == ACRO_TRAINER_LIMITED) {
rate_request += acro_yaw_rate;
}else{
// Scale pitch leveling by stick input
acro_yaw_rate = (float)acro_yaw_rate*acro_level_mix;
// Calculate rate limit to prevent change of rate through inverted
int32_t rate_limit = labs(labs(rate_request)-labs(acro_yaw_rate));
rate_request += acro_yaw_rate;
rate_request = constrain_int32(rate_request, -rate_limit, rate_limit);
}
// add automatic correction
int32_t rate_correction = g.pi_stabilize_yaw.get_p(angle_error);
// set body frame targets for rate controller
set_yaw_rate_target(rate_request+rate_correction, BODY_FRAME);
// Calculate integrated body frame rate error
angle_error += (rate_request - (omega.z * DEGX100)) * G_Dt;
// don't let angle error grow too large
angle_error = constrain_float(angle_error, -MAX_YAW_OVERSHOOT, MAX_YAW_OVERSHOOT);
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
}
// Roll with rate input and stabilized in the earth frame
static void
get_roll_rate_stabilized_ef(int32_t stick_angle)
{
int32_t angle_error = 0;
// convert the input to the desired roll rate
int32_t target_rate = stick_angle * g.acro_rp_p - (acro_roll * g.acro_balance_roll);
// convert the input to the desired roll rate
acro_roll += target_rate * G_Dt;
acro_roll = wrap_180_cd(acro_roll);
// ensure that we don't reach gimbal lock
if (labs(acro_roll) > g.angle_max) {
acro_roll = constrain_int32(acro_roll, -g.angle_max, g.angle_max);
angle_error = wrap_180_cd(acro_roll - ahrs.roll_sensor);
} else {
// angle error with maximum of +- max_angle_overshoot
angle_error = wrap_180_cd(acro_roll - ahrs.roll_sensor);
angle_error = constrain_int32(angle_error, -MAX_ROLL_OVERSHOOT, MAX_ROLL_OVERSHOOT);
}
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
// reset target angle to current angle if motors not spinning
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
// update acro_roll to be within max_angle_overshoot of our current heading
acro_roll = wrap_180_cd(angle_error + ahrs.roll_sensor);
// set earth frame targets for rate controller
set_roll_rate_target(g.pi_stabilize_roll.get_p(angle_error) + target_rate, EARTH_FRAME);
}
// Pitch with rate input and stabilized in the earth frame
static void
get_pitch_rate_stabilized_ef(int32_t stick_angle)
{
int32_t angle_error = 0;
// convert the input to the desired pitch rate
int32_t target_rate = stick_angle * g.acro_rp_p - (acro_pitch * g.acro_balance_pitch);
// convert the input to the desired pitch rate
acro_pitch += target_rate * G_Dt;
acro_pitch = wrap_180_cd(acro_pitch);
// ensure that we don't reach gimbal lock
if (labs(acro_pitch) > g.angle_max) {
acro_pitch = constrain_int32(acro_pitch, -g.angle_max, g.angle_max);
angle_error = wrap_180_cd(acro_pitch - ahrs.pitch_sensor);
} else {
// angle error with maximum of +- max_angle_overshoot
angle_error = wrap_180_cd(acro_pitch - ahrs.pitch_sensor);
angle_error = constrain_int32(angle_error, -MAX_PITCH_OVERSHOOT, MAX_PITCH_OVERSHOOT);
}
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
// reset target angle to current angle if motors not spinning
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
// update acro_pitch to be within max_angle_overshoot of our current heading
acro_pitch = wrap_180_cd(angle_error + ahrs.pitch_sensor);
// set earth frame targets for rate controller
set_pitch_rate_target(g.pi_stabilize_pitch.get_p(angle_error) + target_rate, EARTH_FRAME);
}
// Yaw with rate input and stabilized in the earth frame
static void
get_yaw_rate_stabilized_ef(int32_t stick_angle)
{
int32_t angle_error = 0;
// convert the input to the desired yaw rate
int32_t target_rate = stick_angle * g.acro_yaw_p;
// convert the input to the desired yaw rate
control_yaw += target_rate * G_Dt;
control_yaw = wrap_360_cd(control_yaw);
// calculate difference between desired heading and current heading
angle_error = wrap_180_cd(control_yaw - ahrs.yaw_sensor);
// limit the maximum overshoot
angle_error = constrain_int32(angle_error, -MAX_YAW_OVERSHOOT, MAX_YAW_OVERSHOOT);
#if FRAME_CONFIG == HELI_FRAME
if (!motors.motor_runup_complete()) {
angle_error = 0;
}
#else
// reset target angle to current heading if motors not spinning
if (!motors.armed() || g.rc_3.servo_out == 0) {
angle_error = 0;
}
#endif // HELI_FRAME
// update control_yaw to be within max_angle_overshoot of our current heading
control_yaw = wrap_360_cd(angle_error + ahrs.yaw_sensor);
// set earth frame targets for rate controller
set_yaw_rate_target(g.pi_stabilize_yaw.get_p(angle_error)+target_rate, EARTH_FRAME);
}
// set_roll_rate_target - to be called by upper controllers to set roll rate targets in the earth frame
void set_roll_rate_target( int32_t desired_rate, uint8_t earth_or_body_frame ) {
rate_targets_frame = earth_or_body_frame;
if( earth_or_body_frame == BODY_FRAME ) {
roll_rate_target_bf = desired_rate;
}else{
roll_rate_target_ef = desired_rate;
}
}
// set_pitch_rate_target - to be called by upper controllers to set pitch rate targets in the earth frame
void set_pitch_rate_target( int32_t desired_rate, uint8_t earth_or_body_frame ) {
rate_targets_frame = earth_or_body_frame;
if( earth_or_body_frame == BODY_FRAME ) {
pitch_rate_target_bf = desired_rate;
}else{
pitch_rate_target_ef = desired_rate;
}
}
// set_yaw_rate_target - to be called by upper controllers to set yaw rate targets in the earth frame
void set_yaw_rate_target( int32_t desired_rate, uint8_t earth_or_body_frame ) {
rate_targets_frame = earth_or_body_frame;
if( earth_or_body_frame == BODY_FRAME ) {
yaw_rate_target_bf = desired_rate;
}else{
yaw_rate_target_ef = desired_rate;
}
}
// update_rate_contoller_targets - converts earth frame rates to body frame rates for rate controllers
void
update_rate_contoller_targets()
{
if( rate_targets_frame == EARTH_FRAME ) {
// convert earth frame rates to body frame rates
roll_rate_target_bf = roll_rate_target_ef - sin_pitch * yaw_rate_target_ef;
pitch_rate_target_bf = cos_roll_x * pitch_rate_target_ef + sin_roll * cos_pitch_x * yaw_rate_target_ef;
yaw_rate_target_bf = cos_pitch_x * cos_roll_x * yaw_rate_target_ef - sin_roll * pitch_rate_target_ef;
}else if( rate_targets_frame == BODY_EARTH_FRAME ) {
// add converted earth frame rates to body frame rates
acro_roll_rate = roll_rate_target_ef - sin_pitch * yaw_rate_target_ef;
acro_pitch_rate = cos_roll_x * pitch_rate_target_ef + sin_roll * cos_pitch_x * yaw_rate_target_ef;
acro_yaw_rate = cos_pitch_x * cos_roll_x * yaw_rate_target_ef - sin_roll * pitch_rate_target_ef;
}
}
// run roll, pitch and yaw rate controllers and send output to motors
// targets for these controllers comes from stabilize controllers
void
run_rate_controllers()
{
#if FRAME_CONFIG == HELI_FRAME
// convert desired roll and pitch rate to roll and pitch swash angles
heli_integrated_swash_controller(roll_rate_target_bf, pitch_rate_target_bf);
// helicopters only use rate controllers for yaw and only when not using an external gyro
if(motors.tail_type() != AP_MOTORS_HELI_TAILTYPE_SERVO_EXTGYRO) {
g.rc_4.servo_out = get_heli_rate_yaw(yaw_rate_target_bf);
}else{
// do not use rate controllers for helicotpers with external gyros
g.rc_4.servo_out = constrain_int32(yaw_rate_target_bf, -4500, 4500);
}
#else
// call rate controllers
g.rc_1.servo_out = get_rate_roll(roll_rate_target_bf);
g.rc_2.servo_out = get_rate_pitch(pitch_rate_target_bf);
g.rc_4.servo_out = get_rate_yaw(yaw_rate_target_bf);
#endif
// run throttle controller if accel based throttle controller is enabled and active (active means it has been given a target)
if( throttle_accel_controller_active ) {
set_throttle_out(get_throttle_accel(throttle_accel_target_ef), true);
}
}
#if FRAME_CONFIG != HELI_FRAME
static int16_t
get_rate_roll(int32_t target_rate)
{
int32_t p,i,d; // used to capture pid values for logging
int32_t current_rate; // this iteration's rate
int32_t rate_error; // simply target_rate - current_rate
int32_t output; // output from pid controller
// get current rate
current_rate = (omega.x * DEGX100);
// call pid controller
rate_error = target_rate - current_rate;
p = g.pid_rate_roll.get_p(rate_error);
// get i term
i = g.pid_rate_roll.get_integrator();
// update i term as long as we haven't breached the limits or the I term will certainly reduce
if (!motors.limit.roll_pitch || ((i>0&&rate_error<0)||(i<0&&rate_error>0))) {
i = g.pid_rate_roll.get_i(rate_error, G_Dt);
}
d = g.pid_rate_roll.get_d(rate_error, G_Dt);
output = p + i + d;
// constrain output
output = constrain_int32(output, -5000, 5000);
#if LOGGING_ENABLED == ENABLED
// log output if PID logging is on and we are tuning the rate P, I or D gains
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_RATE_ROLL_PITCH_KP || g.radio_tuning == CH6_RATE_ROLL_PITCH_KI || g.radio_tuning == CH6_RATE_ROLL_PITCH_KD) ) {
pid_log_counter++; // Note: get_rate_pitch pid logging relies on this function to update pid_log_counter so if you change the line above you must change the equivalent line in get_rate_pitch
if( pid_log_counter >= 10 ) { // (update rate / desired output rate) = (100hz / 10hz) = 10
pid_log_counter = 0;
Log_Write_PID(CH6_RATE_ROLL_PITCH_KP, rate_error, p, i, d, output, tuning_value);
}
}
#endif
// output control
return output;
}
static int16_t
get_rate_pitch(int32_t target_rate)
{
int32_t p,i,d; // used to capture pid values for logging
int32_t current_rate; // this iteration's rate
int32_t rate_error; // simply target_rate - current_rate
int32_t output; // output from pid controller
// get current rate
current_rate = (omega.y * DEGX100);
// call pid controller
rate_error = target_rate - current_rate;
p = g.pid_rate_pitch.get_p(rate_error);
// get i term
i = g.pid_rate_pitch.get_integrator();
// update i term as long as we haven't breached the limits or the I term will certainly reduce
if (!motors.limit.roll_pitch || ((i>0&&rate_error<0)||(i<0&&rate_error>0))) {
i = g.pid_rate_pitch.get_i(rate_error, G_Dt);
}
d = g.pid_rate_pitch.get_d(rate_error, G_Dt);
output = p + i + d;
// constrain output
output = constrain_int32(output, -5000, 5000);
#if LOGGING_ENABLED == ENABLED
// log output if PID logging is on and we are tuning the rate P, I or D gains
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_RATE_ROLL_PITCH_KP || g.radio_tuning == CH6_RATE_ROLL_PITCH_KI || g.radio_tuning == CH6_RATE_ROLL_PITCH_KD) ) {
if( pid_log_counter == 0 ) { // relies on get_rate_roll having updated pid_log_counter
Log_Write_PID(CH6_RATE_ROLL_PITCH_KP+100, rate_error, p, i, d, output, tuning_value);
}
}
#endif
// output control
return output;
}
static int16_t
get_rate_yaw(int32_t target_rate)
{
int32_t p,i,d; // used to capture pid values for logging
int32_t rate_error;
int32_t output;
// rate control
rate_error = target_rate - (omega.z * DEGX100);
// separately calculate p, i, d values for logging
p = g.pid_rate_yaw.get_p(rate_error);
// get i term
i = g.pid_rate_yaw.get_integrator();
// update i term as long as we haven't breached the limits or the I term will certainly reduce
if (!motors.limit.yaw || ((i>0&&rate_error<0)||(i<0&&rate_error>0))) {
i = g.pid_rate_yaw.get_i(rate_error, G_Dt);
}
// get d value
d = g.pid_rate_yaw.get_d(rate_error, G_Dt);
output = p+i+d;
output = constrain_int32(output, -4500, 4500);
#if LOGGING_ENABLED == ENABLED
// log output if PID loggins is on and we are tuning the yaw
if( g.log_bitmask & MASK_LOG_PID && g.radio_tuning == CH6_YAW_RATE_KP ) {
pid_log_counter++;
if( pid_log_counter >= 10 ) { // (update rate / desired output rate) = (100hz / 10hz) = 10
pid_log_counter = 0;
Log_Write_PID(CH6_YAW_RATE_KP, rate_error, p, i, d, output, tuning_value);
}
}
#endif
// constrain output
return output;
}
#endif // !HELI_FRAME
// calculate modified roll/pitch depending upon optical flow calculated position
static int32_t
get_of_roll(int32_t input_roll)
{
#if OPTFLOW == ENABLED
static float tot_x_cm = 0; // total distance from target
static uint32_t last_of_roll_update = 0;
int32_t new_roll = 0;
int32_t p,i,d;
// check if new optflow data available
if( optflow.last_update != last_of_roll_update) {
last_of_roll_update = optflow.last_update;
// add new distance moved
tot_x_cm += optflow.x_cm;
// only stop roll if caller isn't modifying roll
if( input_roll == 0 && current_loc.alt < 1500) {
p = g.pid_optflow_roll.get_p(-tot_x_cm);
i = g.pid_optflow_roll.get_i(-tot_x_cm,1.0f); // we could use the last update time to calculate the time change
d = g.pid_optflow_roll.get_d(-tot_x_cm,1.0f);
new_roll = p+i+d;
}else{
g.pid_optflow_roll.reset_I();
tot_x_cm = 0;
p = 0; // for logging
i = 0;
d = 0;
}
// limit amount of change and maximum angle
of_roll = constrain_int32(new_roll, (of_roll-20), (of_roll+20));
#if LOGGING_ENABLED == ENABLED
// log output if PID logging is on and we are tuning the rate P, I or D gains
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_OPTFLOW_KP || g.radio_tuning == CH6_OPTFLOW_KI || g.radio_tuning == CH6_OPTFLOW_KD) ) {
pid_log_counter++; // Note: get_of_pitch pid logging relies on this function updating pid_log_counter so if you change the line above you must change the equivalent line in get_of_pitch
if( pid_log_counter >= 5 ) { // (update rate / desired output rate) = (100hz / 10hz) = 10
pid_log_counter = 0;
Log_Write_PID(CH6_OPTFLOW_KP, tot_x_cm, p, i, d, of_roll, tuning_value);
}
}
#endif // LOGGING_ENABLED == ENABLED
}
// limit max angle
of_roll = constrain_int32(of_roll, -1000, 1000);
return input_roll+of_roll;
#else
return input_roll;
#endif
}
static int32_t
get_of_pitch(int32_t input_pitch)
{
#if OPTFLOW == ENABLED
static float tot_y_cm = 0; // total distance from target
static uint32_t last_of_pitch_update = 0;
int32_t new_pitch = 0;
int32_t p,i,d;
// check if new optflow data available
if( optflow.last_update != last_of_pitch_update ) {
last_of_pitch_update = optflow.last_update;
// add new distance moved
tot_y_cm += optflow.y_cm;
// only stop roll if caller isn't modifying pitch
if( input_pitch == 0 && current_loc.alt < 1500 ) {
p = g.pid_optflow_pitch.get_p(tot_y_cm);
i = g.pid_optflow_pitch.get_i(tot_y_cm, 1.0f); // we could use the last update time to calculate the time change
d = g.pid_optflow_pitch.get_d(tot_y_cm, 1.0f);
new_pitch = p + i + d;
}else{
tot_y_cm = 0;
g.pid_optflow_pitch.reset_I();
p = 0; // for logging
i = 0;
d = 0;
}
// limit amount of change
of_pitch = constrain_int32(new_pitch, (of_pitch-20), (of_pitch+20));
#if LOGGING_ENABLED == ENABLED
// log output if PID logging is on and we are tuning the rate P, I or D gains
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_OPTFLOW_KP || g.radio_tuning == CH6_OPTFLOW_KI || g.radio_tuning == CH6_OPTFLOW_KD) ) {
if( pid_log_counter == 0 ) { // relies on get_of_roll having updated the pid_log_counter
Log_Write_PID(CH6_OPTFLOW_KP+100, tot_y_cm, p, i, d, of_pitch, tuning_value);
}
}
#endif // LOGGING_ENABLED == ENABLED
}
// limit max angle
of_pitch = constrain_int32(of_pitch, -1000, 1000);
return input_pitch+of_pitch;
#else
return input_pitch;
#endif
}
/*************************************************************
* yaw controllers
*************************************************************/
// get_look_at_yaw - updates bearing to look at center of circle or do a panorama
// should be called at 100hz
static void get_circle_yaw()
{
static uint8_t look_at_yaw_counter = 0; // used to reduce update rate to 10hz
// if circle radius is zero do panorama
if( g.circle_radius == 0 ) {
// slew yaw towards circle angle
control_yaw = get_yaw_slew(control_yaw, ToDeg(circle_angle)*100, AUTO_YAW_SLEW_RATE);
}else{
look_at_yaw_counter++;
if( look_at_yaw_counter >= 10 ) {
look_at_yaw_counter = 0;
yaw_look_at_WP_bearing = pv_get_bearing_cd(inertial_nav.get_position(), yaw_look_at_WP);
}
// slew yaw
control_yaw = get_yaw_slew(control_yaw, yaw_look_at_WP_bearing, AUTO_YAW_SLEW_RATE);
}
// call stabilize yaw controller
get_stabilize_yaw(control_yaw);
}
// get_look_at_yaw - updates bearing to location held in look_at_yaw_WP and calls stabilize yaw controller
// should be called at 100hz
static void get_look_at_yaw()
{
static uint8_t look_at_yaw_counter = 0; // used to reduce update rate to 10hz
look_at_yaw_counter++;
if( look_at_yaw_counter >= 10 ) {
look_at_yaw_counter = 0;
yaw_look_at_WP_bearing = pv_get_bearing_cd(inertial_nav.get_position(), yaw_look_at_WP);
}
// slew yaw and call stabilize controller
control_yaw = get_yaw_slew(control_yaw, yaw_look_at_WP_bearing, AUTO_YAW_SLEW_RATE);
get_stabilize_yaw(control_yaw);
}
static void get_look_ahead_yaw(int16_t pilot_yaw)
{
// Commanded Yaw to automatically look ahead.
if (g_gps->fix && g_gps->ground_speed_cm > YAW_LOOK_AHEAD_MIN_SPEED) {
control_yaw = get_yaw_slew(control_yaw, g_gps->ground_course_cd, AUTO_YAW_SLEW_RATE);
get_stabilize_yaw(wrap_360_cd(control_yaw + pilot_yaw)); // Allow pilot to "skid" around corners up to 45 degrees
}else{
control_yaw += pilot_yaw * g.acro_yaw_p * G_Dt;
control_yaw = wrap_360_cd(control_yaw);
get_stabilize_yaw(control_yaw);
}
}
/*************************************************************
* throttle control
****************************************************************/
// update_throttle_cruise - update throttle cruise if necessary
static void update_throttle_cruise(int16_t throttle)
{
// ensure throttle_avg has been initialised
if( throttle_avg == 0 ) {
throttle_avg = g.throttle_cruise;
}
// calc average throttle if we are in a level hover
if (throttle > g.throttle_min && abs(climb_rate) < 60 && labs(ahrs.roll_sensor) < 500 && labs(ahrs.pitch_sensor) < 500) {
throttle_avg = throttle_avg * 0.99f + (float)throttle * 0.01f;
g.throttle_cruise = throttle_avg;
}
}
#if FRAME_CONFIG == HELI_FRAME
// get_angle_boost - returns a throttle including compensation for roll/pitch angle
// throttle value should be 0 ~ 1000
// for traditional helicopters
static int16_t get_angle_boost(int16_t throttle)
{
float angle_boost_factor = cos_pitch_x * cos_roll_x;
angle_boost_factor = 1.0f - constrain_float(angle_boost_factor, .5f, 1.0f);
int16_t throttle_above_mid = max(throttle - motors.get_collective_mid(),0);
// to allow logging of angle boost
angle_boost = throttle_above_mid*angle_boost_factor;
return throttle + angle_boost;
}
#else // all multicopters
// get_angle_boost - returns a throttle including compensation for roll/pitch angle
// throttle value should be 0 ~ 1000
static int16_t get_angle_boost(int16_t throttle)
{
float temp = cos_pitch_x * cos_roll_x;
int16_t throttle_out;
temp = constrain_float(temp, 0.5f, 1.0f);
// reduce throttle if we go inverted
temp = constrain_float(9000-max(labs(ahrs.roll_sensor),labs(ahrs.pitch_sensor)), 0, 3000) / (3000 * temp);
// apply scale and constrain throttle
throttle_out = constrain_float((float)(throttle-g.throttle_min) * temp + g.throttle_min, g.throttle_min, 1000);
// to allow logging of angle boost
angle_boost = throttle_out - throttle;
return throttle_out;
}
#endif // FRAME_CONFIG == HELI_FRAME
// set_throttle_out - to be called by upper throttle controllers when they wish to provide throttle output directly to motors
// provide 0 to cut motors
void set_throttle_out( int16_t throttle_out, bool apply_angle_boost )
{
if( apply_angle_boost ) {
g.rc_3.servo_out = get_angle_boost(throttle_out);
}else{
g.rc_3.servo_out = throttle_out;
// clear angle_boost for logging purposes
angle_boost = 0;
}
// update compass with throttle value
compass.set_throttle((float)g.rc_3.servo_out/1000.0f);
}
// set_throttle_accel_target - to be called by upper throttle controllers to set desired vertical acceleration in earth frame
void set_throttle_accel_target( int16_t desired_acceleration )
{
throttle_accel_target_ef = desired_acceleration;
throttle_accel_controller_active = true;
}
// disable_throttle_accel - disables the accel based throttle controller
// it will be re-enasbled on the next set_throttle_accel_target
// required when we wish to set motors to zero when pilot inputs zero throttle
void throttle_accel_deactivate()
{
throttle_accel_controller_active = false;
}
// set_throttle_takeoff - allows parents to tell throttle controller we are taking off so I terms can be cleared
static void
set_throttle_takeoff()
{
// set alt target
controller_desired_alt = current_loc.alt + ALT_HOLD_TAKEOFF_JUMP;
// clear i term from acceleration controller
if (g.pid_throttle_accel.get_integrator() < 0) {
g.pid_throttle_accel.reset_I();
}
// tell motors to do a slow start
motors.slow_start(true);
}
// get_throttle_accel - accelerometer based throttle controller
// returns an actual throttle output (0 ~ 1000) to be sent to the motors
static int16_t
get_throttle_accel(int16_t z_target_accel)
{
static float z_accel_error = 0; // The acceleration error in cm.
static uint32_t last_call_ms = 0; // the last time this controller was called
int32_t p,i,d; // used to capture pid values for logging
int16_t output;
float z_accel_meas;
uint32_t now = millis();
// Calculate Earth Frame Z acceleration
z_accel_meas = -(ahrs.get_accel_ef().z + GRAVITY_MSS) * 100;
// reset target altitude if this controller has just been engaged
if( now - last_call_ms > 100 ) {
// Reset Filter
z_accel_error = 0;
} else {
// calculate accel error and Filter with fc = 2 Hz
z_accel_error = z_accel_error + 0.11164f * (constrain_float(z_target_accel - z_accel_meas, -32000, 32000) - z_accel_error);
}
last_call_ms = now;
// separately calculate p, i, d values for logging
p = g.pid_throttle_accel.get_p(z_accel_error);
// get i term
i = g.pid_throttle_accel.get_integrator();
// update i term as long as we haven't breached the limits or the I term will certainly reduce
if ((!motors.limit.throttle_lower && !motors.limit.throttle_upper) || (i>0&&z_accel_error<0) || (i<0&&z_accel_error>0)) {
i = g.pid_throttle_accel.get_i(z_accel_error, .01f);
}
d = g.pid_throttle_accel.get_d(z_accel_error, .01f);
output = constrain_float(p+i+d+g.throttle_cruise, g.throttle_min, g.throttle_max);
#if LOGGING_ENABLED == ENABLED
// log output if PID loggins is on and we are tuning the yaw
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_THROTTLE_ACCEL_KP || g.radio_tuning == CH6_THROTTLE_ACCEL_KI || g.radio_tuning == CH6_THROTTLE_ACCEL_KD) ) {
pid_log_counter++;
if( pid_log_counter >= 10 ) { // (update rate / desired output rate) = (50hz / 10hz) = 5hz
pid_log_counter = 0;
Log_Write_PID(CH6_THROTTLE_ACCEL_KP, z_accel_error, p, i, d, output, tuning_value);
}
}
#endif
return output;
}
// get_pilot_desired_throttle - transform pilot's throttle input to make cruise throttle mid stick
// used only for manual throttle modes
// returns throttle output 0 to 1000
#define THROTTLE_IN_MIDDLE 500 // the throttle mid point
static int16_t get_pilot_desired_throttle(int16_t throttle_control)
{
int16_t throttle_out;
// exit immediately in the simple cases
if( throttle_control == 0 || g.throttle_mid == 500) {
return throttle_control;
}
// ensure reasonable throttle values
throttle_control = constrain_int16(throttle_control,0,1000);
g.throttle_mid = constrain_int16(g.throttle_mid,300,700);
// check throttle is above, below or in the deadband
if (throttle_control < THROTTLE_IN_MIDDLE) {
// below the deadband
throttle_out = g.throttle_min + ((float)(throttle_control-g.throttle_min))*((float)(g.throttle_mid - g.throttle_min))/((float)(500-g.throttle_min));
}else if(throttle_control > THROTTLE_IN_MIDDLE) {
// above the deadband
throttle_out = g.throttle_mid + ((float)(throttle_control-500))*(float)(1000-g.throttle_mid)/500.0f;
}else{
// must be in the deadband
throttle_out = g.throttle_mid;
}
return throttle_out;
}
// get_pilot_desired_climb_rate - transform pilot's throttle input to
// climb rate in cm/s. we use radio_in instead of control_in to get the full range
// without any deadzone at the bottom
#define THROTTLE_IN_DEADBAND_TOP (THROTTLE_IN_MIDDLE+THROTTLE_IN_DEADBAND) // top of the deadband
#define THROTTLE_IN_DEADBAND_BOTTOM (THROTTLE_IN_MIDDLE-THROTTLE_IN_DEADBAND) // bottom of the deadband
static int16_t get_pilot_desired_climb_rate(int16_t throttle_control)
{
int16_t desired_rate = 0;
// throttle failsafe check
if( failsafe.radio ) {
return 0;
}
// ensure a reasonable throttle value
throttle_control = constrain_int16(throttle_control,0,1000);
// check throttle is above, below or in the deadband
if (throttle_control < THROTTLE_IN_DEADBAND_BOTTOM) {
// below the deadband
desired_rate = (int32_t)g.pilot_velocity_z_max * (throttle_control-THROTTLE_IN_DEADBAND_BOTTOM) / (THROTTLE_IN_MIDDLE - THROTTLE_IN_DEADBAND);
}else if (throttle_control > THROTTLE_IN_DEADBAND_TOP) {
// above the deadband
desired_rate = (int32_t)g.pilot_velocity_z_max * (throttle_control-THROTTLE_IN_DEADBAND_TOP) / (THROTTLE_IN_MIDDLE - THROTTLE_IN_DEADBAND);
}else{
// must be in the deadband
desired_rate = 0;
}
// desired climb rate for logging
desired_climb_rate = desired_rate;
return desired_rate;
}
// get_initial_alt_hold - get new target altitude based on current altitude and climb rate
static int32_t
get_initial_alt_hold( int32_t alt_cm, int16_t climb_rate_cms)
{
int32_t target_alt;
int32_t linear_distance; // half the distace we swap between linear and sqrt and the distace we offset sqrt.
int32_t linear_velocity; // the velocity we swap between linear and sqrt.
linear_velocity = ALT_HOLD_ACCEL_MAX/g.pi_alt_hold.kP();
if (abs(climb_rate_cms) < linear_velocity) {
target_alt = alt_cm + climb_rate_cms/g.pi_alt_hold.kP();
} else {
linear_distance = ALT_HOLD_ACCEL_MAX/(2*g.pi_alt_hold.kP()*g.pi_alt_hold.kP());
if (climb_rate_cms > 0){
target_alt = alt_cm + linear_distance + (int32_t)climb_rate_cms*(int32_t)climb_rate_cms/(2*ALT_HOLD_ACCEL_MAX);
} else {
target_alt = alt_cm - ( linear_distance + (int32_t)climb_rate_cms*(int32_t)climb_rate_cms/(2*ALT_HOLD_ACCEL_MAX) );
}
}
return constrain_int32(target_alt, alt_cm - ALT_HOLD_INIT_MAX_OVERSHOOT, alt_cm + ALT_HOLD_INIT_MAX_OVERSHOOT);
}
// get_throttle_rate - calculates desired accel required to achieve desired z_target_speed
// sets accel based throttle controller target
static void
get_throttle_rate(float z_target_speed)
{
static uint32_t last_call_ms = 0;
static float z_rate_error = 0; // The velocity error in cm.
static float z_target_speed_filt = 0; // The filtered requested speed
float z_target_speed_delta; // The change in requested speed
int32_t p; // used to capture pid values for logging
int32_t output; // the target acceleration if the accel based throttle is enabled, otherwise the output to be sent to the motors
uint32_t now = millis();
// reset target altitude if this controller has just been engaged
if( now - last_call_ms > 100 ) {
// Reset Filter
z_rate_error = 0;
z_target_speed_filt = z_target_speed;
output = 0;
} else {
// calculate rate error and filter with cut off frequency of 2 Hz
z_rate_error = z_rate_error + 0.20085f * ((z_target_speed - climb_rate) - z_rate_error);
// feed forward acceleration based on change in the filtered desired speed.
z_target_speed_delta = 0.20085f * (z_target_speed - z_target_speed_filt);
z_target_speed_filt = z_target_speed_filt + z_target_speed_delta;
output = z_target_speed_delta * 50.0f; // To-Do: replace 50 with dt
}
last_call_ms = now;
// calculate p
p = g.pid_throttle_rate.kP() * z_rate_error;
// consolidate and constrain target acceleration
output += p;
output = constrain_int32(output, -32000, 32000);
#if LOGGING_ENABLED == ENABLED
// log output if PID loggins is on and we are tuning the yaw
if( g.log_bitmask & MASK_LOG_PID && (g.radio_tuning == CH6_THROTTLE_RATE_KP || g.radio_tuning == CH6_THROTTLE_RATE_KD) ) {
pid_log_counter++;
if( pid_log_counter >= 10 ) { // (update rate / desired output rate) = (50hz / 10hz) = 5hz
pid_log_counter = 0;
Log_Write_PID(CH6_THROTTLE_RATE_KP, z_rate_error, p, 0, 0, output, tuning_value);
}
}
#endif
// set target for accel based throttle controller
set_throttle_accel_target(output);
// update throttle cruise
// TO-DO: this may not be correct because g.rc_3.servo_out has not been updated for this iteration
if( z_target_speed == 0 ) {
update_throttle_cruise(g.rc_3.servo_out);
}
}
// get_throttle_althold - hold at the desired altitude in cm
// updates accel based throttle controller targets
// Note: max_climb_rate is an optional parameter to allow reuse of this function by landing controller
static void
get_throttle_althold(int32_t target_alt, int16_t min_climb_rate, int16_t max_climb_rate)
{
int32_t alt_error;
float desired_rate;
int32_t linear_distance; // half the distace we swap between linear and sqrt and the distace we offset sqrt.
// calculate altitude error
alt_error = target_alt - current_loc.alt;
// check kP to avoid division by zero
if( g.pi_alt_hold.kP() != 0 ) {
linear_distance = ALT_HOLD_ACCEL_MAX/(2*g.pi_alt_hold.kP()*g.pi_alt_hold.kP());
if( alt_error > 2*linear_distance ) {
desired_rate = safe_sqrt(2*ALT_HOLD_ACCEL_MAX*(alt_error-linear_distance));
}else if( alt_error < -2*linear_distance ) {
desired_rate = -safe_sqrt(2*ALT_HOLD_ACCEL_MAX*(-alt_error-linear_distance));
}else{
desired_rate = g.pi_alt_hold.get_p(alt_error);
}
}else{
desired_rate = 0;
}
desired_rate = constrain_float(desired_rate, min_climb_rate, max_climb_rate);
// call rate based throttle controller which will update accel based throttle controller targets
get_throttle_rate(desired_rate);
// update altitude error reported to GCS
altitude_error = alt_error;
// TO-DO: enabled PID logging for this controller
}
// get_throttle_althold_with_slew - altitude controller with slew to avoid step changes in altitude target
// calls normal althold controller which updates accel based throttle controller targets
static void
get_throttle_althold_with_slew(int32_t target_alt, int16_t min_climb_rate, int16_t max_climb_rate)
{
float alt_change = target_alt-controller_desired_alt;
// adjust desired alt if motors have not hit their limits
if ((alt_change<0 && !motors.limit.throttle_lower) || (alt_change>0 && !motors.limit.throttle_upper)) {
controller_desired_alt += constrain_float(alt_change, min_climb_rate*0.02f, max_climb_rate*0.02f);
}
// do not let target altitude get too far from current altitude
controller_desired_alt = constrain_float(controller_desired_alt,current_loc.alt-750,current_loc.alt+750);
get_throttle_althold(controller_desired_alt, min_climb_rate-250, max_climb_rate+250); // 250 is added to give head room to alt hold controller
}
// get_throttle_rate_stabilized - rate controller with additional 'stabilizer'
// 'stabilizer' ensure desired rate is being met
// calls normal throttle rate controller which updates accel based throttle controller targets
static void
get_throttle_rate_stabilized(int16_t target_rate)
{
// adjust desired alt if motors have not hit their limits
if ((target_rate<0 && !motors.limit.throttle_lower) || (target_rate>0 && !motors.limit.throttle_upper)) {
controller_desired_alt += target_rate * 0.02f;
}
// do not let target altitude get too far from current altitude
controller_desired_alt = constrain_float(controller_desired_alt,current_loc.alt-750,current_loc.alt+750);
#if AC_FENCE == ENABLED
// do not let target altitude be too close to the fence
// To-Do: add this to other altitude controllers
if((fence.get_enabled_fences() & AC_FENCE_TYPE_ALT_MAX) != 0) {
float alt_limit = fence.get_safe_alt() * 100.0f;
if (controller_desired_alt > alt_limit) {
controller_desired_alt = alt_limit;
}
}
#endif
// update target altitude for reporting purposes
set_target_alt_for_reporting(controller_desired_alt);
get_throttle_althold(controller_desired_alt, -g.pilot_velocity_z_max-250, g.pilot_velocity_z_max+250); // 250 is added to give head room to alt hold controller
}
// get_throttle_land - high level landing logic
// sends the desired acceleration in the accel based throttle controller
// called at 50hz
static void
get_throttle_land()
{
// if we are above 10m and the sonar does not sense anything perform regular alt hold descent
if (current_loc.alt >= LAND_START_ALT && !(g.sonar_enabled && sonar_alt_health >= SONAR_ALT_HEALTH_MAX)) {
get_throttle_althold_with_slew(LAND_START_ALT, -wp_nav.get_descent_velocity(), -abs(g.land_speed));
}else{
get_throttle_rate_stabilized(-abs(g.land_speed));
// disarm when the landing detector says we've landed and throttle is at min (or we're in failsafe so we have no pilot thorottle input)
if( ap.land_complete && (g.rc_3.control_in == 0 || failsafe.radio) ) {
init_disarm_motors();
}
}
}
// reset_land_detector - initialises land detector
static void reset_land_detector()
{
set_land_complete(false);
land_detector = 0;
}
// update_land_detector - checks if we have landed and updates the ap.land_complete flag
// returns true if we have landed
static bool update_land_detector()
{
// detect whether we have landed by watching for low climb rate and minimum throttle
if (abs(climb_rate) < 20 && motors.limit.throttle_lower) {
if (!ap.land_complete) {
// run throttle controller if accel based throttle controller is enabled and active (active means it has been given a target)
if( land_detector < LAND_DETECTOR_TRIGGER) {
land_detector++;
}else{
set_land_complete(true);
land_detector = 0;
}
}
}else{
// we've sensed movement up or down so reset land_detector
land_detector = 0;
if(ap.land_complete) {
set_land_complete(false);
}
}
// return current state of landing
return ap.land_complete;
}
// get_throttle_surface_tracking - hold copter at the desired distance above the ground
// updates accel based throttle controller targets
static void
get_throttle_surface_tracking(int16_t target_rate)
{
static uint32_t last_call_ms = 0;
float distance_error;
float velocity_correction;
uint32_t now = millis();
// reset target altitude if this controller has just been engaged
if( now - last_call_ms > 200 ) {
target_sonar_alt = sonar_alt + controller_desired_alt - current_loc.alt;
}
last_call_ms = now;
// adjust sonar target alt if motors have not hit their limits
if ((target_rate<0 && !motors.limit.throttle_lower) || (target_rate>0 && !motors.limit.throttle_upper)) {
target_sonar_alt += target_rate * 0.02f;
}
// do not let target altitude get too far from current altitude above ground
// Note: the 750cm limit is perhaps too wide but is consistent with the regular althold limits and helps ensure a smooth transition
target_sonar_alt = constrain_float(target_sonar_alt,sonar_alt-750,sonar_alt+750);
// calc desired velocity correction from target sonar alt vs actual sonar alt
distance_error = target_sonar_alt-sonar_alt;
velocity_correction = distance_error * g.sonar_gain;
velocity_correction = constrain_float(velocity_correction, -THR_SURFACE_TRACKING_VELZ_MAX, THR_SURFACE_TRACKING_VELZ_MAX);
// call regular rate stabilize alt hold controller
get_throttle_rate_stabilized(target_rate + velocity_correction);
}
/*
* reset all I integrators
*/
static void reset_I_all(void)
{
reset_rate_I();
reset_throttle_I();
reset_optflow_I();
}
static void reset_rate_I()
{
g.pid_rate_roll.reset_I();
g.pid_rate_pitch.reset_I();
g.pid_rate_yaw.reset_I();
}
static void reset_optflow_I(void)
{
g.pid_optflow_roll.reset_I();
g.pid_optflow_pitch.reset_I();
of_roll = 0;
of_pitch = 0;
}
static void reset_throttle_I(void)
{
// For Altitude Hold
g.pi_alt_hold.reset_I();
g.pid_throttle_accel.reset_I();
}
static void set_accel_throttle_I_from_pilot_throttle(int16_t pilot_throttle)
{
// shift difference between pilot's throttle and hover throttle into accelerometer I
g.pid_throttle_accel.set_integrator(pilot_throttle-g.throttle_cruise);
}
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