mirror of
https://github.com/PX4/PX4-Autopilot.git
synced 2026-06-04 05:05:19 +08:00
Merged with fixed-wing stabilization work, multirotor control tested
This commit is contained in:
@@ -2,6 +2,7 @@
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*
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*
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* Copyright (C) 2012 PX4 Development Team. All rights reserved.
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* Copyright (C) 2012 PX4 Development Team. All rights reserved.
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* Author: @author Ivan Ovinnikov <oivan@ethz.ch>
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* Author: @author Ivan Ovinnikov <oivan@ethz.ch>
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* Modifications: Doug Weibel <douglas.weibel@colorado.edu>
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*
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*
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* Redistribution and use in source and binary forms, with or without
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* modification, are permitted provided that the following conditions
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@@ -31,7 +32,7 @@
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* POSSIBILITY OF SUCH DAMAGE.
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* POSSIBILITY OF SUCH DAMAGE.
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*
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*
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****************************************************************************/
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****************************************************************************/
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// Workflow test comment - DEW
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/**
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/**
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* @file fixedwing_control.c
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* @file fixedwing_control.c
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* Implementation of a fixed wing attitude and position controller.
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* Implementation of a fixed wing attitude and position controller.
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@@ -86,27 +87,61 @@ static void usage(const char *reason);
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* Controller parameters, accessible via MAVLink
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* Controller parameters, accessible via MAVLink
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*
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*
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*/
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*/
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PARAM_DEFINE_FLOAT(FW_ROLL_POS_P, 0.3f);
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// Roll control parameters
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PARAM_DEFINE_FLOAT(FW_ROLL_POS_I, 0.002f);
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PARAM_DEFINE_FLOAT(FW_ROLLRATE_P, 0.3f);
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PARAM_DEFINE_FLOAT(FW_ROLL_POS_AWU, 0.2f);
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// Need to add functionality to suppress integrator windup while on the ground
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PARAM_DEFINE_FLOAT(FW_ROLL_POS_LIM, 0.6f);
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// Suggested value of FW_ROLLRATE_I is 0.0 till this is in place
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PARAM_DEFINE_FLOAT(FW_ROLLRATE_I, 0.0f);
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PARAM_DEFINE_FLOAT(FW_ROLLRATE_AWU, 0.0f);
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PARAM_DEFINE_FLOAT(FW_ROLLRATE_LIM, 0.7f); // Roll rate limit in radians/sec
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PARAM_DEFINE_FLOAT(FW_ROLL_P, 0.3f);
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PARAM_DEFINE_FLOAT(FW_ROLL_LIM, 0.7f); // Roll angle limit in radians
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//Pitch control parameters
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PARAM_DEFINE_FLOAT(FW_PITCHRATE_P, 0.3f);
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// Need to add functionality to suppress integrator windup while on the ground
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// Suggested value of FW_PITCHRATE_I is 0.0 till this is in place
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PARAM_DEFINE_FLOAT(FW_PITCHRATE_I, 0.0f);
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PARAM_DEFINE_FLOAT(FW_PITCHRATE_AWU, 0.0f);
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PARAM_DEFINE_FLOAT(FW_PITCHRATE_LIM, 0.35f); // Pitch rate limit in radians/sec
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PARAM_DEFINE_FLOAT(FW_PITCH_P, 0.3f);
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PARAM_DEFINE_FLOAT(FW_PITCH_LIM, 0.35f); // Pitch angle limit in radians
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struct fw_att_control_params {
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struct fw_att_control_params {
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float roll_pos_p;
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float rollrate_p;
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float roll_pos_i;
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float rollrate_i;
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float roll_pos_awu;
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float rollrate_awu;
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float roll_pos_lim;
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float rollrate_lim;
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float roll_p;
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float roll_lim;
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float pitchrate_p;
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float pitchrate_i;
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float pitchrate_awu;
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float pitchrate_lim;
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float pitch_p;
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float pitch_lim;
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};
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};
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struct fw_att_control_param_handles {
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struct fw_att_control_param_handles {
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param_t roll_pos_p;
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param_t rollrate_p;
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param_t roll_pos_i;
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param_t rollrate_i;
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param_t roll_pos_awu;
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param_t rollrate_awu;
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param_t roll_pos_lim;
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param_t rollrate_lim;
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param_t roll_p;
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param_t roll_lim;
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param_t pitchrate_p;
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param_t pitchrate_i;
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param_t pitchrate_awu;
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param_t pitchrate_lim;
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param_t pitch_p;
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param_t pitch_lim;
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};
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};
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// XXX outsource position control to a separate app some time
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// TO_DO - Navigation control will be moved to a separate app
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// Attitude control will just handle the inner angle and rate loops
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// to control pitch and roll, and turn coordination via rudder and
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// possibly throttle compensation for battery voltage sag.
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PARAM_DEFINE_FLOAT(FW_HEADING_P, 0.1f);
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PARAM_DEFINE_FLOAT(FW_HEADING_P, 0.1f);
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PARAM_DEFINE_FLOAT(FW_HEADING_LIM, 0.15f);
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PARAM_DEFINE_FLOAT(FW_HEADING_LIM, 0.15f);
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@@ -147,9 +182,9 @@ static int pos_parameters_update(const struct fw_pos_control_param_handles *h, s
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/**
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/**
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* The fixed wing control main loop.
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* The fixed wing control main thread.
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*
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*
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* This loop executes continously and calculates the control
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* The main loop executes continously and calculates the control
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* response.
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* response.
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*
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*
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* @param argc number of arguments
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* @param argc number of arguments
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@@ -223,19 +258,31 @@ int fixedwing_control_thread_main(int argc, char *argv[])
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pos_parameters_init(&hpos);
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pos_parameters_init(&hpos);
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pos_parameters_update(&hpos, &ppos);
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pos_parameters_update(&hpos, &ppos);
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PID_t roll_pos_controller;
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// TO_DO Fix output limit functionallity of PID controller or add that function elsewhere
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pid_init(&roll_pos_controller, p.roll_pos_p, p.roll_pos_i, 0.0f, p.roll_pos_awu,
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PID_t roll_rate_controller;
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PID_MODE_DERIVATIV_SET);
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pid_init(&roll_rate_controller, p.rollrate_p, p.rollrate_i, 0.0f, p.rollrate_awu,
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p.rollrate_lim,PID_MODE_DERIVATIV_NONE);
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PID_t roll_angle_controller;
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pid_init(&roll_angle_controller, p.roll_p, 0.0f, 0.0f, 0.0f,
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p.roll_lim,PID_MODE_DERIVATIV_NONE);
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PID_t pitch_rate_controller;
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pid_init(&pitch_rate_controller, p.pitchrate_p, p.pitchrate_i, 0.0f, p.pitchrate_awu,
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p.pitchrate_lim,PID_MODE_DERIVATIV_NONE);
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PID_t pitch_angle_controller;
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pid_init(&pitch_angle_controller, p.pitch_p, 0.0f, 0.0f, 0.0f,
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p.pitch_lim,PID_MODE_DERIVATIV_NONE);
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PID_t heading_controller;
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PID_t heading_controller;
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pid_init(&heading_controller, ppos.heading_p, 0.0f, 0.0f, 0.0f,
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pid_init(&heading_controller, ppos.heading_p, 0.0f, 0.0f, 0.0f,
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PID_MODE_DERIVATIV_SET);
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100.0f,PID_MODE_DERIVATIV_SET); // Temporary arbitrarily large limit
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// XXX remove in production
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// XXX remove in production
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/* advertise debug value */
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/* advertise debug value */
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struct debug_key_value_s dbg = { .key = "", .value = 0.0f };
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struct debug_key_value_s dbg = { .key = "", .value = 0.0f };
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orb_advert_t pub_dbg = orb_advertise(ORB_ID(debug_key_value), &dbg);
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orb_advert_t pub_dbg = orb_advertise(ORB_ID(debug_key_value), &dbg);
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// This is the top of the main loop
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while(!thread_should_exit) {
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while(!thread_should_exit) {
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struct pollfd fds[1] = {
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struct pollfd fds[1] = {
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@@ -251,11 +298,20 @@ int fixedwing_control_thread_main(int argc, char *argv[])
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} else {
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} else {
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// FIXME SUBSCRIBE
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// FIXME SUBSCRIBE
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if (loopcounter % 20 == 0) {
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if (loopcounter % 100 == 0) {
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att_parameters_update(&h, &p);
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att_parameters_update(&h, &p);
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pos_parameters_update(&hpos, &ppos);
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pos_parameters_update(&hpos, &ppos);
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pid_set_parameters(&roll_pos_controller, p.roll_pos_p, p.roll_pos_i, 0.0f, p.roll_pos_awu);
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pid_set_parameters(&roll_rate_controller, p.rollrate_p, p.rollrate_i, 0.0f,
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pid_set_parameters(&heading_controller, ppos.heading_p, 0.0f, 0.0f, 0.0f);
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p.rollrate_awu, p.rollrate_lim);
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pid_set_parameters(&roll_angle_controller, p.roll_p, 0.0f, 0.0f,
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0.0f, p.roll_lim);
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pid_set_parameters(&pitch_rate_controller, p.pitchrate_p, p.pitchrate_i, 0.0f,
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p.pitchrate_awu, p.pitchrate_lim);
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pid_set_parameters(&pitch_angle_controller, p.pitch_p, 0.0f, 0.0f,
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0.0f, p.pitch_lim);
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pid_set_parameters(&heading_controller, ppos.heading_p, 0.0f, 0.0f, 0.0f, 90.0f);
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//printf("[fixedwing control debug] p: %8.4f, i: %8.4f, limit: %8.4f \n",
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//p.rollrate_p, p.rollrate_i, p.rollrate_lim);
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}
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}
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/* if position updated, run position control loop */
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/* if position updated, run position control loop */
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@@ -359,12 +415,23 @@ int fixedwing_control_thread_main(int argc, char *argv[])
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printf("[fixedwing control] roll sp: %8.4f, \n", att_sp.roll_body);
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printf("[fixedwing control] roll sp: %8.4f, \n", att_sp.roll_body);
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}
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}
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// actuators.control[0] = pid_calculate(&roll_pos_controller, att_sp.roll_body,
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// actuator control[0] is aileron (or elevon roll control)
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// att.roll, att.rollspeed, deltaTpos);
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// Commanded roll rate from P controller on roll angle
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actuators.control[0] = pid_calculate(&roll_pos_controller, att_sp.roll_body,
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float roll_rate_command = pid_calculate(&roll_angle_controller, att_sp.roll_body,
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att.roll, att.rollspeed, deltaTpos);
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att.roll, 0.0f, deltaTpos);
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actuators.control[1] = 0;
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// actuator control from PI controller on roll rate
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actuators.control[2] = 0;
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actuators.control[0] = pid_calculate(&roll_rate_controller, roll_rate_command,
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att.rollspeed, 0.0f, deltaTpos);
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// actuator control[1] is elevator (or elevon pitch control)
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// Commanded pitch rate from P controller on pitch angle
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float pitch_rate_command = pid_calculate(&pitch_angle_controller, att_sp.pitch_body,
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att.pitch, 0.0f, deltaTpos);
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// actuator control from PI controller on pitch rate
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actuators.control[1] = pid_calculate(&pitch_rate_controller, pitch_rate_command,
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att.pitchspeed, 0.0f, deltaTpos);
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// actuator control[3] is throttle
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actuators.control[3] = att_sp.thrust;
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actuators.control[3] = att_sp.thrust;
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/* publish attitude setpoint (for MAVLink) */
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/* publish attitude setpoint (for MAVLink) */
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@@ -446,20 +513,37 @@ int fixedwing_control_main(int argc, char *argv[])
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static int att_parameters_init(struct fw_att_control_param_handles *h)
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static int att_parameters_init(struct fw_att_control_param_handles *h)
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{
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{
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/* PID parameters */
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/* PID parameters */
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h->roll_pos_p = param_find("FW_ROLL_POS_P");
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h->roll_pos_i = param_find("FW_ROLL_POS_I");
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h->rollrate_p = param_find("FW_ROLLRATE_P");
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h->roll_pos_lim = param_find("FW_ROLL_POS_LIM");
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h->rollrate_i = param_find("FW_ROLLRATE_I");
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h->roll_pos_awu = param_find("FW_ROLL_POS_AWU");
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h->rollrate_awu = param_find("FW_ROLLRATE_AWU");
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h->rollrate_lim = param_find("FW_ROLLRATE_LIM");
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h->roll_p = param_find("FW_ROLL_P");
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h->roll_lim = param_find("FW_ROLL_LIM");
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h->pitchrate_p = param_find("FW_PITCHRATE_P");
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h->pitchrate_i = param_find("FW_PITCHRATE_I");
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h->pitchrate_awu = param_find("FW_PITCHRATE_AWU");
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h->pitchrate_lim = param_find("FW_PITCHRATE_LIM");
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h->pitch_p = param_find("FW_PITCH_P");
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h->pitch_lim = param_find("FW_PITCH_LIM");
|
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|
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return OK;
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return OK;
|
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}
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}
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|
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static int att_parameters_update(const struct fw_att_control_param_handles *h, struct fw_att_control_params *p)
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static int att_parameters_update(const struct fw_att_control_param_handles *h, struct fw_att_control_params *p)
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{
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{
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param_get(h->roll_pos_p, &(p->roll_pos_p));
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param_get(h->rollrate_p, &(p->rollrate_p));
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param_get(h->roll_pos_i, &(p->roll_pos_i));
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param_get(h->rollrate_i, &(p->rollrate_i));
|
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param_get(h->roll_pos_lim, &(p->roll_pos_lim));
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param_get(h->rollrate_awu, &(p->rollrate_awu));
|
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param_get(h->roll_pos_awu, &(p->roll_pos_awu));
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param_get(h->rollrate_lim, &(p->rollrate_lim));
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param_get(h->roll_p, &(p->roll_p));
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param_get(h->roll_lim, &(p->roll_lim));
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param_get(h->pitchrate_p, &(p->pitchrate_p));
|
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param_get(h->pitchrate_i, &(p->pitchrate_i));
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param_get(h->pitchrate_awu, &(p->pitchrate_awu));
|
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param_get(h->pitchrate_lim, &(p->pitchrate_lim));
|
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param_get(h->pitch_p, &(p->pitch_p));
|
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param_get(h->pitch_lim, &(p->pitch_lim));
|
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|
|
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return OK;
|
return OK;
|
||||||
}
|
}
|
||||||
|
|||||||
@@ -60,11 +60,9 @@ PARAM_DEFINE_FLOAT(MC_YAWPOS_D, 0.0f);
|
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PARAM_DEFINE_FLOAT(MC_YAWPOS_AWU, 1.0f);
|
PARAM_DEFINE_FLOAT(MC_YAWPOS_AWU, 1.0f);
|
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PARAM_DEFINE_FLOAT(MC_YAWPOS_LIM, 3.0f);
|
PARAM_DEFINE_FLOAT(MC_YAWPOS_LIM, 3.0f);
|
||||||
|
|
||||||
|
PARAM_DEFINE_FLOAT(MC_ATT_P, 0.2f);
|
||||||
|
|
||||||
PARAM_DEFINE_FLOAT(MC_ATT_P, 0.2f); /* 0.15 F405 Flamewheel */
|
|
||||||
PARAM_DEFINE_FLOAT(MC_ATT_I, 0.0f);
|
PARAM_DEFINE_FLOAT(MC_ATT_I, 0.0f);
|
||||||
PARAM_DEFINE_FLOAT(MC_ATT_D, 0.05f); /* 0.025 F405 Flamewheel */
|
PARAM_DEFINE_FLOAT(MC_ATT_D, 0.05f);
|
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PARAM_DEFINE_FLOAT(MC_ATT_AWU, 0.05f);
|
PARAM_DEFINE_FLOAT(MC_ATT_AWU, 0.05f);
|
||||||
PARAM_DEFINE_FLOAT(MC_ATT_LIM, 0.4f);
|
PARAM_DEFINE_FLOAT(MC_ATT_LIM, 0.4f);
|
||||||
|
|
||||||
@@ -78,12 +76,6 @@ struct mc_att_control_params {
|
|||||||
float yaw_awu;
|
float yaw_awu;
|
||||||
float yaw_lim;
|
float yaw_lim;
|
||||||
|
|
||||||
// float yawrate_p;
|
|
||||||
// float yawrate_i;
|
|
||||||
// float yawrate_d;
|
|
||||||
// float yawrate_awu;
|
|
||||||
// float yawrate_lim;
|
|
||||||
|
|
||||||
float att_p;
|
float att_p;
|
||||||
float att_i;
|
float att_i;
|
||||||
float att_d;
|
float att_d;
|
||||||
@@ -101,12 +93,6 @@ struct mc_att_control_param_handles {
|
|||||||
param_t yaw_awu;
|
param_t yaw_awu;
|
||||||
param_t yaw_lim;
|
param_t yaw_lim;
|
||||||
|
|
||||||
// param_t yawrate_p;
|
|
||||||
// param_t yawrate_i;
|
|
||||||
// param_t yawrate_d;
|
|
||||||
// param_t yawrate_awu;
|
|
||||||
// param_t yawrate_lim;
|
|
||||||
|
|
||||||
param_t att_p;
|
param_t att_p;
|
||||||
param_t att_i;
|
param_t att_i;
|
||||||
param_t att_d;
|
param_t att_d;
|
||||||
@@ -139,12 +125,6 @@ static int parameters_init(struct mc_att_control_param_handles *h)
|
|||||||
h->yaw_awu = param_find("MC_YAWPOS_AWU");
|
h->yaw_awu = param_find("MC_YAWPOS_AWU");
|
||||||
h->yaw_lim = param_find("MC_YAWPOS_LIM");
|
h->yaw_lim = param_find("MC_YAWPOS_LIM");
|
||||||
|
|
||||||
// h->yawrate_p = param_find("MC_YAWRATE_P");
|
|
||||||
// h->yawrate_i = param_find("MC_YAWRATE_I");
|
|
||||||
// h->yawrate_d = param_find("MC_YAWRATE_D");
|
|
||||||
// h->yawrate_awu = param_find("MC_YAWRATE_AWU");
|
|
||||||
// h->yawrate_lim = param_find("MC_YAWRATE_LIM");
|
|
||||||
|
|
||||||
h->att_p = param_find("MC_ATT_P");
|
h->att_p = param_find("MC_ATT_P");
|
||||||
h->att_i = param_find("MC_ATT_I");
|
h->att_i = param_find("MC_ATT_I");
|
||||||
h->att_d = param_find("MC_ATT_D");
|
h->att_d = param_find("MC_ATT_D");
|
||||||
@@ -165,12 +145,6 @@ static int parameters_update(const struct mc_att_control_param_handles *h, struc
|
|||||||
param_get(h->yaw_awu, &(p->yaw_awu));
|
param_get(h->yaw_awu, &(p->yaw_awu));
|
||||||
param_get(h->yaw_lim, &(p->yaw_lim));
|
param_get(h->yaw_lim, &(p->yaw_lim));
|
||||||
|
|
||||||
// param_get(h->yawrate_p, &(p->yawrate_p));
|
|
||||||
// param_get(h->yawrate_i, &(p->yawrate_i));
|
|
||||||
// param_get(h->yawrate_d, &(p->yawrate_d));
|
|
||||||
// param_get(h->yawrate_awu, &(p->yawrate_awu));
|
|
||||||
// param_get(h->yawrate_lim, &(p->yawrate_lim));
|
|
||||||
|
|
||||||
param_get(h->att_p, &(p->att_p));
|
param_get(h->att_p, &(p->att_p));
|
||||||
param_get(h->att_i, &(p->att_i));
|
param_get(h->att_i, &(p->att_i));
|
||||||
param_get(h->att_d, &(p->att_d));
|
param_get(h->att_d, &(p->att_d));
|
||||||
@@ -199,8 +173,6 @@ void multirotor_control_attitude(const struct vehicle_attitude_setpoint_s *att_s
|
|||||||
|
|
||||||
static int motor_skip_counter = 0;
|
static int motor_skip_counter = 0;
|
||||||
|
|
||||||
// static PID_t yaw_pos_controller;
|
|
||||||
// static PID_t yaw_speed_controller;
|
|
||||||
static PID_t pitch_controller;
|
static PID_t pitch_controller;
|
||||||
static PID_t roll_controller;
|
static PID_t roll_controller;
|
||||||
|
|
||||||
@@ -214,14 +186,10 @@ void multirotor_control_attitude(const struct vehicle_attitude_setpoint_s *att_s
|
|||||||
parameters_init(&h);
|
parameters_init(&h);
|
||||||
parameters_update(&h, &p);
|
parameters_update(&h, &p);
|
||||||
|
|
||||||
// pid_init(&yaw_pos_controller, p.yaw_p, p.yaw_i, p.yaw_d, p.yaw_awu,
|
|
||||||
// PID_MODE_DERIVATIV_SET, 154);
|
|
||||||
// pid_init(&yaw_speed_controller, p.yawrate_p, p.yawrate_i, p.yawrate_d, p.yawrate_awu,
|
|
||||||
// PID_MODE_DERIVATIV_SET);
|
|
||||||
pid_init(&pitch_controller, p.att_p, p.att_i, p.att_d, p.att_awu,
|
pid_init(&pitch_controller, p.att_p, p.att_i, p.att_d, p.att_awu,
|
||||||
PID_MODE_DERIVATIV_SET);
|
p.att_lim, PID_MODE_DERIVATIV_SET);
|
||||||
pid_init(&roll_controller, p.att_p, p.att_i, p.att_d, p.att_awu,
|
pid_init(&roll_controller, p.att_p, p.att_i, p.att_d, p.att_awu,
|
||||||
PID_MODE_DERIVATIV_SET);
|
p.att_lim, PID_MODE_DERIVATIV_SET);
|
||||||
|
|
||||||
initialized = true;
|
initialized = true;
|
||||||
}
|
}
|
||||||
@@ -230,12 +198,12 @@ void multirotor_control_attitude(const struct vehicle_attitude_setpoint_s *att_s
|
|||||||
if (motor_skip_counter % 1000 == 0) {
|
if (motor_skip_counter % 1000 == 0) {
|
||||||
/* update parameters from storage */
|
/* update parameters from storage */
|
||||||
parameters_update(&h, &p);
|
parameters_update(&h, &p);
|
||||||
|
|
||||||
/* apply parameters */
|
/* apply parameters */
|
||||||
// pid_set_parameters(&yaw_pos_controller, p.yaw_p, p.yaw_i, p.yaw_d, p.yaw_awu);
|
|
||||||
// pid_set_parameters(&yaw_speed_controller, p.yawrate_p, p.yawrate_i, p.yawrate_d, p.yawrate_awu);
|
|
||||||
pid_set_parameters(&pitch_controller, p.att_p, p.att_i, p.att_d, p.att_awu);
|
|
||||||
pid_set_parameters(&roll_controller, p.att_p, p.att_i, p.att_d, p.att_awu);
|
|
||||||
printf("att ctrl: delays: %d us sens->ctrl, rate: %d Hz, input: %d Hz\n", sensor_delay, (int)(1.0f/deltaT), (int)(1.0f/dT_input));
|
printf("att ctrl: delays: %d us sens->ctrl, rate: %d Hz, input: %d Hz\n", sensor_delay, (int)(1.0f/deltaT), (int)(1.0f/dT_input));
|
||||||
|
|
||||||
|
pid_set_parameters(&pitch_controller, p.att_p, p.att_i, p.att_d, p.att_awu, p.att_lim);
|
||||||
|
pid_set_parameters(&roll_controller, p.att_p, p.att_i, p.att_d, p.att_awu, p.att_lim);
|
||||||
}
|
}
|
||||||
|
|
||||||
/* calculate current control outputs */
|
/* calculate current control outputs */
|
||||||
@@ -251,10 +219,7 @@ void multirotor_control_attitude(const struct vehicle_attitude_setpoint_s *att_s
|
|||||||
/* control yaw rate */
|
/* control yaw rate */
|
||||||
rates_sp->yaw = p.yaw_p * atan2f(sinf(att->yaw - att_sp->yaw_body), cosf(att->yaw - att_sp->yaw_body));
|
rates_sp->yaw = p.yaw_p * atan2f(sinf(att->yaw - att_sp->yaw_body), cosf(att->yaw - att_sp->yaw_body));
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
rates_sp->thrust = att_sp->thrust;
|
rates_sp->thrust = att_sp->thrust;
|
||||||
|
|
||||||
|
|
||||||
motor_skip_counter++;
|
motor_skip_counter++;
|
||||||
}
|
}
|
||||||
|
|||||||
+193
-11
@@ -68,10 +68,10 @@ __EXPORT float get_distance_to_next_waypoint(double lat_now, double lon_now, dou
|
|||||||
|
|
||||||
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next)
|
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next)
|
||||||
{
|
{
|
||||||
double lat_now_rad = lat_now / 180.0 * M_PI;
|
double lat_now_rad = lat_now * M_DEG_TO_RAD;
|
||||||
double lon_now_rad = lon_now / 180.0 * M_PI;
|
double lon_now_rad = lon_now * M_DEG_TO_RAD;
|
||||||
double lat_next_rad = lat_next / 180.0 * M_PI;
|
double lat_next_rad = lat_next * M_DEG_TO_RAD;
|
||||||
double lon_next_rad = lon_next / 180.0 * M_PI;
|
double lon_next_rad = lon_next * M_DEG_TO_RAD;
|
||||||
|
|
||||||
double d_lat = lat_next_rad - lat_now_rad;
|
double d_lat = lat_next_rad - lat_now_rad;
|
||||||
double d_lon = lon_next_rad - lon_now_rad;
|
double d_lon = lon_next_rad - lon_now_rad;
|
||||||
@@ -79,13 +79,195 @@ __EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, doub
|
|||||||
/* conscious mix of double and float trig function to maximize speed and efficiency */
|
/* conscious mix of double and float trig function to maximize speed and efficiency */
|
||||||
float theta = atan2f(sin(d_lon) * cos(lat_next_rad) , cos(lat_now_rad) * sin(lat_next_rad) - sin(lat_now_rad) * cos(lat_next_rad) * cos(d_lon));
|
float theta = atan2f(sin(d_lon) * cos(lat_next_rad) , cos(lat_now_rad) * sin(lat_next_rad) - sin(lat_now_rad) * cos(lat_next_rad) * cos(d_lon));
|
||||||
|
|
||||||
if (theta < M_PI_F) {
|
theta = _wrapPI(theta);
|
||||||
theta += 2.0f * M_PI_F;
|
|
||||||
}
|
|
||||||
|
|
||||||
if (theta > M_PI_F) {
|
|
||||||
theta -= 2.0f * M_PI_F;
|
|
||||||
}
|
|
||||||
|
|
||||||
return theta;
|
return theta;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// Additional functions - @author Doug Weibel <douglas.weibel@colorado.edu>
|
||||||
|
|
||||||
|
__EXPORT crosstrack_error_s get_distance_to_line(double lat_now, double lon_now, double lat_start, double lon_start, double lat_end, double lon_end)
|
||||||
|
{
|
||||||
|
// This function returns the distance to the nearest point on the track line. Distance is positive if current
|
||||||
|
// position is right of the track and negative if left of the track as seen from a point on the track line
|
||||||
|
// headed towards the end point.
|
||||||
|
|
||||||
|
crosstrack_error_s return_var;
|
||||||
|
float dist_to_end;
|
||||||
|
float bearing_end;
|
||||||
|
float bearing_track;
|
||||||
|
float bearing_diff;
|
||||||
|
|
||||||
|
return_var.error = true; // Set error flag, cleared when valid result calculated.
|
||||||
|
return_var.past_end = false;
|
||||||
|
return_var.distance = 0.0f;
|
||||||
|
return_var.bearing = 0.0f;
|
||||||
|
|
||||||
|
// Return error if arguments are bad
|
||||||
|
if(lat_now == 0.0d || lon_now == 0.0d || lat_start == 0.0d || lon_start == 0.0d || lat_end == 0.0d || lon_end == 0.0d) return return_var;
|
||||||
|
|
||||||
|
bearing_end = get_bearing_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
|
||||||
|
bearing_track = get_bearing_to_next_waypoint(lat_start, lon_start, lat_end, lon_end);
|
||||||
|
bearing_diff = bearing_track - bearing_end;
|
||||||
|
bearing_diff = _wrapPI(bearing_diff);
|
||||||
|
|
||||||
|
// Return past_end = true if past end point of line
|
||||||
|
if(bearing_diff > M_PI_2_F || bearing_diff < -M_PI_2_F) {
|
||||||
|
return_var.past_end = true;
|
||||||
|
return_var.error = false;
|
||||||
|
return return_var;
|
||||||
|
}
|
||||||
|
|
||||||
|
dist_to_end = get_distance_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
|
||||||
|
return_var.distance = (dist_to_end)*sin(bearing_diff);
|
||||||
|
if(sin(bearing_diff) >=0 ) {
|
||||||
|
return_var.bearing = _wrapPI(bearing_track - M_PI_2_F);
|
||||||
|
} else {
|
||||||
|
return_var.bearing = _wrapPI(bearing_track + M_PI_2_F);
|
||||||
|
}
|
||||||
|
return_var.error = false;
|
||||||
|
|
||||||
|
return return_var;
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
__EXPORT crosstrack_error_s get_distance_to_arc(double lat_now, double lon_now, double lat_center, double lon_center,
|
||||||
|
float radius, float arc_start_bearing, float arc_sweep)
|
||||||
|
{
|
||||||
|
// This function returns the distance to the nearest point on the track arc. Distance is positive if current
|
||||||
|
// position is right of the arc and negative if left of the arc as seen from the closest point on the arc and
|
||||||
|
// headed towards the end point.
|
||||||
|
crosstrack_error_s return_var;
|
||||||
|
|
||||||
|
// Determine if the current position is inside or outside the sector between the line from the center
|
||||||
|
// to the arc start and the line from the center to the arc end
|
||||||
|
float bearing_sector_start;
|
||||||
|
float bearing_sector_end;
|
||||||
|
float bearing_now = get_bearing_to_next_waypoint(lat_now, lon_now, lat_center, lon_center);
|
||||||
|
bool in_sector;
|
||||||
|
|
||||||
|
return_var.error = true; // Set error flag, cleared when valid result calculated.
|
||||||
|
return_var.past_end = false;
|
||||||
|
return_var.distance = 0.0f;
|
||||||
|
return_var.bearing = 0.0f;
|
||||||
|
|
||||||
|
// Return error if arguments are bad
|
||||||
|
if(lat_now == 0.0d || lon_now == 0.0d || lat_center == 0.0d || lon_center == 0.0d || radius == 0.0d) return return_var;
|
||||||
|
|
||||||
|
|
||||||
|
if(arc_sweep >= 0) {
|
||||||
|
bearing_sector_start = arc_start_bearing;
|
||||||
|
bearing_sector_end = arc_start_bearing + arc_sweep;
|
||||||
|
if(bearing_sector_end > 2.0f*M_PI_F) bearing_sector_end -= M_TWOPI_F;
|
||||||
|
} else {
|
||||||
|
bearing_sector_end = arc_start_bearing;
|
||||||
|
bearing_sector_start = arc_start_bearing - arc_sweep;
|
||||||
|
if(bearing_sector_start < 0.0) bearing_sector_start += M_TWOPI_F;
|
||||||
|
}
|
||||||
|
in_sector = false;
|
||||||
|
|
||||||
|
// Case where sector does not span zero
|
||||||
|
if(bearing_sector_end >= bearing_sector_start && bearing_now >= bearing_sector_start && bearing_now <= bearing_sector_end) in_sector = true;
|
||||||
|
|
||||||
|
// Case where sector does span zero
|
||||||
|
if(bearing_sector_end < bearing_sector_start && ( bearing_now > bearing_sector_start || bearing_now < bearing_sector_end ) ) in_sector = true;
|
||||||
|
|
||||||
|
// If in the sector then calculate distance and bearing to closest point
|
||||||
|
if(in_sector) {
|
||||||
|
return_var.past_end = false;
|
||||||
|
float dist_to_center = get_distance_to_next_waypoint(lat_now, lon_now, lat_center, lon_center);
|
||||||
|
|
||||||
|
if(dist_to_center <= radius) {
|
||||||
|
return_var.distance = radius - dist_to_center;
|
||||||
|
return_var.bearing = bearing_now + M_PI_F;
|
||||||
|
} else {
|
||||||
|
return_var.distance = dist_to_center - radius;
|
||||||
|
return_var.bearing = bearing_now;
|
||||||
|
}
|
||||||
|
|
||||||
|
// If out of the sector then calculate dist and bearing to start or end point
|
||||||
|
} else {
|
||||||
|
|
||||||
|
// Use the approximation that 111,111 meters in the y direction is 1 degree (of latitude)
|
||||||
|
// and 111,111 * cos(latitude) meters in the x direction is 1 degree (of longitude) to
|
||||||
|
// calculate the position of the start and end points. We should not be doing this often
|
||||||
|
// as this function generally will not be called repeatedly when we are out of the sector.
|
||||||
|
|
||||||
|
// TO DO - this is messed up and won't compile
|
||||||
|
float start_disp_x = radius * sin(arc_start_bearing);
|
||||||
|
float start_disp_y = radius * cos(arc_start_bearing);
|
||||||
|
float end_disp_x = radius * sin(_wrapPI(arc_start_bearing+arc_sweep));
|
||||||
|
float end_disp_y = radius * cos(_wrapPI(arc_start_bearing+arc_sweep));
|
||||||
|
float lon_start = lon_now + start_disp_x/111111.0d;
|
||||||
|
float lat_start = lat_now + start_disp_y*cos(lat_now)/111111.0d;
|
||||||
|
float lon_end = lon_now + end_disp_x/111111.0d;
|
||||||
|
float lat_end = lat_now + end_disp_y*cos(lat_now)/111111.0d;
|
||||||
|
float dist_to_start = get_distance_to_next_waypoint(lat_now, lon_now, lat_start, lon_start);
|
||||||
|
float dist_to_end = get_distance_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
|
||||||
|
if(dist_to_start < dist_to_end) {
|
||||||
|
return_var.distance = dist_to_start;
|
||||||
|
return_var.bearing = get_bearing_to_next_waypoint(lat_now, lon_now, lat_start, lon_start);
|
||||||
|
} else {
|
||||||
|
return_var.past_end = true;
|
||||||
|
return_var.distance = dist_to_end;
|
||||||
|
return_var.bearing = get_bearing_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
return_var.bearing = _wrapPI(return_var.bearing);
|
||||||
|
return_var.error = false;
|
||||||
|
return return_var;
|
||||||
|
}
|
||||||
|
|
||||||
|
float _wrapPI(float bearing)
|
||||||
|
{
|
||||||
|
|
||||||
|
while (bearing > M_PI_F) {
|
||||||
|
bearing = bearing - M_TWOPI_F;
|
||||||
|
}
|
||||||
|
while (bearing <= -M_PI_F) {
|
||||||
|
bearing = bearing + M_TWOPI_F;
|
||||||
|
}
|
||||||
|
return bearing;
|
||||||
|
}
|
||||||
|
|
||||||
|
float _wrap2PI(float bearing)
|
||||||
|
{
|
||||||
|
|
||||||
|
while (bearing >= M_TWOPI_F) {
|
||||||
|
bearing = bearing - M_TWOPI_F;
|
||||||
|
}
|
||||||
|
while (bearing < 0.0f) {
|
||||||
|
bearing = bearing + M_TWOPI_F;
|
||||||
|
}
|
||||||
|
return bearing;
|
||||||
|
}
|
||||||
|
|
||||||
|
float _wrap180(float bearing)
|
||||||
|
{
|
||||||
|
|
||||||
|
while (bearing > 180.0f) {
|
||||||
|
bearing = bearing - 360.0f;
|
||||||
|
}
|
||||||
|
while (bearing <= -180.0f) {
|
||||||
|
bearing = bearing + 360.0f;
|
||||||
|
}
|
||||||
|
return bearing;
|
||||||
|
}
|
||||||
|
|
||||||
|
float _wrap360(float bearing)
|
||||||
|
{
|
||||||
|
|
||||||
|
while (bearing >= 360.0f) {
|
||||||
|
bearing = bearing - 360.0f;
|
||||||
|
}
|
||||||
|
while (bearing < 0.0f) {
|
||||||
|
bearing = bearing + 360.0f;
|
||||||
|
}
|
||||||
|
return bearing;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
@@ -42,8 +42,31 @@
|
|||||||
* @author Thomas Gubler <thomasgubler@student.ethz.ch>
|
* @author Thomas Gubler <thomasgubler@student.ethz.ch>
|
||||||
* @author Julian Oes <joes@student.ethz.ch>
|
* @author Julian Oes <joes@student.ethz.ch>
|
||||||
* @author Lorenz Meier <lm@inf.ethz.ch>
|
* @author Lorenz Meier <lm@inf.ethz.ch>
|
||||||
|
* Additional functions - @author Doug Weibel <douglas.weibel@colorado.edu>
|
||||||
*/
|
*/
|
||||||
|
|
||||||
|
|
||||||
|
#include <stdbool.h>
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
bool error; // Flag that the calculation failed
|
||||||
|
bool past_end; // Flag indicating we are past the end of the line/arc segment
|
||||||
|
float distance; // Distance in meters to closest point on line/arc
|
||||||
|
float bearing; // Bearing in radians to closest point on line/arc
|
||||||
|
} crosstrack_error_s;
|
||||||
|
|
||||||
__EXPORT float get_distance_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
|
__EXPORT float get_distance_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
|
||||||
|
|
||||||
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
|
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
|
||||||
|
|
||||||
|
//
|
||||||
|
|
||||||
|
__EXPORT crosstrack_error_s get_distance_to_line(double lat_now, double lon_now, double lat_start, double lon_start, double lat_end, double lon_end);
|
||||||
|
|
||||||
|
__EXPORT crosstrack_error_s get_distance_to_arc(double lat_now, double lon_now, double lat_center, double lon_center,
|
||||||
|
float radius, float arc_start_bearing, float arc_sweep);
|
||||||
|
|
||||||
|
float _wrap180(float bearing);
|
||||||
|
float _wrap360(float bearing);
|
||||||
|
float _wrapPI(float bearing);
|
||||||
|
float _wrap2PI(float bearing);
|
||||||
+40
-58
@@ -43,12 +43,13 @@
|
|||||||
#include <math.h>
|
#include <math.h>
|
||||||
|
|
||||||
__EXPORT void pid_init(PID_t *pid, float kp, float ki, float kd, float intmax,
|
__EXPORT void pid_init(PID_t *pid, float kp, float ki, float kd, float intmax,
|
||||||
uint8_t mode)
|
float limit, uint8_t mode)
|
||||||
{
|
{
|
||||||
pid->kp = kp;
|
pid->kp = kp;
|
||||||
pid->ki = ki;
|
pid->ki = ki;
|
||||||
pid->kd = kd;
|
pid->kd = kd;
|
||||||
pid->intmax = intmax;
|
pid->intmax = intmax;
|
||||||
|
pid->limit = limit;
|
||||||
pid->mode = mode;
|
pid->mode = mode;
|
||||||
pid->count = 0;
|
pid->count = 0;
|
||||||
pid->saturated = 0;
|
pid->saturated = 0;
|
||||||
@@ -58,7 +59,7 @@ __EXPORT void pid_init(PID_t *pid, float kp, float ki, float kd, float intmax,
|
|||||||
pid->error_previous = 0;
|
pid->error_previous = 0;
|
||||||
pid->integral = 0;
|
pid->integral = 0;
|
||||||
}
|
}
|
||||||
__EXPORT int pid_set_parameters(PID_t *pid, float kp, float ki, float kd, float intmax)
|
__EXPORT int pid_set_parameters(PID_t *pid, float kp, float ki, float kd, float intmax, float limit)
|
||||||
{
|
{
|
||||||
int ret = 0;
|
int ret = 0;
|
||||||
|
|
||||||
@@ -86,7 +87,12 @@ __EXPORT int pid_set_parameters(PID_t *pid, float kp, float ki, float kd, float
|
|||||||
ret = 1;
|
ret = 1;
|
||||||
}
|
}
|
||||||
|
|
||||||
// pid->limit = limit;
|
if (isfinite(limit)) {
|
||||||
|
pid->limit = limit;
|
||||||
|
} else {
|
||||||
|
ret = 1;
|
||||||
|
}
|
||||||
|
|
||||||
return ret;
|
return ret;
|
||||||
}
|
}
|
||||||
|
|
||||||
@@ -122,72 +128,48 @@ __EXPORT float pid_calculate(PID_t *pid, float sp, float val, float val_dot, flo
|
|||||||
|
|
||||||
float i, d;
|
float i, d;
|
||||||
pid->sp = sp;
|
pid->sp = sp;
|
||||||
|
|
||||||
|
// Calculated current error value
|
||||||
float error = pid->sp - val;
|
float error = pid->sp - val;
|
||||||
|
|
||||||
if (pid->saturated && (pid->integral * error > 0)) {
|
if (isfinite(error)) { // Why is this necessary? DEW
|
||||||
//Output is saturated and the integral would get bigger (positive or negative)
|
|
||||||
i = pid->integral;
|
|
||||||
|
|
||||||
//Reset saturation. If we are still saturated this will be set again at output limit check.
|
|
||||||
pid->saturated = 0;
|
|
||||||
|
|
||||||
} else {
|
|
||||||
i = pid->integral + (error * dt);
|
|
||||||
}
|
|
||||||
|
|
||||||
// Anti-Windup. Needed if we don't use the saturation above.
|
|
||||||
if (pid->intmax != 0.0f) {
|
|
||||||
if (i > pid->intmax) {
|
|
||||||
pid->integral = pid->intmax;
|
|
||||||
|
|
||||||
} else if (i < -pid->intmax) {
|
|
||||||
|
|
||||||
pid->integral = -pid->intmax;
|
|
||||||
|
|
||||||
} else {
|
|
||||||
pid->integral = i;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
if (pid->mode == PID_MODE_DERIVATIV_CALC) {
|
|
||||||
d = (error - pid->error_previous) / dt;
|
|
||||||
|
|
||||||
} else if (pid->mode == PID_MODE_DERIVATIV_SET) {
|
|
||||||
d = -val_dot;
|
|
||||||
|
|
||||||
} else {
|
|
||||||
d = 0.0f;
|
|
||||||
}
|
|
||||||
|
|
||||||
if (pid->kd == 0.0f) {
|
|
||||||
d = 0.0f;
|
|
||||||
}
|
|
||||||
|
|
||||||
if (pid->ki == 0.0f) {
|
|
||||||
i = 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
float p;
|
|
||||||
|
|
||||||
if (pid->kp == 0.0f) {
|
|
||||||
p = 0.0f;
|
|
||||||
} else {
|
|
||||||
p = error;
|
|
||||||
}
|
|
||||||
|
|
||||||
if (isfinite(error)) {
|
|
||||||
pid->error_previous = error;
|
pid->error_previous = error;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// Calculate or measured current error derivative
|
||||||
|
|
||||||
|
if (pid->mode == PID_MODE_DERIVATIV_CALC) {
|
||||||
|
d = (error - pid->error_previous) / dt;
|
||||||
|
} else if (pid->mode == PID_MODE_DERIVATIV_SET) {
|
||||||
|
d = -val_dot;
|
||||||
|
} else {
|
||||||
|
d = 0.0f;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Calculate the error integral and check for saturation
|
||||||
|
i = pid->integral + (error * dt);
|
||||||
|
if( fabs((error * pid->kp) + (i * pid->ki) + (d * pid->kd)) > pid->limit ||
|
||||||
|
fabs(i) > pid->intmax )
|
||||||
|
{
|
||||||
|
i = pid->integral; // If saturated then do not update integral value
|
||||||
|
pid->saturated = 1;
|
||||||
|
} else {
|
||||||
|
if (!isfinite(i)) {
|
||||||
|
i = 0;
|
||||||
|
}
|
||||||
|
pid->integral = i;
|
||||||
|
pid->saturated = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Calculate the output. Limit output magnitude to pid->limit
|
||||||
float output = (pid->error_previous * pid->kp) + (i * pid->ki) + (d * pid->kd);
|
float output = (pid->error_previous * pid->kp) + (i * pid->ki) + (d * pid->kd);
|
||||||
|
if (output > pid->limit) output = pid->limit;
|
||||||
|
if (output < -pid->limit) output = -pid->limit;
|
||||||
|
|
||||||
if (isfinite(output)) {
|
if (isfinite(output)) {
|
||||||
pid->last_output = output;
|
pid->last_output = output;
|
||||||
}
|
}
|
||||||
|
|
||||||
if (!isfinite(pid->integral)) {
|
|
||||||
pid->integral = 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
return pid->last_output;
|
return pid->last_output;
|
||||||
}
|
}
|
||||||
|
|||||||
@@ -49,6 +49,8 @@
|
|||||||
#define PID_MODE_DERIVATIV_CALC 0
|
#define PID_MODE_DERIVATIV_CALC 0
|
||||||
/* Use PID_MODE_DERIVATIV_SET if you have the derivative already (Gyros, Kalman) */
|
/* Use PID_MODE_DERIVATIV_SET if you have the derivative already (Gyros, Kalman) */
|
||||||
#define PID_MODE_DERIVATIV_SET 1
|
#define PID_MODE_DERIVATIV_SET 1
|
||||||
|
// Use PID_MODE_DERIVATIV_NONE for a PI controller (vs PID)
|
||||||
|
#define PID_MODE_DERIVATIV_NONE 9
|
||||||
|
|
||||||
typedef struct {
|
typedef struct {
|
||||||
float kp;
|
float kp;
|
||||||
@@ -65,8 +67,8 @@ typedef struct {
|
|||||||
uint8_t saturated;
|
uint8_t saturated;
|
||||||
} PID_t;
|
} PID_t;
|
||||||
|
|
||||||
__EXPORT void pid_init(PID_t *pid, float kp, float ki, float kd, float intmax, uint8_t mode);
|
__EXPORT void pid_init(PID_t *pid, float kp, float ki, float kd, float intmax, float limit, uint8_t mode);
|
||||||
__EXPORT int pid_set_parameters(PID_t *pid, float kp, float ki, float kd, float intmax);
|
__EXPORT int pid_set_parameters(PID_t *pid, float kp, float ki, float kd, float intmax, float limit);
|
||||||
//void pid_set(PID_t *pid, float sp);
|
//void pid_set(PID_t *pid, float sp);
|
||||||
__EXPORT float pid_calculate(PID_t *pid, float sp, float val, float val_dot, float dt);
|
__EXPORT float pid_calculate(PID_t *pid, float sp, float val, float val_dot, float dt);
|
||||||
|
|
||||||
|
|||||||
@@ -544,6 +544,8 @@ extern int matherr _PARAMS((struct exception *e));
|
|||||||
#define M_1_PI 0.31830988618379067154
|
#define M_1_PI 0.31830988618379067154
|
||||||
#define M_2_PI 0.63661977236758134308
|
#define M_2_PI 0.63661977236758134308
|
||||||
#define M_2_SQRTPI 1.12837916709551257390
|
#define M_2_SQRTPI 1.12837916709551257390
|
||||||
|
#define M_DEG_TO_RAD 0.01745329251994
|
||||||
|
#define M_RAD_TO_DEG 57.2957795130823
|
||||||
#define M_SQRT2 1.41421356237309504880
|
#define M_SQRT2 1.41421356237309504880
|
||||||
#define M_SQRT1_2 0.70710678118654752440
|
#define M_SQRT1_2 0.70710678118654752440
|
||||||
#define M_LN2LO 1.9082149292705877000E-10
|
#define M_LN2LO 1.9082149292705877000E-10
|
||||||
@@ -568,6 +570,8 @@ extern int matherr _PARAMS((struct exception *e));
|
|||||||
#define M_1_PI_F 0.31830988618379067154f
|
#define M_1_PI_F 0.31830988618379067154f
|
||||||
#define M_2_PI_F 0.63661977236758134308f
|
#define M_2_PI_F 0.63661977236758134308f
|
||||||
#define M_2_SQRTPI_F 1.12837916709551257390f
|
#define M_2_SQRTPI_F 1.12837916709551257390f
|
||||||
|
#define M_DEG_TO_RAD_F 0.01745329251994f
|
||||||
|
#define M_RAD_TO_DEG_F 57.2957795130823f
|
||||||
#define M_SQRT2_F 1.41421356237309504880f
|
#define M_SQRT2_F 1.41421356237309504880f
|
||||||
#define M_SQRT1_2_F 0.70710678118654752440f
|
#define M_SQRT1_2_F 0.70710678118654752440f
|
||||||
#define M_LN2LO_F 1.9082149292705877000E-10f
|
#define M_LN2LO_F 1.9082149292705877000E-10f
|
||||||
|
|||||||
Reference in New Issue
Block a user