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ardupilot/libraries/AC_AttitudeControl/AC_PosControl.cpp

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#include <AP_HAL/AP_HAL.h>
#include "AC_PosControl.h"
#include <AP_Math/AP_Math.h>
#include <AP_Logger/AP_Logger.h>
extern const AP_HAL::HAL& hal;
#if APM_BUILD_TYPE(APM_BUILD_ArduPlane)
// default gains for Plane
# define POSCONTROL_POS_Z_P 1.0f // vertical position controller P gain default
# define POSCONTROL_VEL_Z_P 5.0f // vertical velocity controller P gain default
# define POSCONTROL_ACC_Z_P 0.3f // vertical acceleration controller P gain default
# define POSCONTROL_ACC_Z_I 1.0f // vertical acceleration controller I gain default
# define POSCONTROL_ACC_Z_D 0.0f // vertical acceleration controller D gain default
# define POSCONTROL_ACC_Z_IMAX 800 // vertical acceleration controller IMAX gain default
# define POSCONTROL_ACC_Z_FILT_HZ 10.0f // vertical acceleration controller input filter default
# define POSCONTROL_ACC_Z_DT 0.02f // vertical acceleration controller dt default
# define POSCONTROL_POS_XY_P 1.0f // horizontal position controller P gain default
# define POSCONTROL_VEL_XY_P 1.4f // horizontal velocity controller P gain default
# define POSCONTROL_VEL_XY_I 0.7f // horizontal velocity controller I gain default
# define POSCONTROL_VEL_XY_D 0.35f // horizontal velocity controller D gain default
# define POSCONTROL_VEL_XY_IMAX 1000.0f // horizontal velocity controller IMAX gain default
# define POSCONTROL_VEL_XY_FILT_HZ 5.0f // horizontal velocity controller input filter
# define POSCONTROL_VEL_XY_FILT_D_HZ 5.0f // horizontal velocity controller input filter for D
#elif APM_BUILD_TYPE(APM_BUILD_ArduSub)
// default gains for Sub
# define POSCONTROL_POS_Z_P 3.0f // vertical position controller P gain default
# define POSCONTROL_VEL_Z_P 8.0f // vertical velocity controller P gain default
# define POSCONTROL_ACC_Z_P 0.5f // vertical acceleration controller P gain default
# define POSCONTROL_ACC_Z_I 0.1f // vertical acceleration controller I gain default
# define POSCONTROL_ACC_Z_D 0.0f // vertical acceleration controller D gain default
# define POSCONTROL_ACC_Z_IMAX 100 // vertical acceleration controller IMAX gain default
# define POSCONTROL_ACC_Z_FILT_HZ 20.0f // vertical acceleration controller input filter default
# define POSCONTROL_ACC_Z_DT 0.0025f // vertical acceleration controller dt default
# define POSCONTROL_POS_XY_P 1.0f // horizontal position controller P gain default
# define POSCONTROL_VEL_XY_P 1.0f // horizontal velocity controller P gain default
# define POSCONTROL_VEL_XY_I 0.5f // horizontal velocity controller I gain default
# define POSCONTROL_VEL_XY_D 0.0f // horizontal velocity controller D gain default
# define POSCONTROL_VEL_XY_IMAX 1000.0f // horizontal velocity controller IMAX gain default
# define POSCONTROL_VEL_XY_FILT_HZ 5.0f // horizontal velocity controller input filter
# define POSCONTROL_VEL_XY_FILT_D_HZ 5.0f // horizontal velocity controller input filter for D
#else
// default gains for Copter / TradHeli
# define POSCONTROL_POS_Z_P 1.0f // vertical position controller P gain default
# define POSCONTROL_VEL_Z_P 5.0f // vertical velocity controller P gain default
# define POSCONTROL_ACC_Z_P 0.5f // vertical acceleration controller P gain default
# define POSCONTROL_ACC_Z_I 1.0f // vertical acceleration controller I gain default
# define POSCONTROL_ACC_Z_D 0.0f // vertical acceleration controller D gain default
# define POSCONTROL_ACC_Z_IMAX 800 // vertical acceleration controller IMAX gain default
# define POSCONTROL_ACC_Z_FILT_HZ 20.0f // vertical acceleration controller input filter default
# define POSCONTROL_ACC_Z_DT 0.0025f // vertical acceleration controller dt default
# define POSCONTROL_POS_XY_P 1.0f // horizontal position controller P gain default
# define POSCONTROL_VEL_XY_P 2.0f // horizontal velocity controller P gain default
# define POSCONTROL_VEL_XY_I 1.0f // horizontal velocity controller I gain default
# define POSCONTROL_VEL_XY_D 0.5f // horizontal velocity controller D gain default
# define POSCONTROL_VEL_XY_IMAX 1000.0f // horizontal velocity controller IMAX gain default
# define POSCONTROL_VEL_XY_FILT_HZ 5.0f // horizontal velocity controller input filter
# define POSCONTROL_VEL_XY_FILT_D_HZ 5.0f // horizontal velocity controller input filter for D
#endif
const AP_Param::GroupInfo AC_PosControl::var_info[] = {
// 0 was used for HOVER
// @Param: _ACC_XY_FILT
// @DisplayName: XY Acceleration filter cutoff frequency
// @Description: Lower values will slow the response of the navigation controller and reduce twitchiness
// @Units: Hz
// @Range: 0.5 5
// @Increment: 0.1
// @User: Advanced
AP_GROUPINFO("_ACC_XY_FILT", 1, AC_PosControl, _accel_xy_filt_hz, POSCONTROL_ACCEL_FILTER_HZ),
// @Param: _POSZ_P
// @DisplayName: Position (vertical) controller P gain
// @Description: Position (vertical) controller P gain. Converts the difference between the desired altitude and actual altitude into a climb or descent rate which is passed to the throttle rate controller
// @Range: 1.000 3.000
// @User: Standard
AP_SUBGROUPINFO(_p_pos_z, "_POSZ_", 2, AC_PosControl, AC_P),
// @Param: _VELZ_P
// @DisplayName: Velocity (vertical) controller P gain
// @Description: Velocity (vertical) controller P gain. Converts the difference between desired vertical speed and actual speed into a desired acceleration that is passed to the throttle acceleration controller
// @Range: 1.000 8.000
// @User: Standard
AP_SUBGROUPINFO(_p_vel_z, "_VELZ_", 3, AC_PosControl, AC_P),
// @Param: _ACCZ_P
// @DisplayName: Acceleration (vertical) controller P gain
// @Description: Acceleration (vertical) controller P gain. Converts the difference between desired vertical acceleration and actual acceleration into a motor output
// @Range: 0.500 1.500
// @Increment: 0.05
// @User: Standard
// @Param: _ACCZ_I
// @DisplayName: Acceleration (vertical) controller I gain
// @Description: Acceleration (vertical) controller I gain. Corrects long-term difference in desired vertical acceleration and actual acceleration
// @Range: 0.000 3.000
// @User: Standard
// @Param: _ACCZ_IMAX
// @DisplayName: Acceleration (vertical) controller I gain maximum
// @Description: Acceleration (vertical) controller I gain maximum. Constrains the maximum pwm that the I term will generate
// @Range: 0 1000
// @Units: d%
// @User: Standard
// @Param: _ACCZ_D
// @DisplayName: Acceleration (vertical) controller D gain
// @Description: Acceleration (vertical) controller D gain. Compensates for short-term change in desired vertical acceleration vs actual acceleration
// @Range: 0.000 0.400
// @User: Standard
// @Param: _ACCZ_FILT
// @DisplayName: Acceleration (vertical) controller filter
// @Description: Filter applied to acceleration to reduce noise. Lower values reduce noise but add delay.
// @Range: 1.000 100.000
// @Units: Hz
// @User: Standard
AP_SUBGROUPINFO(_pid_accel_z, "_ACCZ_", 4, AC_PosControl, AC_PID),
// @Param: _POSXY_P
// @DisplayName: Position (horizonal) controller P gain
// @Description: Position controller P gain. Converts the distance (in the latitude direction) to the target location into a desired speed which is then passed to the loiter latitude rate controller
// @Range: 0.500 2.000
// @User: Standard
AP_SUBGROUPINFO(_p_pos_xy, "_POSXY_", 5, AC_PosControl, AC_P),
// @Param: _VELXY_P
// @DisplayName: Velocity (horizontal) P gain
// @Description: Velocity (horizontal) P gain. Converts the difference between desired velocity to a target acceleration
// @Range: 0.1 6.0
// @Increment: 0.1
// @User: Advanced
// @Param: _VELXY_I
// @DisplayName: Velocity (horizontal) I gain
// @Description: Velocity (horizontal) I gain. Corrects long-term difference in desired velocity to a target acceleration
// @Range: 0.02 1.00
// @Increment: 0.01
// @User: Advanced
// @Param: _VELXY_D
// @DisplayName: Velocity (horizontal) D gain
// @Description: Velocity (horizontal) D gain. Corrects short-term changes in velocity
// @Range: 0.00 1.00
// @Increment: 0.001
// @User: Advanced
// @Param: _VELXY_IMAX
// @DisplayName: Velocity (horizontal) integrator maximum
// @Description: Velocity (horizontal) integrator maximum. Constrains the target acceleration that the I gain will output
// @Range: 0 4500
// @Increment: 10
// @Units: cm/s/s
// @User: Advanced
// @Param: _VELXY_FILT
// @DisplayName: Velocity (horizontal) input filter
// @Description: Velocity (horizontal) input filter. This filter (in hz) is applied to the input for P and I terms
// @Range: 0 100
// @Units: Hz
// @User: Advanced
// @Param: _VELXY_D_FILT
// @DisplayName: Velocity (horizontal) input filter
// @Description: Velocity (horizontal) input filter. This filter (in hz) is applied to the input for P and I terms
// @Range: 0 100
// @Units: Hz
// @User: Advanced
AP_SUBGROUPINFO(_pid_vel_xy, "_VELXY_", 6, AC_PosControl, AC_PID_2D),
// @Param: _ANGLE_MAX
// @DisplayName: Position Control Angle Max
// @Description: Maximum lean angle autopilot can request. Set to zero to use ANGLE_MAX parameter value
// @Units: deg
// @Range: 0 45
// @Increment: 1
// @User: Advanced
AP_GROUPINFO("_ANGLE_MAX", 7, AC_PosControl, _lean_angle_max, 0.0f),
AP_GROUPEND
};
// Default constructor.
// Note that the Vector/Matrix constructors already implicitly zero
// their values.
//
AC_PosControl::AC_PosControl(const AP_AHRS_View& ahrs, const AP_InertialNav& inav,
const AP_Motors& motors, AC_AttitudeControl& attitude_control) :
_ahrs(ahrs),
_inav(inav),
_motors(motors),
_attitude_control(attitude_control),
_p_pos_z(POSCONTROL_POS_Z_P),
_p_vel_z(POSCONTROL_VEL_Z_P),
_pid_accel_z(POSCONTROL_ACC_Z_P, POSCONTROL_ACC_Z_I, POSCONTROL_ACC_Z_D, POSCONTROL_ACC_Z_IMAX, POSCONTROL_ACC_Z_FILT_HZ, POSCONTROL_ACC_Z_DT),
_p_pos_xy(POSCONTROL_POS_XY_P),
_pid_vel_xy(POSCONTROL_VEL_XY_P, POSCONTROL_VEL_XY_I, POSCONTROL_VEL_XY_D, POSCONTROL_VEL_XY_IMAX, POSCONTROL_VEL_XY_FILT_HZ, POSCONTROL_VEL_XY_FILT_D_HZ, POSCONTROL_DT_50HZ),
_dt(POSCONTROL_DT_400HZ),
_speed_down_cms(POSCONTROL_SPEED_DOWN),
_speed_up_cms(POSCONTROL_SPEED_UP),
_speed_cms(POSCONTROL_SPEED),
_accel_z_cms(POSCONTROL_ACCEL_Z),
_accel_cms(POSCONTROL_ACCEL_XY),
_leash(POSCONTROL_LEASH_LENGTH_MIN),
_leash_down_z(POSCONTROL_LEASH_LENGTH_MIN),
_leash_up_z(POSCONTROL_LEASH_LENGTH_MIN),
_accel_target_filter(POSCONTROL_ACCEL_FILTER_HZ)
{
AP_Param::setup_object_defaults(this, var_info);
// initialise flags
_flags.recalc_leash_z = true;
_flags.recalc_leash_xy = true;
_flags.reset_desired_vel_to_pos = true;
_flags.reset_accel_to_lean_xy = true;
_flags.reset_rate_to_accel_z = true;
_flags.reset_accel_to_throttle = true;
_flags.freeze_ff_z = true;
_flags.use_desvel_ff_z = true;
_limit.pos_up = true;
_limit.pos_down = true;
_limit.vel_up = true;
_limit.vel_down = true;
_limit.accel_xy = true;
}
///
/// z-axis position controller
///
/// set_dt - sets time delta in seconds for all controllers (i.e. 100hz = 0.01, 400hz = 0.0025)
void AC_PosControl::set_dt(float delta_sec)
{
_dt = delta_sec;
// update PID controller dt
_pid_accel_z.set_dt(_dt);
_pid_vel_xy.set_dt(_dt);
// update rate z-axis velocity error and accel error filters
_vel_error_filter.set_cutoff_frequency(POSCONTROL_VEL_ERROR_CUTOFF_FREQ);
}
/// set_max_speed_z - set the maximum climb and descent rates
/// To-Do: call this in the main code as part of flight mode initialisation
void AC_PosControl::set_max_speed_z(float speed_down, float speed_up)
{
// ensure speed_down is always negative
speed_down = -fabsf(speed_down);
if ((fabsf(_speed_down_cms-speed_down) > 1.0f) || (fabsf(_speed_up_cms-speed_up) > 1.0f)) {
_speed_down_cms = speed_down;
_speed_up_cms = speed_up;
_flags.recalc_leash_z = true;
calc_leash_length_z();
}
}
/// set_max_accel_z - set the maximum vertical acceleration in cm/s/s
void AC_PosControl::set_max_accel_z(float accel_cmss)
{
if (fabsf(_accel_z_cms-accel_cmss) > 1.0f) {
_accel_z_cms = accel_cmss;
_flags.recalc_leash_z = true;
calc_leash_length_z();
}
}
/// set_alt_target_with_slew - adjusts target towards a final altitude target
/// should be called continuously (with dt set to be the expected time between calls)
/// actual position target will be moved no faster than the speed_down and speed_up
/// target will also be stopped if the motors hit their limits or leash length is exceeded
void AC_PosControl::set_alt_target_with_slew(float alt_cm, float dt)
{
float alt_change = alt_cm-_pos_target.z;
// do not use z-axis desired velocity feed forward
_flags.use_desvel_ff_z = false;
// 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)) {
if (!is_zero(dt)) {
float climb_rate_cms = constrain_float(alt_change/dt, _speed_down_cms, _speed_up_cms);
_pos_target.z += climb_rate_cms*dt;
_vel_desired.z = climb_rate_cms; // recorded for reporting purposes
}
} else {
// recorded for reporting purposes
_vel_desired.z = 0.0f;
}
// do not let target get too far from current altitude
float curr_alt = _inav.get_altitude();
_pos_target.z = constrain_float(_pos_target.z,curr_alt-_leash_down_z,curr_alt+_leash_up_z);
}
/// set_alt_target_from_climb_rate - adjusts target up or down using a climb rate in cm/s
/// should be called continuously (with dt set to be the expected time between calls)
/// actual position target will be moved no faster than the speed_down and speed_up
/// target will also be stopped if the motors hit their limits or leash length is exceeded
void AC_PosControl::set_alt_target_from_climb_rate(float climb_rate_cms, float dt, bool force_descend)
{
// adjust desired alt if motors have not hit their limits
// To-Do: add check of _limit.pos_down?
if ((climb_rate_cms<0 && (!_motors.limit.throttle_lower || force_descend)) || (climb_rate_cms>0 && !_motors.limit.throttle_upper && !_limit.pos_up)) {
_pos_target.z += climb_rate_cms * dt;
}
// do not use z-axis desired velocity feed forward
// vel_desired set to desired climb rate for reporting and land-detector
_flags.use_desvel_ff_z = false;
_vel_desired.z = climb_rate_cms;
}
/// set_alt_target_from_climb_rate_ff - adjusts target up or down using a climb rate in cm/s using feed-forward
/// should be called continuously (with dt set to be the expected time between calls)
/// actual position target will be moved no faster than the speed_down and speed_up
/// target will also be stopped if the motors hit their limits or leash length is exceeded
/// set force_descend to true during landing to allow target to move low enough to slow the motors
void AC_PosControl::set_alt_target_from_climb_rate_ff(float climb_rate_cms, float dt, bool force_descend)
{
// calculated increased maximum acceleration if over speed
float accel_z_cms = _accel_z_cms;
if (_vel_desired.z < _speed_down_cms && !is_zero(_speed_down_cms)) {
accel_z_cms *= POSCONTROL_OVERSPEED_GAIN_Z * _vel_desired.z / _speed_down_cms;
}
if (_vel_desired.z > _speed_up_cms && !is_zero(_speed_up_cms)) {
accel_z_cms *= POSCONTROL_OVERSPEED_GAIN_Z * _vel_desired.z / _speed_up_cms;
}
accel_z_cms = constrain_float(accel_z_cms, 0.0f, 750.0f);
// jerk_z is calculated to reach full acceleration in 1000ms.
float jerk_z = accel_z_cms * POSCONTROL_JERK_RATIO;
float accel_z_max = MIN(accel_z_cms, safe_sqrt(2.0f*fabsf(_vel_desired.z - climb_rate_cms)*jerk_z));
_accel_last_z_cms += jerk_z * dt;
_accel_last_z_cms = MIN(accel_z_max, _accel_last_z_cms);
float vel_change_limit = _accel_last_z_cms * dt;
_vel_desired.z = constrain_float(climb_rate_cms, _vel_desired.z-vel_change_limit, _vel_desired.z+vel_change_limit);
_flags.use_desvel_ff_z = true;
// adjust desired alt if motors have not hit their limits
// To-Do: add check of _limit.pos_down?
if ((_vel_desired.z<0 && (!_motors.limit.throttle_lower || force_descend)) || (_vel_desired.z>0 && !_motors.limit.throttle_upper && !_limit.pos_up)) {
_pos_target.z += _vel_desired.z * dt;
}
}
/// add_takeoff_climb_rate - adjusts alt target up or down using a climb rate in cm/s
/// should be called continuously (with dt set to be the expected time between calls)
/// almost no checks are performed on the input
void AC_PosControl::add_takeoff_climb_rate(float climb_rate_cms, float dt)
{
_pos_target.z += climb_rate_cms * dt;
}
/// shift altitude target (positive means move altitude up)
void AC_PosControl::shift_alt_target(float z_cm)
{
_pos_target.z += z_cm;
// freeze feedforward to avoid jump
if (!is_zero(z_cm)) {
freeze_ff_z();
}
}
/// relax_alt_hold_controllers - set all desired and targets to measured
void AC_PosControl::relax_alt_hold_controllers(float throttle_setting)
{
_pos_target.z = _inav.get_altitude();
_vel_desired.z = 0.0f;
_flags.use_desvel_ff_z = false;
_vel_target.z = _inav.get_velocity_z();
_vel_last.z = _inav.get_velocity_z();
_accel_desired.z = 0.0f;
_accel_last_z_cms = 0.0f;
_accel_target.z = -(_ahrs.get_accel_ef_blended().z + GRAVITY_MSS) * 100.0f;
_flags.reset_accel_to_throttle = true;
_pid_accel_z.set_integrator((throttle_setting-_motors.get_throttle_hover())*1000.0f);
}
// get_alt_error - returns altitude error in cm
float AC_PosControl::get_alt_error() const
{
return (_pos_target.z - _inav.get_altitude());
}
/// set_target_to_stopping_point_z - returns reasonable stopping altitude in cm above home
void AC_PosControl::set_target_to_stopping_point_z()
{
// check if z leash needs to be recalculated
calc_leash_length_z();
get_stopping_point_z(_pos_target);
}
/// get_stopping_point_z - calculates stopping point based on current position, velocity, vehicle acceleration
void AC_PosControl::get_stopping_point_z(Vector3f& stopping_point) const
{
const float curr_pos_z = _inav.get_altitude();
float curr_vel_z = _inav.get_velocity_z();
float linear_distance; // half the distance we swap between linear and sqrt and the distance we offset sqrt
float linear_velocity; // the velocity we swap between linear and sqrt
// if position controller is active add current velocity error to avoid sudden jump in acceleration
if (is_active_z()) {
curr_vel_z += _vel_error.z;
if (_flags.use_desvel_ff_z) {
curr_vel_z -= _vel_desired.z;
}
}
// avoid divide by zero by using current position if kP is very low or acceleration is zero
if (_p_pos_z.kP() <= 0.0f || _accel_z_cms <= 0.0f) {
stopping_point.z = curr_pos_z;
return;
}
// calculate the velocity at which we switch from calculating the stopping point using a linear function to a sqrt function
linear_velocity = _accel_z_cms/_p_pos_z.kP();
if (fabsf(curr_vel_z) < linear_velocity) {
// if our current velocity is below the cross-over point we use a linear function
stopping_point.z = curr_pos_z + curr_vel_z/_p_pos_z.kP();
} else {
linear_distance = _accel_z_cms/(2.0f*_p_pos_z.kP()*_p_pos_z.kP());
if (curr_vel_z > 0){
stopping_point.z = curr_pos_z + (linear_distance + curr_vel_z*curr_vel_z/(2.0f*_accel_z_cms));
} else {
stopping_point.z = curr_pos_z - (linear_distance + curr_vel_z*curr_vel_z/(2.0f*_accel_z_cms));
}
}
stopping_point.z = constrain_float(stopping_point.z, curr_pos_z - POSCONTROL_STOPPING_DIST_DOWN_MAX, curr_pos_z + POSCONTROL_STOPPING_DIST_UP_MAX);
}
/// init_takeoff - initialises target altitude if we are taking off
void AC_PosControl::init_takeoff()
{
const Vector3f& curr_pos = _inav.get_position();
_pos_target.z = curr_pos.z;
// freeze feedforward to avoid jump
freeze_ff_z();
// shift difference between last motor out and hover throttle into accelerometer I
_pid_accel_z.set_integrator((_motors.get_throttle()-_motors.get_throttle_hover())*1000.0f);
// initialise ekf reset handler
init_ekf_z_reset();
}
// is_active_z - returns true if the z-axis position controller has been run very recently
bool AC_PosControl::is_active_z() const
{
return ((AP_HAL::millis() - _last_update_z_ms) <= POSCONTROL_ACTIVE_TIMEOUT_MS);
}
/// update_z_controller - fly to altitude in cm above home
void AC_PosControl::update_z_controller()
{
// check time since last cast
uint32_t now = AP_HAL::millis();
if (now - _last_update_z_ms > POSCONTROL_ACTIVE_TIMEOUT_MS) {
_flags.reset_rate_to_accel_z = true;
_flags.reset_accel_to_throttle = true;
}
_last_update_z_ms = now;
// check for ekf altitude reset
check_for_ekf_z_reset();
// check if leash lengths need to be recalculated
calc_leash_length_z();
// call z-axis position controller
run_z_controller();
}
/// calc_leash_length - calculates the vertical leash lengths from maximum speed, acceleration
/// called by update_z_controller if z-axis speed or accelerations are changed
void AC_PosControl::calc_leash_length_z()
{
if (_flags.recalc_leash_z) {
_leash_up_z = calc_leash_length(_speed_up_cms, _accel_z_cms, _p_pos_z.kP());
_leash_down_z = calc_leash_length(-_speed_down_cms, _accel_z_cms, _p_pos_z.kP());
_flags.recalc_leash_z = false;
}
}
// run position control for Z axis
// target altitude should be set with one of these functions: set_alt_target, set_target_to_stopping_point_z, init_takeoff
// calculates desired rate in earth-frame z axis and passes to rate controller
// vel_up_max, vel_down_max should have already been set before calling this method
void AC_PosControl::run_z_controller()
{
float curr_alt = _inav.get_altitude();
// clear position limit flags
_limit.pos_up = false;
_limit.pos_down = false;
// calculate altitude error
_pos_error.z = _pos_target.z - curr_alt;
// do not let target altitude get too far from current altitude
if (_pos_error.z > _leash_up_z) {
_pos_target.z = curr_alt + _leash_up_z;
_pos_error.z = _leash_up_z;
_limit.pos_up = true;
}
if (_pos_error.z < -_leash_down_z) {
_pos_target.z = curr_alt - _leash_down_z;
_pos_error.z = -_leash_down_z;
_limit.pos_down = true;
}
// calculate _vel_target.z using from _pos_error.z using sqrt controller
_vel_target.z = AC_AttitudeControl::sqrt_controller(_pos_error.z, _p_pos_z.kP(), _accel_z_cms, _dt);
// check speed limits
// To-Do: check these speed limits here or in the pos->rate controller
_limit.vel_up = false;
_limit.vel_down = false;
if (_vel_target.z < _speed_down_cms) {
_vel_target.z = _speed_down_cms;
_limit.vel_down = true;
}
if (_vel_target.z > _speed_up_cms) {
_vel_target.z = _speed_up_cms;
_limit.vel_up = true;
}
// add feed forward component
if (_flags.use_desvel_ff_z) {
_vel_target.z += _vel_desired.z;
}
// the following section calculates acceleration required to achieve the velocity target
const Vector3f& curr_vel = _inav.get_velocity();
// TODO: remove velocity derivative calculation
// reset last velocity target to current target
if (_flags.reset_rate_to_accel_z) {
_vel_last.z = _vel_target.z;
}
// feed forward desired acceleration calculation
if (_dt > 0.0f) {
if (!_flags.freeze_ff_z) {
_accel_desired.z = (_vel_target.z - _vel_last.z)/_dt;
} else {
// stop the feed forward being calculated during a known discontinuity
_flags.freeze_ff_z = false;
}
} else {
_accel_desired.z = 0.0f;
}
// store this iteration's velocities for the next iteration
_vel_last.z = _vel_target.z;
// reset velocity error and filter if this controller has just been engaged
if (_flags.reset_rate_to_accel_z) {
// Reset Filter
_vel_error.z = 0;
_vel_error_filter.reset(0);
_flags.reset_rate_to_accel_z = false;
} else {
// calculate rate error and filter with cut off frequency of 2 Hz
_vel_error.z = _vel_error_filter.apply(_vel_target.z - curr_vel.z, _dt);
}
_accel_target.z = _p_vel_z.get_p(_vel_error.z);
_accel_target.z += _accel_desired.z;
// the following section calculates a desired throttle needed to achieve the acceleration target
float z_accel_meas; // actual acceleration
float p,i,d; // used to capture pid values for logging
// Calculate Earth Frame Z acceleration
z_accel_meas = -(_ahrs.get_accel_ef_blended().z + GRAVITY_MSS) * 100.0f;
// reset target altitude if this controller has just been engaged
if (_flags.reset_accel_to_throttle) {
// Reset Filter
_accel_error.z = 0;
_flags.reset_accel_to_throttle = false;
} else {
// calculate accel error
_accel_error.z = _accel_target.z - z_accel_meas;
}
// set input to PID
_pid_accel_z.set_input_filter_all(_accel_error.z);
_pid_accel_z.set_desired_rate(_accel_target.z);
// separately calculate p, i, d values for logging
p = _pid_accel_z.get_p();
// get i term
i = _pid_accel_z.get_integrator();
// ensure imax is always large enough to overpower hover throttle
if (_motors.get_throttle_hover() * 1000.0f > _pid_accel_z.imax()) {
_pid_accel_z.imax(_motors.get_throttle_hover() * 1000.0f);
}
// update i term as long as we haven't breached the limits or the I term will certainly reduce
// To-Do: should this be replaced with limits check from attitude_controller?
if ((!_motors.limit.throttle_lower && !_motors.limit.throttle_upper) || (i>0&&_accel_error.z<0) || (i<0&&_accel_error.z>0)) {
i = _pid_accel_z.get_i();
}
// get d term
d = _pid_accel_z.get_d();
float thr_out = (p+i+d)*0.001f +_motors.get_throttle_hover();
// send throttle to attitude controller with angle boost
_attitude_control.set_throttle_out(thr_out, true, POSCONTROL_THROTTLE_CUTOFF_FREQ);
}
///
/// lateral position controller
///
/// set_max_accel_xy - set the maximum horizontal acceleration in cm/s/s
void AC_PosControl::set_max_accel_xy(float accel_cmss)
{
if (fabsf(_accel_cms-accel_cmss) > 1.0f) {
_accel_cms = accel_cmss;
_flags.recalc_leash_xy = true;
calc_leash_length_xy();
}
}
/// set_max_speed_xy - set the maximum horizontal speed maximum in cm/s
void AC_PosControl::set_max_speed_xy(float speed_cms)
{
if (fabsf(_speed_cms-speed_cms) > 1.0f) {
_speed_cms = speed_cms;
_flags.recalc_leash_xy = true;
calc_leash_length_xy();
}
}
/// set_pos_target in cm from home
void AC_PosControl::set_pos_target(const Vector3f& position)
{
_pos_target = position;
_flags.use_desvel_ff_z = false;
_vel_desired.z = 0.0f;
// initialise roll and pitch to current roll and pitch. This avoids a twitch between when the target is set and the pos controller is first run
// To-Do: this initialisation of roll and pitch targets needs to go somewhere between when pos-control is initialised and when it completes it's first cycle
//_roll_target = constrain_int32(_ahrs.roll_sensor,-_attitude_control.lean_angle_max(),_attitude_control.lean_angle_max());
//_pitch_target = constrain_int32(_ahrs.pitch_sensor,-_attitude_control.lean_angle_max(),_attitude_control.lean_angle_max());
}
/// set_xy_target in cm from home
void AC_PosControl::set_xy_target(float x, float y)
{
_pos_target.x = x;
_pos_target.y = y;
}
/// shift position target target in x, y axis
void AC_PosControl::shift_pos_xy_target(float x_cm, float y_cm)
{
// move pos controller target
_pos_target.x += x_cm;
_pos_target.y += y_cm;
}
/// set_target_to_stopping_point_xy - sets horizontal target to reasonable stopping position in cm from home
void AC_PosControl::set_target_to_stopping_point_xy()
{
// check if xy leash needs to be recalculated
calc_leash_length_xy();
get_stopping_point_xy(_pos_target);
}
/// get_stopping_point_xy - calculates stopping point based on current position, velocity, vehicle acceleration
/// distance_max allows limiting distance to stopping point
/// results placed in stopping_position vector
/// set_max_accel_xy() should be called before this method to set vehicle acceleration
/// set_leash_length() should have been called before this method
void AC_PosControl::get_stopping_point_xy(Vector3f &stopping_point) const
{
const Vector3f curr_pos = _inav.get_position();
Vector3f curr_vel = _inav.get_velocity();
float linear_distance; // the distance at which we swap from a linear to sqrt response
float linear_velocity; // the velocity above which we swap from a linear to sqrt response
float stopping_dist; // the distance within the vehicle can stop
float kP = _p_pos_xy.kP();
// add velocity error to current velocity
if (is_active_xy()) {
curr_vel.x += _vel_error.x;
curr_vel.y += _vel_error.y;
}
// calculate current velocity
float vel_total = norm(curr_vel.x, curr_vel.y);
// avoid divide by zero by using current position if the velocity is below 10cm/s, kP is very low or acceleration is zero
if (kP <= 0.0f || _accel_cms <= 0.0f || is_zero(vel_total)) {
stopping_point.x = curr_pos.x;
stopping_point.y = curr_pos.y;
return;
}
// calculate point at which velocity switches from linear to sqrt
linear_velocity = _accel_cms/kP;
// calculate distance within which we can stop
if (vel_total < linear_velocity) {
stopping_dist = vel_total/kP;
} else {
linear_distance = _accel_cms/(2.0f*kP*kP);
stopping_dist = linear_distance + (vel_total*vel_total)/(2.0f*_accel_cms);
}
// constrain stopping distance
stopping_dist = constrain_float(stopping_dist, 0, _leash);
// convert the stopping distance into a stopping point using velocity vector
stopping_point.x = curr_pos.x + (stopping_dist * curr_vel.x / vel_total);
stopping_point.y = curr_pos.y + (stopping_dist * curr_vel.y / vel_total);
}
/// get_distance_to_target - get horizontal distance to target position in cm
float AC_PosControl::get_distance_to_target() const
{
return norm(_pos_error.x, _pos_error.y);
}
/// get_bearing_to_target - get bearing to target position in centi-degrees
int32_t AC_PosControl::get_bearing_to_target() const
{
return get_bearing_cd(_inav.get_position(), _pos_target);
}
// is_active_xy - returns true if the xy position controller has been run very recently
bool AC_PosControl::is_active_xy() const
{
return ((AP_HAL::millis() - _last_update_xy_ms) <= POSCONTROL_ACTIVE_TIMEOUT_MS);
}
/// get_lean_angle_max_cd - returns the maximum lean angle the autopilot may request
float AC_PosControl::get_lean_angle_max_cd() const
{
if (is_zero(_lean_angle_max)) {
return _attitude_control.lean_angle_max();
}
return _lean_angle_max * 100.0f;
}
/// init_xy_controller - initialise the xy controller
/// this should be called after setting the position target and the desired velocity and acceleration
/// sets target roll angle, pitch angle and I terms based on vehicle current lean angles
/// should be called once whenever significant changes to the position target are made
/// this does not update the xy target
void AC_PosControl::init_xy_controller()
{
// set roll, pitch lean angle targets to current attitude
// todo: this should probably be based on the desired attitude not the current attitude
_roll_target = _ahrs.roll_sensor;
_pitch_target = _ahrs.pitch_sensor;
// initialise I terms from lean angles
_pid_vel_xy.reset_filter();
lean_angles_to_accel(_accel_target.x, _accel_target.y);
_pid_vel_xy.set_integrator(_accel_target-_accel_desired);
// flag reset required in rate to accel step
_flags.reset_desired_vel_to_pos = true;
_flags.reset_accel_to_lean_xy = true;
// initialise ekf xy reset handler
init_ekf_xy_reset();
}
/// update_xy_controller - run the horizontal position controller - should be called at 100hz or higher
void AC_PosControl::update_xy_controller()
{
// compute dt
uint32_t now = AP_HAL::millis();
float dt = (now - _last_update_xy_ms)*0.001f;
// sanity check dt
if (dt >= POSCONTROL_ACTIVE_TIMEOUT_MS*1.0e-3f) {
dt = 0.0f;
}
// check for ekf xy position reset
check_for_ekf_xy_reset();
// check if xy leash needs to be recalculated
calc_leash_length_xy();
// translate any adjustments from pilot to loiter target
desired_vel_to_pos(dt);
// run horizontal position controller
run_xy_controller(dt);
// update xy update time
_last_update_xy_ms = now;
}
float AC_PosControl::time_since_last_xy_update() const
{
uint32_t now = AP_HAL::millis();
return (now - _last_update_xy_ms)*0.001f;
}
// write log to dataflash
void AC_PosControl::write_log()
{
const Vector3f &pos_target = get_pos_target();
const Vector3f &vel_target = get_vel_target();
const Vector3f &accel_target = get_accel_target();
const Vector3f &position = _inav.get_position();
const Vector3f &velocity = _inav.get_velocity();
float accel_x, accel_y;
lean_angles_to_accel(accel_x, accel_y);
AP::logger().Write("PSC", "TimeUS,TPX,TPY,PX,PY,TVX,TVY,VX,VY,TAX,TAY,AX,AY",
"smmmmnnnnoooo", "FBBBBBBBBBBBB", "Qffffffffffff",
AP_HAL::micros64(),
(double)pos_target.x,
(double)pos_target.y,
(double)position.x,
(double)position.y,
(double)vel_target.x,
(double)vel_target.y,
(double)velocity.x,
(double)velocity.y,
(double)accel_target.x,
(double)accel_target.y,
(double)accel_x,
(double)accel_y);
}
/// init_vel_controller_xyz - initialise the velocity controller - should be called once before the caller attempts to use the controller
void AC_PosControl::init_vel_controller_xyz()
{
// set roll, pitch lean angle targets to current attitude
_roll_target = _ahrs.roll_sensor;
_pitch_target = _ahrs.pitch_sensor;
_pid_vel_xy.reset_filter();
lean_angles_to_accel(_accel_target.x, _accel_target.y);
_pid_vel_xy.set_integrator(_accel_target);
// flag reset required in rate to accel step
_flags.reset_desired_vel_to_pos = true;
_flags.reset_accel_to_lean_xy = true;
// set target position
const Vector3f& curr_pos = _inav.get_position();
set_xy_target(curr_pos.x, curr_pos.y);
set_alt_target(curr_pos.z);
// move current vehicle velocity into feed forward velocity
const Vector3f& curr_vel = _inav.get_velocity();
set_desired_velocity(curr_vel);
// set vehicle acceleration to zero
set_desired_accel_xy(0.0f,0.0f);
// initialise ekf reset handlers
init_ekf_xy_reset();
init_ekf_z_reset();
}
/// update_velocity_controller_xy - run the velocity controller - should be called at 100hz or higher
/// velocity targets should we set using set_desired_velocity_xy() method
/// callers should use get_roll() and get_pitch() methods and sent to the attitude controller
/// throttle targets will be sent directly to the motors
void AC_PosControl::update_vel_controller_xy()
{
// capture time since last iteration
uint32_t now = AP_HAL::millis();
float dt = (now - _last_update_xy_ms)*0.001f;
// sanity check dt
if (dt >= 0.2f) {
dt = 0.0f;
}
// check for ekf xy position reset
check_for_ekf_xy_reset();
// check if xy leash needs to be recalculated
calc_leash_length_xy();
// apply desired velocity request to position target
// TODO: this will need to be removed and added to the calling function.
desired_vel_to_pos(dt);
// run position controller
run_xy_controller(dt);
// update xy update time
_last_update_xy_ms = now;
}
/// update_velocity_controller_xyz - run the velocity controller - should be called at 100hz or higher
/// velocity targets should we set using set_desired_velocity_xyz() method
/// callers should use get_roll() and get_pitch() methods and sent to the attitude controller
/// throttle targets will be sent directly to the motors
void AC_PosControl::update_vel_controller_xyz()
{
update_vel_controller_xy();
// update altitude target
set_alt_target_from_climb_rate_ff(_vel_desired.z, _dt, false);
// run z-axis position controller
update_z_controller();
}
float AC_PosControl::get_horizontal_error() const
{
return norm(_pos_error.x, _pos_error.y);
}
///
/// private methods
///
/// calc_leash_length - calculates the horizontal leash length given a maximum speed, acceleration
/// should be called whenever the speed, acceleration or position kP is modified
void AC_PosControl::calc_leash_length_xy()
{
// todo: remove _flags.recalc_leash_xy or don't call this function after each variable change.
if (_flags.recalc_leash_xy) {
_leash = calc_leash_length(_speed_cms, _accel_cms, _p_pos_xy.kP());
_flags.recalc_leash_xy = false;
}
}
/// move velocity target using desired acceleration
void AC_PosControl::desired_accel_to_vel(float nav_dt)
{
// range check nav_dt
if (nav_dt < 0) {
return;
}
// update target velocity
if (_flags.reset_desired_vel_to_pos) {
_flags.reset_desired_vel_to_pos = false;
} else {
_vel_desired.x += _accel_desired.x * nav_dt;
_vel_desired.y += _accel_desired.y * nav_dt;
}
}
/// desired_vel_to_pos - move position target using desired velocities
void AC_PosControl::desired_vel_to_pos(float nav_dt)
{
// range check nav_dt
if( nav_dt < 0 ) {
return;
}
// update target position
if (_flags.reset_desired_vel_to_pos) {
_flags.reset_desired_vel_to_pos = false;
} else {
_pos_target.x += _vel_desired.x * nav_dt;
_pos_target.y += _vel_desired.y * nav_dt;
}
}
/// run horizontal position controller correcting position and velocity
/// converts position (_pos_target) to target velocity (_vel_target)
/// desired velocity (_vel_desired) is combined into final target velocity
/// converts desired velocities in lat/lon directions to accelerations in lat/lon frame
/// converts desired accelerations provided in lat/lon frame to roll/pitch angles
void AC_PosControl::run_xy_controller(float dt)
{
float ekfGndSpdLimit, ekfNavVelGainScaler;
AP::ahrs_navekf().getEkfControlLimits(ekfGndSpdLimit, ekfNavVelGainScaler);
Vector3f curr_pos = _inav.get_position();
float kP = ekfNavVelGainScaler * _p_pos_xy.kP(); // scale gains to compensate for noisy optical flow measurement in the EKF
// avoid divide by zero
if (kP <= 0.0f) {
_vel_target.x = 0.0f;
_vel_target.y = 0.0f;
}else{
// calculate distance error
_pos_error.x = _pos_target.x - curr_pos.x;
_pos_error.y = _pos_target.y - curr_pos.y;
// Constrain _pos_error and target position
// Constrain the maximum length of _vel_target to the maximum position correction velocity
// TODO: replace the leash length with a user definable maximum position correction
if (limit_vector_length(_pos_error.x, _pos_error.y, _leash))
{
_pos_target.x = curr_pos.x + _pos_error.x;
_pos_target.y = curr_pos.y + _pos_error.y;
}
_vel_target = sqrt_controller(_pos_error, kP, _accel_cms);
}
// add velocity feed-forward
_vel_target.x += _vel_desired.x;
_vel_target.y += _vel_desired.y;
// the following section converts desired velocities in lat/lon directions to accelerations in lat/lon frame
Vector2f accel_target, vel_xy_p, vel_xy_i, vel_xy_d;
// check if vehicle velocity is being overridden
if (_flags.vehicle_horiz_vel_override) {
_flags.vehicle_horiz_vel_override = false;
} else {
_vehicle_horiz_vel.x = _inav.get_velocity().x;
_vehicle_horiz_vel.y = _inav.get_velocity().y;
}
// calculate velocity error
_vel_error.x = _vel_target.x - _vehicle_horiz_vel.x;
_vel_error.y = _vel_target.y - _vehicle_horiz_vel.y;
// TODO: constrain velocity error and velocity target
// call pi controller
_pid_vel_xy.set_input(_vel_error);
// get p
vel_xy_p = _pid_vel_xy.get_p();
// update i term if we have not hit the accel or throttle limits OR the i term will reduce
// TODO: move limit handling into the PI and PID controller
if (!_limit.accel_xy && !_motors.limit.throttle_upper) {
vel_xy_i = _pid_vel_xy.get_i();
} else {
vel_xy_i = _pid_vel_xy.get_i_shrink();
}
// get d
vel_xy_d = _pid_vel_xy.get_d();
// acceleration to correct for velocity error and scale PID output to compensate for optical flow measurement induced EKF noise
accel_target.x = (vel_xy_p.x + vel_xy_i.x + vel_xy_d.x) * ekfNavVelGainScaler;
accel_target.y = (vel_xy_p.y + vel_xy_i.y + vel_xy_d.y) * ekfNavVelGainScaler;
// reset accel to current desired acceleration
if (_flags.reset_accel_to_lean_xy) {
_accel_target_filter.reset(Vector2f(accel_target.x, accel_target.y));
_flags.reset_accel_to_lean_xy = false;
}
// filter correction acceleration
_accel_target_filter.set_cutoff_frequency(MIN(_accel_xy_filt_hz, 5.0f*ekfNavVelGainScaler));
_accel_target_filter.apply(accel_target, dt);
// pass the correction acceleration to the target acceleration output
_accel_target.x = _accel_target_filter.get().x;
_accel_target.y = _accel_target_filter.get().y;
// Add feed forward into the target acceleration output
_accel_target.x += _accel_desired.x;
_accel_target.y += _accel_desired.y;
// the following section converts desired accelerations provided in lat/lon frame to roll/pitch angles
// limit acceleration using maximum lean angles
float angle_max = MIN(_attitude_control.get_althold_lean_angle_max(), get_lean_angle_max_cd());
float accel_max = MIN(GRAVITY_MSS * 100.0f * tanf(ToRad(angle_max * 0.01f)), POSCONTROL_ACCEL_XY_MAX);
_limit.accel_xy = limit_vector_length(_accel_target.x, _accel_target.y, accel_max);
// update angle targets that will be passed to stabilize controller
accel_to_lean_angles(_accel_target.x, _accel_target.y, _roll_target, _pitch_target);
}
// get_lean_angles_to_accel - convert roll, pitch lean angles to lat/lon frame accelerations in cm/s/s
void AC_PosControl::accel_to_lean_angles(float accel_x_cmss, float accel_y_cmss, float& roll_target, float& pitch_target) const
{
float accel_right, accel_forward;
// rotate accelerations into body forward-right frame
// todo: this should probably be based on the desired heading not the current heading
accel_forward = accel_x_cmss*_ahrs.cos_yaw() + accel_y_cmss*_ahrs.sin_yaw();
accel_right = -accel_x_cmss*_ahrs.sin_yaw() + accel_y_cmss*_ahrs.cos_yaw();
// update angle targets that will be passed to stabilize controller
pitch_target = atanf(-accel_forward/(GRAVITY_MSS * 100.0f))*(18000.0f/M_PI);
float cos_pitch_target = cosf(pitch_target*M_PI/18000.0f);
roll_target = atanf(accel_right*cos_pitch_target/(GRAVITY_MSS * 100.0f))*(18000.0f/M_PI);
}
// get_lean_angles_to_accel - convert roll, pitch lean angles to lat/lon frame accelerations in cm/s/s
void AC_PosControl::lean_angles_to_accel(float& accel_x_cmss, float& accel_y_cmss) const
{
// rotate our roll, pitch angles into lat/lon frame
// todo: this should probably be based on the desired attitude not the current attitude
accel_x_cmss = (GRAVITY_MSS * 100) * (-_ahrs.cos_yaw() * _ahrs.sin_pitch() * _ahrs.cos_roll() - _ahrs.sin_yaw() * _ahrs.sin_roll()) / MAX(_ahrs.cos_roll()*_ahrs.cos_pitch(), 0.5f);
accel_y_cmss = (GRAVITY_MSS * 100) * (-_ahrs.sin_yaw() * _ahrs.sin_pitch() * _ahrs.cos_roll() + _ahrs.cos_yaw() * _ahrs.sin_roll()) / MAX(_ahrs.cos_roll()*_ahrs.cos_pitch(), 0.5f);
}
/// calc_leash_length - calculates the horizontal leash length given a maximum speed, acceleration and position kP gain
float AC_PosControl::calc_leash_length(float speed_cms, float accel_cms, float kP) const
{
float leash_length;
// sanity check acceleration and avoid divide by zero
if (accel_cms <= 0.0f) {
accel_cms = POSCONTROL_ACCELERATION_MIN;
}
// avoid divide by zero
if (kP <= 0.0f) {
return POSCONTROL_LEASH_LENGTH_MIN;
}
// calculate leash length
if(speed_cms <= accel_cms / kP) {
// linear leash length based on speed close in
leash_length = speed_cms / kP;
}else{
// leash length grows at sqrt of speed further out
leash_length = (accel_cms / (2.0f*kP*kP)) + (speed_cms*speed_cms / (2.0f*accel_cms));
}
// ensure leash is at least 1m long
if( leash_length < POSCONTROL_LEASH_LENGTH_MIN ) {
leash_length = POSCONTROL_LEASH_LENGTH_MIN;
}
return leash_length;
}
/// initialise ekf xy position reset check
void AC_PosControl::init_ekf_xy_reset()
{
Vector2f pos_shift;
_ekf_xy_reset_ms = _ahrs.getLastPosNorthEastReset(pos_shift);
}
/// check for ekf position reset and adjust loiter or brake target position
void AC_PosControl::check_for_ekf_xy_reset()
{
// check for position shift
Vector2f pos_shift;
uint32_t reset_ms = _ahrs.getLastPosNorthEastReset(pos_shift);
if (reset_ms != _ekf_xy_reset_ms) {
shift_pos_xy_target(pos_shift.x * 100.0f, pos_shift.y * 100.0f);
_ekf_xy_reset_ms = reset_ms;
}
}
/// initialise ekf z axis reset check
void AC_PosControl::init_ekf_z_reset()
{
float alt_shift;
_ekf_z_reset_ms = _ahrs.getLastPosDownReset(alt_shift);
}
/// check for ekf position reset and adjust loiter or brake target position
void AC_PosControl::check_for_ekf_z_reset()
{
// check for position shift
float alt_shift;
uint32_t reset_ms = _ahrs.getLastPosDownReset(alt_shift);
if (reset_ms != 0 && reset_ms != _ekf_z_reset_ms) {
shift_alt_target(-alt_shift * 100.0f);
_ekf_z_reset_ms = reset_ms;
}
}
/// limit vector to a given length, returns true if vector was limited
bool AC_PosControl::limit_vector_length(float& vector_x, float& vector_y, float max_length)
{
float vector_length = norm(vector_x, vector_y);
if ((vector_length > max_length) && is_positive(vector_length)) {
vector_x *= (max_length / vector_length);
vector_y *= (max_length / vector_length);
return true;
}
return false;
}
/// Proportional controller with piecewise sqrt sections to constrain second derivative
Vector3f AC_PosControl::sqrt_controller(const Vector3f& error, float p, float second_ord_lim)
{
if (second_ord_lim < 0.0f || is_zero(second_ord_lim) || is_zero(p)) {
return Vector3f(error.x*p, error.y*p, error.z);
}
float linear_dist = second_ord_lim/sq(p);
float error_length = norm(error.x, error.y);
if (error_length > linear_dist) {
float first_order_scale = safe_sqrt(2.0f*second_ord_lim*(error_length-(linear_dist * 0.5f)))/error_length;
return Vector3f(error.x*first_order_scale, error.y*first_order_scale, error.z);
} else {
return Vector3f(error.x*p, error.y*p, error.z);
}
}
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