mirror of https://github.com/ArduPilot/ardupilot
469 lines
28 KiB
C++
469 lines
28 KiB
C++
#pragma once
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#include <AP_Common/AP_Common.h>
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#include <AP_Param/AP_Param.h>
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#include <AP_Math/AP_Math.h>
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#include <AC_PID/AC_P.h> // P library
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#include <AC_PID/AC_PID.h> // PID library
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#include <AC_PID/AC_P_1D.h> // P library (1-axis)
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#include <AC_PID/AC_P_2D.h> // P library (2-axis)
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#include <AC_PID/AC_PI_2D.h> // PI library (2-axis)
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#include <AC_PID/AC_PID_Basic.h> // PID library (1-axis)
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#include <AC_PID/AC_PID_2D.h> // PID library (2-axis)
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#include <AP_InertialNav/AP_InertialNav.h> // Inertial Navigation library
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#include "AC_AttitudeControl.h" // Attitude control library
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#include <AP_Motors/AP_Motors.h> // motors library
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#include <AP_Vehicle/AP_Vehicle.h> // common vehicle parameters
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// position controller default definitions
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#define POSCONTROL_ACCEL_XY 100.0f // default horizontal acceleration in cm/s/s. This is overwritten by waypoint and loiter controllers
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#define POSCONTROL_JERK_XY 5.0f // default horizontal jerk m/s/s/s
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#define POSCONTROL_STOPPING_DIST_UP_MAX 300.0f // max stopping distance (in cm) vertically while climbing
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#define POSCONTROL_STOPPING_DIST_DOWN_MAX 200.0f // max stopping distance (in cm) vertically while descending
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#define POSCONTROL_SPEED 500.0f // default horizontal speed in cm/s
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#define POSCONTROL_SPEED_DOWN -150.0f // default descent rate in cm/s
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#define POSCONTROL_SPEED_UP 250.0f // default climb rate in cm/s
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#define POSCONTROL_ACCEL_Z 250.0f // default vertical acceleration in cm/s/s.
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#define POSCONTROL_JERK_Z 5.0f // default vertical jerk m/s/s/s
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#define POSCONTROL_THROTTLE_CUTOFF_FREQ_HZ 2.0f // low-pass filter on acceleration error (unit: Hz)
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#define POSCONTROL_OVERSPEED_GAIN_Z 2.0f // gain controlling rate at which z-axis speed is brought back within SPEED_UP and SPEED_DOWN range
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#define POSCONTROL_RELAX_TC 0.16f // This is used to decay the I term to 5% in half a second.
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class AC_PosControl
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{
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public:
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/// Constructor
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AC_PosControl(AP_AHRS_View& ahrs, const AP_InertialNav& inav,
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const AP_Motors& motors, AC_AttitudeControl& attitude_control, float dt);
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/// get_dt - gets time delta in seconds for all position controllers
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float get_dt() const { return _dt; }
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/// get_shaping_jerk_xy_cmsss - gets the jerk limit of the xy kinematic path generation in cm/s/s/s
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float get_shaping_jerk_xy_cmsss() const { return _shaping_jerk_xy*100.0; }
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///
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/// 3D position shaper
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///
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/// input_pos_xyz - calculate a jerk limited path from the current position, velocity and acceleration to an input position.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_xy.
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void input_pos_xyz(const Vector3p& pos, float pos_offset_z, float pos_offset_z_buffer);
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/// pos_offset_z_scaler - calculates a multiplier used to reduce the horizontal velocity to allow the z position controller to stay within the provided buffer range
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float pos_offset_z_scaler(float pos_offset_z, float pos_offset_z_buffer) const;
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///
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/// Lateral position controller
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///
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/// set_max_speed_accel_xy - set the maximum horizontal speed in cm/s and acceleration in cm/s/s
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/// This function only needs to be called if using the kinematic shaping.
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/// This can be done at any time as changes in these parameters are handled smoothly
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/// by the kinematic shaping.
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void set_max_speed_accel_xy(float speed_cms, float accel_cmss);
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/// set_max_speed_accel_xy - set the position controller correction velocity and acceleration limit
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/// This should be done only during initialisation to avoid discontinuities
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void set_correction_speed_accel_xy(float speed_cms, float accel_cmss);
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/// get_max_speed_xy_cms - get the maximum horizontal speed in cm/s
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float get_max_speed_xy_cms() const { return _vel_max_xy_cms; }
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/// get_max_accel_xy_cmss - get the maximum horizontal acceleration in cm/s/s
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float get_max_accel_xy_cmss() const { return _accel_max_xy_cmss; }
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// set the maximum horizontal position error that will be allowed in the horizontal plane
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void set_pos_error_max_xy_cm(float error_max) { _p_pos_xy.set_error_max(error_max); }
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float get_pos_error_max_xy_cm() { return _p_pos_xy.get_error_max(); }
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/// init_xy_controller_stopping_point - initialise the position controller to the stopping point with zero velocity and acceleration.
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/// This function should be used when the expected kinematic path assumes a stationary initial condition but does not specify a specific starting position.
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/// The starting position can be retrieved by getting the position target using get_pos_target_cm() after calling this function.
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void init_xy_controller_stopping_point();
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// relax_velocity_controller_xy - initialise the position controller to the current position and velocity with decaying acceleration.
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/// This function decays the output acceleration by 95% every half second to achieve a smooth transition to zero requested acceleration.
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void relax_velocity_controller_xy();
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// init_xy_controller - initialise the position controller to the current position, velocity, acceleration and attitude.
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/// This function is the default initialisation for any position control that provides position, velocity and acceleration.
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/// This function is private and contains all the shared xy axis initialisation functions
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void init_xy_controller();
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/// input_accel_xy - calculate a jerk limited path from the current position, velocity and acceleration to an input acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_xy.
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/// The jerk limit defines the acceleration error decay in the kinematic path as the system approaches constant acceleration.
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/// The jerk limit also defines the time taken to achieve the maximum acceleration.
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void input_accel_xy(const Vector3f& accel);
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/// input_vel_accel_xy - calculate a jerk limited path from the current position, velocity and acceleration to an input velocity and acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_xy.
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/// The function alters the vel to be the kinematic path based on accel
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/// The parameter limit_output specifies if the velocity and acceleration limits are applied to the sum of commanded and correction values or just correction.
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void input_vel_accel_xy(Vector2f& vel, const Vector2f& accel, bool limit_output = true);
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/// input_pos_vel_accel_xy - calculate a jerk limited path from the current position, velocity and acceleration to an input position velocity and acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_xy.
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/// The function alters the pos and vel to be the kinematic path based on accel
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/// The parameter limit_output specifies if the velocity and acceleration limits are applied to the sum of commanded and correction values or just correction.
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void input_pos_vel_accel_xy(Vector2p& pos, Vector2f& vel, const Vector2f& accel, bool limit_output = true);
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// is_active_xy - returns true if the xy position controller has been run in the previous 5 loop times
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bool is_active_xy() const;
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/// stop_pos_xy_stabilisation - sets the target to the current position to remove any position corrections from the system
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void stop_pos_xy_stabilisation();
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/// stop_vel_xy_stabilisation - sets the target to the current position and velocity to the current velocity to remove any position and velocity corrections from the system
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void stop_vel_xy_stabilisation();
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/// update_xy_controller - runs the horizontal position controller correcting position, velocity and acceleration errors.
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/// Position and velocity errors are converted to velocity and acceleration targets using PID objects
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/// Desired velocity and accelerations are added to these corrections as they are calculated
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/// Kinematically consistent target position and desired velocity and accelerations should be provided before calling this function
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void update_xy_controller();
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///
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/// Vertical position controller
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///
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/// set_max_speed_accel_z - set the maximum vertical speed in cm/s and acceleration in cm/s/s
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/// speed_down can be positive or negative but will always be interpreted as a descent speed
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/// This can be done at any time as changes in these parameters are handled smoothly
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/// by the kinematic shaping.
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void set_max_speed_accel_z(float speed_down, float speed_up, float accel_cmss);
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/// set_correction_speed_accel_z - set the position controller correction velocity and acceleration limit
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/// speed_down can be positive or negative but will always be interpreted as a descent speed
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/// This should be done only during initialisation to avoid discontinuities
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void set_correction_speed_accel_z(float speed_down, float speed_up, float accel_cmss);
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/// get_max_accel_z_cmss - get the maximum vertical acceleration in cm/s/s
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float get_max_accel_z_cmss() const { return _accel_max_z_cmss; }
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// get_pos_error_z_up_cm - get the maximum vertical position error up that will be allowed
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float get_pos_error_z_up_cm() { return _p_pos_z.get_error_max(); }
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// get_pos_error_z_down_cm - get the maximum vertical position error down that will be allowed
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float get_pos_error_z_down_cm() { return _p_pos_z.get_error_min(); }
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/// get_max_speed_up_cms - accessors for current maximum up speed in cm/s
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float get_max_speed_up_cms() const { return _vel_max_up_cms; }
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/// get_max_speed_down_cms - accessors for current maximum down speed in cm/s. Will be a negative number
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float get_max_speed_down_cms() const { return _vel_max_down_cms; }
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/// init_z_controller_no_descent - initialise the position controller to the current position, velocity, acceleration and attitude.
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/// This function is the default initialisation for any position control that provides position, velocity and acceleration.
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/// This function does not allow any negative velocity or acceleration
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void init_z_controller_no_descent();
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/// init_z_controller_stopping_point - initialise the position controller to the stopping point with zero velocity and acceleration.
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/// This function should be used when the expected kinematic path assumes a stationary initial condition but does not specify a specific starting position.
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/// The starting position can be retrieved by getting the position target using get_pos_target_cm() after calling this function.
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void init_z_controller_stopping_point();
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// relax_z_controller - initialise the position controller to the current position and velocity with decaying acceleration.
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/// This function decays the output acceleration by 95% every half second to achieve a smooth transition to zero requested acceleration.
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void relax_z_controller(float throttle_setting);
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// init_z_controller - initialise the position controller to the current position, velocity, acceleration and attitude.
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/// This function is the default initialisation for any position control that provides position, velocity and acceleration.
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/// This function is private and contains all the shared z axis initialisation functions
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void init_z_controller();
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/// input_accel_z - calculate a jerk limited path from the current position, velocity and acceleration to an input acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_z.
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virtual void input_accel_z(float accel);
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/// input_vel_accel_z - calculate a jerk limited path from the current position, velocity and acceleration to an input velocity and acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The kinematic path is constrained by the maximum acceleration and jerk set using the function set_max_speed_accel_z.
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/// The function alters the vel to be the kinematic path based on accel
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/// The parameter limit_output specifies if the velocity and acceleration limits are applied to the sum of commanded and correction values or just correction.
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virtual void input_vel_accel_z(float &vel, float accel, bool ignore_descent_limit, bool limit_output = true);
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/// set_pos_target_z_from_climb_rate_cm - adjusts target up or down using a commanded climb rate in cm/s
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/// using the default position control kinematic path.
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/// The zero target altitude is varied to follow pos_offset_z
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void set_pos_target_z_from_climb_rate_cm(float vel);
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/// land_at_climb_rate_cm - adjusts target up or down using a commanded climb rate in cm/s
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/// using the default position control kinematic path.
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/// ignore_descent_limit turns off output saturation handling to aid in landing detection. ignore_descent_limit should be true unless landing.
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void land_at_climb_rate_cm(float vel, bool ignore_descent_limit);
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/// input_pos_vel_accel_z - calculate a jerk limited path from the current position, velocity and acceleration to an input position velocity and acceleration.
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/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
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/// The function alters the pos and vel to be the kinematic path based on accel
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/// The parameter limit_output specifies if the velocity and acceleration limits are applied to the sum of commanded and correction values or just correction.
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void input_pos_vel_accel_z(float &pos, float &vel, float accel, bool limit_output = true);
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/// set_alt_target_with_slew - adjusts target up or down using a commanded altitude in cm
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/// using the default position control kinematic path.
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void set_alt_target_with_slew(float pos);
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/// update_pos_offset_z - updates the vertical offsets used by terrain following
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void update_pos_offset_z(float pos_offset);
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// is_active_z - returns true if the z position controller has been run in the previous 5 loop times
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bool is_active_z() const;
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/// update_z_controller - runs the vertical position controller correcting position, velocity and acceleration errors.
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/// Position and velocity errors are converted to velocity and acceleration targets using PID objects
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/// Desired velocity and accelerations are added to these corrections as they are calculated
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/// Kinematically consistent target position and desired velocity and accelerations should be provided before calling this function
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void update_z_controller();
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///
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/// Accessors
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///
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/// set commanded position (cm), velocity (cm/s) and acceleration (cm/s/s) inputs when the path is created externally.
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void set_pos_vel_accel(const Vector3p& pos, const Vector3f& vel, const Vector3f& accel);
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void set_pos_vel_accel_xy(const Vector2p& pos, const Vector2f& vel, const Vector2f& accel);
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/// Position
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/// set_pos_target_xy_cm - sets the position target, frame NEU in cm relative to the EKF origin
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void set_pos_target_xy_cm(float pos_x, float pos_y) { _pos_target.x = pos_x; _pos_target.y = pos_y; }
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/// get_pos_target_cm - returns the position target, frame NEU in cm relative to the EKF origin
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const Vector3p& get_pos_target_cm() const { return _pos_target; }
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/// set_pos_target_z_cm - set altitude target in cm above the EKF origin
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void set_pos_target_z_cm(float pos_target) { _pos_target.z = pos_target; }
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/// get_pos_target_z_cm - get target altitude (in cm above the EKF origin)
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float get_pos_target_z_cm() const { return _pos_target.z; }
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/// get_stopping_point_xy_cm - calculates stopping point in NEU cm based on current position, velocity, vehicle acceleration
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void get_stopping_point_xy_cm(Vector2p &stopping_point) const;
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/// get_stopping_point_z_cm - calculates stopping point in NEU cm based on current position, velocity, vehicle acceleration
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void get_stopping_point_z_cm(postype_t &stopping_point) const;
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/// get_pos_error_cm - get position error vector between the current and target position
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const Vector3f get_pos_error_cm() const { return (_pos_target - _inav.get_position_neu_cm().topostype()).tofloat(); }
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/// get_pos_error_xy_cm - get the length of the position error vector in the xy plane
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float get_pos_error_xy_cm() const { return get_horizontal_distance_cm(_inav.get_position_xy_cm().topostype(), _pos_target.xy()); }
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/// get_pos_error_z_cm - returns altitude error in cm
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float get_pos_error_z_cm() const { return (_pos_target.z - _inav.get_position_z_up_cm()); }
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/// Velocity
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/// set_vel_desired_cms - sets desired velocity in NEU cm/s
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void set_vel_desired_cms(const Vector3f &des_vel) { _vel_desired = des_vel; }
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/// set_vel_desired_xy_cms - sets horizontal desired velocity in NEU cm/s
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void set_vel_desired_xy_cms(const Vector2f &vel) {_vel_desired.xy() = vel; }
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/// get_vel_desired_cms - returns desired velocity (i.e. feed forward) in cm/s in NEU
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const Vector3f& get_vel_desired_cms() { return _vel_desired; }
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// get_vel_target_cms - returns the target velocity in NEU cm/s
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const Vector3f& get_vel_target_cms() const { return _vel_target; }
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/// set_vel_desired_z_cms - sets desired velocity in cm/s in z axis
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void set_vel_desired_z_cms(float vel_z_cms) {_vel_desired.z = vel_z_cms;}
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/// get_vel_target_z_cms - returns current vertical speed in cm/s
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float get_vel_target_z_cms() const { return _vel_target.z; }
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/// Acceleration
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// set_accel_desired_xy_cmss set desired acceleration in cm/s in xy axis
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void set_accel_desired_xy_cmss(const Vector2f &accel_cms) { _accel_desired.xy() = accel_cms; }
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// get_accel_target_cmss - returns the target acceleration in NEU cm/s/s
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const Vector3f& get_accel_target_cmss() const { return _accel_target; }
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/// Offset
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/// set_pos_offset_target_z_cm - set altitude offset target in cm above the EKF origin
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void set_pos_offset_target_z_cm(float pos_offset_target_z) { _pos_offset_target_z = pos_offset_target_z; }
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/// set_pos_offset_z_cm - set altitude offset in cm above the EKF origin
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void set_pos_offset_z_cm(float pos_offset_z) { _pos_offset_z = pos_offset_z; }
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/// get_pos_offset_z_cm - returns altitude offset in cm above the EKF origin
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float get_pos_offset_z_cm() const { return _pos_offset_z; }
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/// get_vel_offset_z_cm - returns current vertical offset speed in cm/s
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float get_vel_offset_z_cms() const { return _vel_offset_z; }
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/// get_accel_offset_z_cm - returns current vertical offset acceleration in cm/s/s
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float get_accel_offset_z_cmss() const { return _accel_offset_z; }
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/// Outputs
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/// get desired roll and pitch to be passed to the attitude controller
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float get_roll_cd() const { return _roll_target; }
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float get_pitch_cd() const { return _pitch_target; }
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/// get desired yaw to be passed to the attitude controller
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float get_yaw_cd() const { return _yaw_target; }
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/// get desired yaw rate to be passed to the attitude controller
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float get_yaw_rate_cds() const { return _yaw_rate_target; }
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/// get desired roll and pitch to be passed to the attitude controller
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Vector3f get_thrust_vector() const;
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/// get_bearing_to_target_cd - get bearing to target position in centi-degrees
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int32_t get_bearing_to_target_cd() const;
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/// get_lean_angle_max_cd - returns the maximum lean angle the autopilot may request
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float get_lean_angle_max_cd() const;
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/// Other
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/// get pid controllers
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AC_P_2D& get_pos_xy_p() { return _p_pos_xy; }
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AC_P_1D& get_pos_z_p() { return _p_pos_z; }
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AC_PID_2D& get_vel_xy_pid() { return _pid_vel_xy; }
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AC_PID_Basic& get_vel_z_pid() { return _pid_vel_z; }
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AC_PID& get_accel_z_pid() { return _pid_accel_z; }
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/// set_limit_accel_xy - mark that accel has been limited
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/// this prevents integrator buildup
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void set_externally_limited_xy() { _limit_vector.x = _accel_target.x; _limit_vector.y = _accel_target.y; }
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// lean_angles_to_accel - convert roll, pitch lean angles to lat/lon frame accelerations in cm/s/s
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Vector3f lean_angles_to_accel(const Vector3f& att_target_euler) const;
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// write PSC and/or PSCZ logs
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void write_log();
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// provide feedback on whether arming would be a good idea right now:
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bool pre_arm_checks(const char *param_prefix,
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char *failure_msg,
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const uint8_t failure_msg_len);
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// enable or disable high vibration compensation
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void set_vibe_comp(bool on_off) { _vibe_comp_enabled = on_off; }
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/// get_vel_z_error_ratio - returns the proportion of error relative to the maximum request
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float get_vel_z_control_ratio() const { return constrain_float(_vel_z_control_ratio, 0.0f, 1.0f); }
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/// crosstrack_error - returns horizontal error to the closest point to the current track
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float crosstrack_error() const;
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/// standby_xyz_reset - resets I terms and removes position error
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/// This function will let Loiter and Alt Hold continue to operate
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/// in the event that the flight controller is in control of the
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/// aircraft when in standby.
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void standby_xyz_reset();
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static const struct AP_Param::GroupInfo var_info[];
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protected:
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// get throttle using vibration-resistant calculation (uses feed forward with manually calculated gain)
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float get_throttle_with_vibration_override();
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// get earth-frame Z-axis acceleration with gravity removed in cm/s/s with +ve being up
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float get_z_accel_cmss() const { return -(_ahrs.get_accel_ef_blended().z + GRAVITY_MSS) * 100.0f; }
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// lean_angles_to_accel - convert roll, pitch lean angles to lat/lon frame accelerations in cm/s/s
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void accel_to_lean_angles(float accel_x_cmss, float accel_y_cmss, float& roll_target, float& pitch_target) const;
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// lean_angles_to_accel - convert roll, pitch lean angles to lat/lon frame accelerations in cm/s/s
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void lean_angles_to_accel_xy(float& accel_x_cmss, float& accel_y_cmss) const;
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// calculate_yaw_and_rate_yaw - calculate the vehicle yaw and rate of yaw.
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bool calculate_yaw_and_rate_yaw();
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// calculate_overspeed_gain - calculated increased maximum acceleration and jerk if over speed condition is detected
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float calculate_overspeed_gain();
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/// initialise and check for ekf position resets
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void init_ekf_xy_reset();
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void handle_ekf_xy_reset();
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void init_ekf_z_reset();
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void handle_ekf_z_reset();
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// references to inertial nav and ahrs libraries
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AP_AHRS_View& _ahrs;
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const AP_InertialNav& _inav;
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const AP_Motors& _motors;
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AC_AttitudeControl& _attitude_control;
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// parameters
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AP_Float _lean_angle_max; // Maximum autopilot commanded angle (in degrees). Set to zero for Angle Max
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AP_Float _shaping_jerk_xy; // Jerk limit of the xy kinematic path generation in m/s^3 used to determine how quickly the aircraft varies the acceleration target
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AP_Float _shaping_jerk_z; // Jerk limit of the z kinematic path generation in m/s^3 used to determine how quickly the aircraft varies the acceleration target
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AC_P_2D _p_pos_xy; // XY axis position controller to convert distance error to desired velocity
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AC_P_1D _p_pos_z; // Z axis position controller to convert altitude error to desired climb rate
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AC_PID_2D _pid_vel_xy; // XY axis velocity controller to convert velocity error to desired acceleration
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AC_PID_Basic _pid_vel_z; // Z axis velocity controller to convert climb rate error to desired acceleration
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AC_PID _pid_accel_z; // Z axis acceleration controller to convert desired acceleration to throttle output
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// internal variables
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float _dt; // time difference (in seconds) between calls from the main program
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uint64_t _last_update_xy_us; // system time (in microseconds) since last update_xy_controller call
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uint64_t _last_update_z_us; // system time (in microseconds) since last update_z_controller call
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float _vel_max_xy_cms; // max horizontal speed in cm/s used for kinematic shaping
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float _vel_max_up_cms; // max climb rate in cm/s used for kinematic shaping
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float _vel_max_down_cms; // max descent rate in cm/s used for kinematic shaping
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float _accel_max_xy_cmss; // max horizontal acceleration in cm/s/s used for kinematic shaping
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float _accel_max_z_cmss; // max vertical acceleration in cm/s/s used for kinematic shaping
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float _jerk_max_xy_cmsss; // Jerk limit of the xy kinematic path generation in cm/s^3 used to determine how quickly the aircraft varies the acceleration target
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float _jerk_max_z_cmsss; // Jerk limit of the z kinematic path generation in cm/s^3 used to determine how quickly the aircraft varies the acceleration target
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float _vel_z_control_ratio = 2.0f; // confidence that we have control in the vertical axis
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// output from controller
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float _roll_target; // desired roll angle in centi-degrees calculated by position controller
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float _pitch_target; // desired roll pitch in centi-degrees calculated by position controller
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float _yaw_target; // desired yaw in centi-degrees calculated by position controller
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float _yaw_rate_target; // desired yaw rate in centi-degrees per second calculated by position controller
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// position controller internal variables
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Vector3p _pos_target; // target location, frame NEU in cm relative to the EKF origin
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Vector3f _vel_desired; // desired velocity in NEU cm/s
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Vector3f _vel_target; // velocity target in NEU cm/s calculated by pos_to_rate step
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Vector3f _accel_desired; // desired acceleration in NEU cm/s/s (feed forward)
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Vector3f _accel_target; // acceleration target in NEU cm/s/s
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Vector3f _limit_vector; // the direction that the position controller is limited, zero when not limited
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float _pos_offset_target_z; // vertical position offset target, frame NEU in cm relative to the EKF origin
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float _pos_offset_z; // vertical position offset, frame NEU in cm relative to the EKF origin
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float _vel_offset_z; // vertical velocity offset in NEU cm/s calculated by pos_to_rate step
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float _accel_offset_z; // vertical acceleration offset in NEU cm/s/s
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// ekf reset handling
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uint32_t _ekf_xy_reset_ms; // system time of last recorded ekf xy position reset
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uint32_t _ekf_z_reset_ms; // system time of last recorded ekf altitude reset
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// high vibration handling
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bool _vibe_comp_enabled; // true when high vibration compensation is on
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// return true if on a real vehicle or SITL with lock-step scheduling
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bool has_good_timing(void) const;
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};
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