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- #pragma once
- /// @file AC_AttitudeControl.h
- /// @brief ArduCopter attitude control library
- #include <AP_Common/AP_Common.h>
- #include <AP_Param/AP_Param.h>
- #include <AP_Math/AP_Math.h>
- #include <AP_AHRS/AP_AHRS_View.h>
- #include <AP_Motors/AP_Motors.h>
- #include <AC_PID/AC_PID.h>
- #include <AC_PID/AC_P.h>
- #define AC_ATTITUDE_CONTROL_ANGLE_P 4.5f // default angle P gain for roll, pitch and yaw
- #define AC_ATTITUDE_ACCEL_RP_CONTROLLER_MIN_RADSS radians(40.0f) // minimum body-frame acceleration limit for the stability controller (for roll and pitch axis)
- #define AC_ATTITUDE_ACCEL_RP_CONTROLLER_MAX_RADSS radians(720.0f) // maximum body-frame acceleration limit for the stability controller (for roll and pitch axis)
- #define AC_ATTITUDE_ACCEL_Y_CONTROLLER_MIN_RADSS radians(10.0f) // minimum body-frame acceleration limit for the stability controller (for yaw axis)
- #define AC_ATTITUDE_ACCEL_Y_CONTROLLER_MAX_RADSS radians(120.0f) // maximum body-frame acceleration limit for the stability controller (for yaw axis)
- #define AC_ATTITUDE_CONTROL_SLEW_YAW_DEFAULT_CDS 6000 // constraint on yaw angle error in degrees. This should lead to maximum turn rate of 10deg/sec * Stab Rate P so by default will be 45deg/sec.
- #define AC_ATTITUDE_CONTROL_ACCEL_RP_MAX_DEFAULT_CDSS 4500.0f//110000.0f // default maximum acceleration for roll/pitch axis in centidegrees/sec/sec
- #define AC_ATTITUDE_CONTROL_ACCEL_Y_MAX_DEFAULT_CDSS 22000//27000.0f // default maximum acceleration for yaw axis in centidegrees/sec/sec
- #define AC_ATTITUDE_RATE_CONTROLLER_TIMEOUT 1.0f // body-frame rate controller timeout in seconds
- #define AC_ATTITUDE_RATE_RP_CONTROLLER_OUT_MAX 1.0f // body-frame rate controller maximum output (for roll-pitch axis)
- #define AC_ATTITUDE_RATE_YAW_CONTROLLER_OUT_MAX 1.0f // body-frame rate controller maximum output (for yaw axis)
- #define AC_ATTITUDE_THRUST_ERROR_ANGLE radians(30.0f) // Thrust angle error above which yaw corrections are limited
- #define AC_ATTITUDE_400HZ_DT 0.0025f // delta time in seconds for 400hz update rate
- #define AC_ATTITUDE_CONTROL_RATE_BF_FF_DEFAULT 1 // body-frame rate feedforward enabled by default
- #define AC_ATTITUDE_CONTROL_ANGLE_LIMIT_TC_DEFAULT 1.0f // Time constant used to limit lean angle so that vehicle does not lose altitude
- #define AC_ATTITUDE_CONTROL_ANGLE_LIMIT_THROTTLE_MAX 0.8f // Max throttle used to limit lean angle so that vehicle does not lose altitude
- #define AC_ATTITUDE_CONTROL_ANGLE_LIMIT_MIN 10.0f // Min lean angle so that vehicle can maintain limited control
- #define AC_ATTITUDE_CONTROL_MIN_DEFAULT 0.1f // minimum throttle mix default
- #define AC_ATTITUDE_CONTROL_MAN_DEFAULT 0.1f // manual throttle mix default
- #define AC_ATTITUDE_CONTROL_MAX_DEFAULT 0.5f // maximum throttle mix default
- #define AC_ATTITUDE_CONTROL_MAX 5.0f // maximum throttle mix default
- #define AC_ATTITUDE_CONTROL_THR_MIX_DEFAULT 0.5f // ratio controlling the max throttle output during competing requests of low throttle from the pilot (or autopilot) and higher throttle for attitude control. Higher favours Attitude over pilot input
- class AC_AttitudeControl {
- public:
- AC_AttitudeControl( AP_AHRS_View &ahrs,
- const AP_Vehicle::MultiCopter &aparm,
- AP_Motors& motors,
- float dt) :
- _p_angle_roll(AC_ATTITUDE_CONTROL_ANGLE_P),
- _p_angle_pitch(AC_ATTITUDE_CONTROL_ANGLE_P),
- _p_angle_yaw(AC_ATTITUDE_CONTROL_ANGLE_P),
- _dt(dt),
- _angle_boost(0),
- _use_sqrt_controller(true),
- _throttle_rpy_mix_desired(AC_ATTITUDE_CONTROL_THR_MIX_DEFAULT),
- _throttle_rpy_mix(AC_ATTITUDE_CONTROL_THR_MIX_DEFAULT),
- _ahrs(ahrs),
- _aparm(aparm),
- _motors(motors)
- {
- AP_Param::setup_object_defaults(this, var_info);
- //self define init start-------------------
- ATOM_sensor_Roll=0.0;
- ATOM_sensor_pitch=0.0;
- ATOM_sensor_yaw=0.0;
- ATOM_sensor_RollRate=0.0;
- ATOM_sensor_pitchRate=0.0;
- ATOM_sensor_yawRate=0.0;
- //self define init end-------------------
- }
- //self define start-------------------
- float ATOM_sensor_Roll;
- float ATOM_sensor_pitch;
- float ATOM_sensor_yaw;
- float ATOM_sensor_RollRate;
- float ATOM_sensor_pitchRate;
- float ATOM_sensor_yawRate;
- void update_ATOM_sensor(float r,float p,float y,float rr,float pr,float yr)
- {
- ATOM_sensor_Roll = r;
- ATOM_sensor_pitch =p;
- ATOM_sensor_yaw = y;
- ATOM_sensor_RollRate = rr;
- ATOM_sensor_pitchRate =pr;
- ATOM_sensor_yawRate = yr;
- }
- float Offset_ver;
- int32_t change_angle;
- int16_t roll_pitch_back_orign;
- float deta_angle_901;
- float angle_geiding;
- uint8_t Hor_ver_choose;
- void update_Hor_Ver_Choose(uint8_t c){Hor_ver_choose = c;}
- //self define end-------------------
- // Empty destructor to suppress compiler warning
- virtual ~AC_AttitudeControl() {}
- void input_euler_angle_roll_pitch_yaw_quat_control(float euler_roll_angle_cd, float euler_pitch_angle_cd, float euler_yaw_angle_cd, bool slew_yaw);
- // pid accessors
- AC_P& get_angle_roll_p() { return _p_angle_roll; }
- AC_P& get_angle_pitch_p() { return _p_angle_pitch; }
- AC_P& get_angle_yaw_p() { return _p_angle_yaw; }
- virtual AC_PID& get_rate_roll_pid() = 0;
- virtual AC_PID& get_rate_pitch_pid() = 0;
- virtual AC_PID& get_rate_yaw_pid() = 0;
- // get the roll acceleration limit in centidegrees/s/s or radians/s/s
- float get_accel_roll_max() const { return _accel_roll_max; }
- float get_accel_roll_max_radss() const { return radians(_accel_roll_max * 0.01f); }
- // Sets the roll acceleration limit in centidegrees/s/s
- void set_accel_roll_max(float accel_roll_max) { _accel_roll_max = accel_roll_max; }
- // Sets and saves the roll acceleration limit in centidegrees/s/s
- void save_accel_roll_max(float accel_roll_max) { _accel_roll_max.set_and_save(accel_roll_max); }
- // get the pitch acceleration limit in centidegrees/s/s or radians/s/s
- float get_accel_pitch_max() const { return _accel_pitch_max; }
- float get_accel_pitch_max_radss() const { return radians(_accel_pitch_max * 0.01f); }
- // Sets the pitch acceleration limit in centidegrees/s/s
- void set_accel_pitch_max(float accel_pitch_max) { _accel_pitch_max = accel_pitch_max; }
- // Sets and saves the pitch acceleration limit in centidegrees/s/s
- void save_accel_pitch_max(float accel_pitch_max) { _accel_pitch_max.set_and_save(accel_pitch_max); }
- // get the yaw acceleration limit in centidegrees/s/s or radians/s/s
- float get_accel_yaw_max() const { return _accel_yaw_max; }
- float get_accel_yaw_max_radss() const { return radians(_accel_yaw_max * 0.01f); }
- // Sets the yaw acceleration limit in centidegrees/s/s
- void set_accel_yaw_max(float accel_yaw_max) { _accel_yaw_max = accel_yaw_max; }
- // Sets and saves the yaw acceleration limit in centidegrees/s/s
- void save_accel_yaw_max(float accel_yaw_max) { _accel_yaw_max.set_and_save(accel_yaw_max); }
- // set the rate control input smoothing time constant
- void set_input_tc(float input_tc) { _input_tc = constrain_float(input_tc, 0.0f, 1.0f); }
- // Ensure attitude controller have zero errors to relax rate controller output
- void relax_attitude_controllers();
- // reset rate controller I terms
- void reset_rate_controller_I_terms();
- // Sets attitude target to vehicle attitude
- void set_attitude_target_to_current_attitude() { _ahrs.get_quat_body_to_ned(_attitude_target_quat); }
- // Sets yaw target to vehicle heading
- void set_yaw_target_to_current_heading() { shift_ef_yaw_target(degrees(_ahrs.yaw - _attitude_target_euler_angle.z) * 100.0f); }
- // Shifts earth frame yaw target by yaw_shift_cd. yaw_shift_cd should be in centidegrees and is added to the current target heading
- void shift_ef_yaw_target(float yaw_shift_cd);
- // handle reset of attitude from EKF since the last iteration
- void inertial_frame_reset();
- // Command a Quaternion attitude with feedforward and smoothing
- void input_quaternion(Quaternion attitude_desired_quat);
- // Command an euler roll and pitch angle and an euler yaw rate with angular velocity feedforward and smoothing
- virtual void input_euler_angle_roll_pitch_euler_rate_yaw(float euler_roll_angle_cd, float euler_pitch_angle_cd, float euler_yaw_rate_cds);
- // Command an euler roll, pitch and yaw angle with angular velocity feedforward and smoothing
- virtual void input_euler_angle_roll_pitch_yaw(float euler_roll_angle_cd, float euler_pitch_angle_cd, float euler_yaw_angle_cd, bool slew_yaw);
- // Command euler yaw rate and pitch angle with roll angle specified in body frame with multicopter style controls
- // (used only by tailsitter quadplanes)
- virtual void input_euler_rate_yaw_euler_angle_pitch_bf_roll_m(float euler_roll_angle_cd, float euler_pitch_angle_cd, float euler_yaw_rate_cds);
- // Command euler yaw rate and pitch angle with roll angle specified in body frame with plane style controls
- // (used only by tailsitter quadplanes)
- virtual void input_euler_rate_yaw_euler_angle_pitch_bf_roll_p(float euler_roll_angle_cd, float euler_pitch_angle_cd, float euler_yaw_rate_cds);
- // Command an euler roll, pitch, and yaw rate with angular velocity feedforward and smoothing
- void input_euler_rate_roll_pitch_yaw(float euler_roll_rate_cds, float euler_pitch_rate_cds, float euler_yaw_rate_cds);
- // Command an angular velocity with angular velocity feedforward and smoothing
- virtual void input_rate_bf_roll_pitch_yaw(float roll_rate_bf_cds, float pitch_rate_bf_cds, float yaw_rate_bf_cds);
- // Command an angular velocity with angular velocity feedforward and smoothing
- void input_rate_bf_roll_pitch_yaw_2(float roll_rate_bf_cds, float pitch_rate_bf_cds, float yaw_rate_bf_cds);
- // Command an angular velocity with angular velocity smoothing using rate loops only with integrated rate error stabilization
- void input_rate_bf_roll_pitch_yaw_3(float roll_rate_bf_cds, float pitch_rate_bf_cds, float yaw_rate_bf_cds);
- // Command an angular step (i.e change) in body frame angle
- virtual void input_angle_step_bf_roll_pitch_yaw(float roll_angle_step_bf_cd, float pitch_angle_step_bf_cd, float yaw_angle_step_bf_cd);
- // Run angular velocity controller and send outputs to the motors
- virtual void rate_controller_run() = 0;
- // Convert a 321-intrinsic euler angle derivative to an angular velocity vector
- void euler_rate_to_ang_vel(const Vector3f& euler_rad, const Vector3f& euler_rate_rads, Vector3f& ang_vel_rads);
- // Convert an angular velocity vector to a 321-intrinsic euler angle derivative
- // Returns false if the vehicle is pitched 90 degrees up or down
- bool ang_vel_to_euler_rate(const Vector3f& euler_rad, const Vector3f& ang_vel_rads, Vector3f& euler_rate_rads);
- // Specifies whether the attitude controller should use the square root controller in the attitude correction.
- // This is used during Autotune to ensure the P term is tuned without being influenced by the acceleration limit of the square root controller.
- void use_sqrt_controller(bool use_sqrt_cont) { _use_sqrt_controller = use_sqrt_cont; }
- // Return 321-intrinsic euler angles in centidegrees representing the rotation from NED earth frame to the
- // attitude controller's target attitude.
- // **NOTE** Using vector3f*deg(100) is more efficient than deg(vector3f)*100 or deg(vector3d*100) because it gives the
- // same result with the fewest multiplications. Even though it may look like a bug, it is intentional. See issue 4895.
- Vector3f get_att_target_euler_cd() const { return _attitude_target_euler_angle * degrees(100.0f); }
- // Return the body-to-NED target attitude used by the quadplane-specific attitude control input methods
- Quaternion get_attitude_target_quat() const { return _attitude_target_quat; }
- // Return the angle between the target thrust vector and the current thrust vector.
- float get_att_error_angle_deg() const { return degrees(_thrust_error_angle); }
- // Set x-axis angular velocity in centidegrees/s
- void rate_bf_roll_target(float rate_cds) { _rate_target_ang_vel.x = radians(rate_cds * 0.01f); }
- // Set y-axis angular velocity in centidegrees/s
- void rate_bf_pitch_target(float rate_cds) { _rate_target_ang_vel.y = radians(rate_cds * 0.01f); }
- // Set z-axis angular velocity in centidegrees/s
- void rate_bf_yaw_target(float rate_cds) { _rate_target_ang_vel.z = radians(rate_cds * 0.01f); }
- // Return roll rate step size in radians/s that results in maximum output after 4 time steps
- float max_rate_step_bf_roll();
- // Return pitch rate step size in radians/s that results in maximum output after 4 time steps
- float max_rate_step_bf_pitch();
- // Return yaw rate step size in radians/s that results in maximum output after 4 time steps
- float max_rate_step_bf_yaw();
- // Return roll step size in radians that results in maximum output after 4 time steps
- float max_angle_step_bf_roll() { return max_rate_step_bf_roll() / _p_angle_roll.kP(); }
- // Return pitch step size in radians that results in maximum output after 4 time steps
- float max_angle_step_bf_pitch() { return max_rate_step_bf_pitch() / _p_angle_pitch.kP(); }
- // Return yaw step size in radians that results in maximum output after 4 time steps
- float max_angle_step_bf_yaw() { return max_rate_step_bf_yaw() / _p_angle_yaw.kP(); }
- // Return angular velocity in radians used in the angular velocity controller
- Vector3f rate_bf_targets() const { return _rate_target_ang_vel; }
- // Enable or disable body-frame feed forward
- void bf_feedforward(bool enable_or_disable) { _rate_bf_ff_enabled = enable_or_disable; }
- // Enable or disable body-frame feed forward and save
- void bf_feedforward_save(bool enable_or_disable) { _rate_bf_ff_enabled.set_and_save(enable_or_disable); }
- // Return body-frame feed forward setting
- bool get_bf_feedforward() { return _rate_bf_ff_enabled; }
- // Enable or disable body-frame feed forward
- void accel_limiting(bool enable_or_disable);
- // Update Alt_Hold angle maximum
- virtual void update_althold_lean_angle_max(float throttle_in) = 0;
- // Set output throttle
- virtual void set_throttle_out(float throttle_in, bool apply_angle_boost, float filt_cutoff) = 0;
- // get throttle passed into attitude controller (i.e. throttle_in provided to set_throttle_out)
- float get_throttle_in() const { return _throttle_in; }
- // Return throttle increase applied for tilt compensation
- float angle_boost() const { return _angle_boost; }
- // Return tilt angle limit for pilot input that prioritises altitude hold over lean angle
- float get_althold_lean_angle_max() const;
- // Return configured tilt angle limit in centidegrees
- float lean_angle_max() const { return _aparm.angle_max; }
- // Proportional controller with piecewise sqrt sections to constrain second derivative
- static float sqrt_controller(float error, float p, float second_ord_lim, float dt);
- // Inverse proportional controller with piecewise sqrt sections to constrain second derivative
- static float stopping_point(float first_ord_mag, float p, float second_ord_lim);
- // calculates the velocity correction from an angle error. The angular velocity has acceleration and
- // deceleration limits including basic jerk limiting using smoothing_gain
- static float input_shaping_angle(float error_angle, float smoothing_gain, float accel_max, float target_ang_vel, float dt);
- // limits the acceleration and deceleration of a velocity request
- static float input_shaping_ang_vel(float target_ang_vel, float desired_ang_vel, float accel_max, float dt);
- // calculates the expected angular velocity correction from an angle error based on the AC_AttitudeControl settings.
- // This function can be used to predict the delay associated with angle requests.
- void input_shaping_rate_predictor(const Vector2f &error_angle, Vector2f& target_ang_vel, float dt) const;
- // translates body frame acceleration limits to the euler axis
- void ang_vel_limit(Vector3f& euler_rad, float ang_vel_roll_max, float ang_vel_pitch_max, float ang_vel_yaw_max) const;
- // translates body frame acceleration limits to the euler axis
- Vector3f euler_accel_limit(const Vector3f &euler_rad, const Vector3f &euler_accel);
- // thrust_heading_rotation_angles - calculates two ordered rotations to move the att_from_quat quaternion to the att_to_quat quaternion.
- // The first rotation corrects the thrust vector and the second rotation corrects the heading vector.
- void thrust_heading_rotation_angles(Quaternion& att_to_quat, const Quaternion& att_from_quat, Vector3f& att_diff_angle, float& thrust_vec_dot);
- // Calculates the body frame angular velocities to follow the target attitude
- void attitude_controller_run_quat();
- // sanity check parameters. should be called once before take-off
- virtual void parameter_sanity_check() {}
- // return true if the rpy mix is at lowest value
- virtual bool is_throttle_mix_min() const { return true; }
- // control rpy throttle mix
- virtual void set_throttle_mix_min() {}
- virtual void set_throttle_mix_man() {}
- virtual void set_throttle_mix_max() {}
- virtual void set_throttle_mix_value(float value) {}
- virtual float get_throttle_mix(void) const { return 0; }
- // enable use of flybass passthrough on heli
- virtual void use_flybar_passthrough(bool passthrough, bool tail_passthrough) {}
- // use_leaky_i - controls whether we use leaky i term for body-frame to motor output stage on heli
- virtual void use_leaky_i(bool leaky_i) {}
- // set_hover_roll_scalar - scales Hover Roll Trim parameter. To be used by vehicle code according to vehicle condition.
- virtual void set_hover_roll_trim_scalar(float scalar) {}
- // passthrough_bf_roll_pitch_rate_yaw - roll and pitch are passed through directly, body-frame rate target for yaw
- virtual void passthrough_bf_roll_pitch_rate_yaw(float roll_passthrough, float pitch_passthrough, float yaw_rate_bf_cds) {};
- // provide feedback on whether arming would be a good idea right now:
- bool pre_arm_checks(const char *param_prefix,
- char *failure_msg,
- const uint8_t failure_msg_len);
- // enable inverted flight on backends that support it
- virtual void set_inverted_flight(bool inverted) {}
-
- // User settable parameters
- static const struct AP_Param::GroupInfo var_info[];
- protected:
- // Update rate_target_ang_vel using attitude_error_rot_vec_rad
- Vector3f update_ang_vel_target_from_att_error(const Vector3f &attitude_error_rot_vec_rad);
- // Return angle in radians to be added to roll angle. Used by heli to counteract
- // tail rotor thrust in hover. Overloaded by AC_Attitude_Heli to return angle.
- virtual float get_roll_trim_rad() { return 0;}
- // Return the yaw slew rate limit in radians/s
- float get_slew_yaw_rads() { return radians(_slew_yaw * 0.01f); }
- // Maximum rate the yaw target can be updated in Loiter, RTL, Auto flight modes
- AP_Float _slew_yaw;
- // Maximum angular velocity (in degrees/second) for earth-frame roll, pitch and yaw axis
- AP_Float _ang_vel_roll_max;
- AP_Float _ang_vel_pitch_max;
- AP_Float _ang_vel_yaw_max;
- // Maximum rotation acceleration for earth-frame roll axis
- AP_Float _accel_roll_max;
- // Maximum rotation acceleration for earth-frame pitch axis
- AP_Float _accel_pitch_max;
- // Maximum rotation acceleration for earth-frame yaw axis
- AP_Float _accel_yaw_max;
- // Enable/Disable body frame rate feed forward
- AP_Int8 _rate_bf_ff_enabled;
- // Enable/Disable angle boost
- AP_Int8 _angle_boost_enabled;
- // angle controller P objects
- AC_P _p_angle_roll;
- AC_P _p_angle_pitch;
- AC_P _p_angle_yaw;
- // Angle limit time constant (to maintain altitude)
- AP_Float _angle_limit_tc;
- // rate controller input smoothing time constant
- AP_Float _input_tc;
- // Intersampling period in seconds
- float _dt;
- // This represents a 321-intrinsic rotation in NED frame to the target (setpoint)
- // attitude used in the attitude controller, in radians.
- Vector3f _attitude_target_euler_angle;
- // This represents the angular velocity of the target (setpoint) attitude used in
- // the attitude controller as 321-intrinsic euler angle derivatives, in radians per
- // second.
- Vector3f _attitude_target_euler_rate;
- // This represents a quaternion rotation in NED frame to the target (setpoint)
- // attitude used in the attitude controller.
- Quaternion _attitude_target_quat;
- // This represents the angular velocity of the target (setpoint) attitude used in
- // the attitude controller as an angular velocity vector, in radians per second in
- // the target attitude frame.
- Vector3f _attitude_target_ang_vel;
- // This represents the angular velocity in radians per second in the body frame, used in the angular
- // velocity controller.
- Vector3f _rate_target_ang_vel;
- // This represents a quaternion attitude error in the body frame, used for inertial frame reset handling.
- Quaternion _attitude_ang_error;
- // The angle between the target thrust vector and the current thrust vector.
- float _thrust_error_angle;
- // throttle provided as input to attitude controller. This does not include angle boost.
- float _throttle_in = 0.0f;
- // This represents the throttle increase applied for tilt compensation.
- // Used only for logging.
- float _angle_boost;
- // Specifies whether the attitude controller should use the square root controller in the attitude correction.
- // This is used during Autotune to ensure the P term is tuned without being influenced by the acceleration limit of the square root controller.
- bool _use_sqrt_controller;
- // Filtered Alt_Hold lean angle max - used to limit lean angle when throttle is saturated using Alt_Hold
- float _althold_lean_angle_max = 0.0f;
- // desired throttle_low_comp value, actual throttle_low_comp is slewed towards this value over 1~2 seconds
- float _throttle_rpy_mix_desired;
- // mix between throttle and hover throttle for 0 to 1 and ratio above hover throttle for >1
- float _throttle_rpy_mix;
- // References to external libraries
- const AP_AHRS_View& _ahrs;
- const AP_Vehicle::MultiCopter &_aparm;
- AP_Motors& _motors;
- protected:
- /*
- state of control monitoring
- */
- struct {
- float rms_roll_P;
- float rms_roll_D;
- float rms_pitch_P;
- float rms_pitch_D;
- float rms_yaw;
- } _control_monitor;
- // update state in ControlMonitor
- void control_monitor_filter_pid(float value, float &rms_P);
- void control_monitor_update(void);
- // true in inverted flight mode
- bool _inverted_flight;
- public:
- // log a CTRL message
- void control_monitor_log(void);
- // return current RMS controller filter for each axis
- float control_monitor_rms_output_roll(void) const;
- float control_monitor_rms_output_roll_P(void) const;
- float control_monitor_rms_output_roll_D(void) const;
- float control_monitor_rms_output_pitch_P(void) const;
- float control_monitor_rms_output_pitch_D(void) const;
- float control_monitor_rms_output_pitch(void) const;
- float control_monitor_rms_output_yaw(void) const;
- };
- #define AC_ATTITUDE_CONTROL_LOG_FORMAT(msg) { msg, sizeof(AC_AttitudeControl::log_Attitude), \
- "ATT", "cccccCC", "RollIn,Roll,PitchIn,Pitch,YawIn,Yaw,NavYaw" }
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