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/*
* @file attitude_estimator_so3_main.cpp
*
* @author Hyon Lim <limhyon@gmail.com>
* @author Anton Babushkin <anton.babushkin@me.com>
*
* Implementation of nonlinear complementary filters on the SO(3).
* This code performs attitude estimation by using accelerometer, gyroscopes and magnetometer.
* Result is provided as quaternion, 1-2-3 Euler angle and rotation matrix.
*
* Theory of nonlinear complementary filters on the SO(3) is based on [1].
* Quaternion realization of [1] is based on [2].
* Optmized quaternion update code is based on Sebastian Madgwick's implementation.
*
* References
* [1] Mahony, R.; Hamel, T.; Pflimlin, Jean-Michel, "Nonlinear Complementary Filters on the Special Orthogonal Group," Automatic Control, IEEE Transactions on , vol.53, no.5, pp.1203,1218, June 2008
* [2] Euston, M.; Coote, P.; Mahony, R.; Jonghyuk Kim; Hamel, T., "A complementary filter for attitude estimation of a fixed-wing UAV," Intelligent Robots and Systems, 2008. IROS 2008. IEEE/RSJ International Conference on , vol., no., pp.340,345, 22-26 Sept. 2008
*/
#include <nuttx/config.h>
#include <unistd.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <stdbool.h>
#include <poll.h>
#include <fcntl.h>
#include <float.h>
#include <nuttx/sched.h>
#include <sys/prctl.h>
#include <termios.h>
#include <errno.h>
#include <limits.h>
#include <math.h>
#include <uORB/uORB.h>
#include <uORB/topics/debug_key_value.h>
#include <uORB/topics/sensor_combined.h>
#include <uORB/topics/vehicle_attitude.h>
#include <uORB/topics/vehicle_control_mode.h>
#include <uORB/topics/parameter_update.h>
#include <drivers/drv_hrt.h>
#include <systemlib/systemlib.h>
#include <systemlib/perf_counter.h>
#include <systemlib/err.h>
#ifdef __cplusplus
extern "C" {
#endif
#include "attitude_estimator_so3_params.h"
#ifdef __cplusplus
}
#endif
extern "C" __EXPORT int attitude_estimator_so3_main(int argc, char *argv[]);
static bool thread_should_exit = false; /**< Deamon exit flag */
static bool thread_running = false; /**< Deamon status flag */
static int attitude_estimator_so3_task; /**< Handle of deamon task / thread */
//! Auxiliary variables to reduce number of repeated operations
static float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; /** quaternion of sensor frame relative to auxiliary frame */
static float dq0 = 0.0f, dq1 = 0.0f, dq2 = 0.0f, dq3 = 0.0f; /** quaternion of sensor frame relative to auxiliary frame */
static float gyro_bias[3] = {0.0f, 0.0f, 0.0f}; /** bias estimation */
static float q0q0, q0q1, q0q2, q0q3;
static float q1q1, q1q2, q1q3;
static float q2q2, q2q3;
static float q3q3;
static bool bFilterInit = false;
/**
* Mainloop of attitude_estimator_so3.
*/
int attitude_estimator_so3_thread_main(int argc, char *argv[]);
/**
* Print the correct usage.
*/
static void usage(const char *reason);
/* Function prototypes */
float invSqrt(float number);
void NonlinearSO3AHRSinit(float ax, float ay, float az, float mx, float my, float mz);
void NonlinearSO3AHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float twoKp, float twoKi, float dt);
static void
usage(const char *reason)
{
if (reason)
fprintf(stderr, "%s\n", reason);
fprintf(stderr, "usage: attitude_estimator_so3 {start|stop|status}\n");
exit(1);
}
/**
* The attitude_estimator_so3 app only briefly exists to start
* the background job. The stack size assigned in the
* Makefile does only apply to this management task.
*
* The actual stack size should be set in the call
* to task_spawn_cmd().
*/
int attitude_estimator_so3_main(int argc, char *argv[])
{
if (argc < 2) {
usage("missing command");
}
if (!strcmp(argv[1], "start")) {
if (thread_running) {
warnx("already running\n");
/* this is not an error */
exit(0);
}
thread_should_exit = false;
attitude_estimator_so3_task = task_spawn_cmd("attitude_estimator_so3",
SCHED_DEFAULT,
SCHED_PRIORITY_MAX - 5,
14000,
attitude_estimator_so3_thread_main,
(argv) ? (char * const *)&argv[2] : (char * const *)NULL);
exit(0);
}
if (!strcmp(argv[1], "stop")) {
thread_should_exit = true;
while (thread_running){
usleep(200000);
}
warnx("stopped");
exit(0);
}
if (!strcmp(argv[1], "status")) {
if (thread_running) {
warnx("running");
exit(0);
} else {
warnx("not started");
exit(1);
}
exit(0);
}
usage("unrecognized command");
exit(1);
}
//---------------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
float invSqrt(float number)
{
volatile long i;
volatile float x, y;
volatile const float f = 1.5F;
x = number * 0.5F;
y = number;
i = * (( long * ) &y);
i = 0x5f375a86 - ( i >> 1 );
y = * (( float * ) &i);
y = y * ( f - ( x * y * y ) );
return y;
}
//! Using accelerometer, sense the gravity vector.
//! Using magnetometer, sense yaw.
void NonlinearSO3AHRSinit(float ax, float ay, float az, float mx, float my, float mz)
{
float initialRoll, initialPitch;
float cosRoll, sinRoll, cosPitch, sinPitch;
float magX, magY;
float initialHdg, cosHeading, sinHeading;
initialRoll = atan2(-ay, -az);
initialPitch = atan2(ax, -az);
cosRoll = cosf(initialRoll);
sinRoll = sinf(initialRoll);
cosPitch = cosf(initialPitch);
sinPitch = sinf(initialPitch);
magX = mx * cosPitch + my * sinRoll * sinPitch + mz * cosRoll * sinPitch;
magY = my * cosRoll - mz * sinRoll;
initialHdg = atan2f(-magY, magX);
cosRoll = cosf(initialRoll * 0.5f);
sinRoll = sinf(initialRoll * 0.5f);
cosPitch = cosf(initialPitch * 0.5f);
sinPitch = sinf(initialPitch * 0.5f);
cosHeading = cosf(initialHdg * 0.5f);
sinHeading = sinf(initialHdg * 0.5f);
q0 = cosRoll * cosPitch * cosHeading + sinRoll * sinPitch * sinHeading;
q1 = sinRoll * cosPitch * cosHeading - cosRoll * sinPitch * sinHeading;
q2 = cosRoll * sinPitch * cosHeading + sinRoll * cosPitch * sinHeading;
q3 = cosRoll * cosPitch * sinHeading - sinRoll * sinPitch * cosHeading;
// auxillary variables to reduce number of repeated operations, for 1st pass
q0q0 = q0 * q0;
q0q1 = q0 * q1;
q0q2 = q0 * q2;
q0q3 = q0 * q3;
q1q1 = q1 * q1;
q1q2 = q1 * q2;
q1q3 = q1 * q3;
q2q2 = q2 * q2;
q2q3 = q2 * q3;
q3q3 = q3 * q3;
}
void NonlinearSO3AHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float twoKp, float twoKi, float dt)
{
float recipNorm;
float halfex = 0.0f, halfey = 0.0f, halfez = 0.0f;
// Make filter converge to initial solution faster
// This function assumes you are in static position.
// WARNING : in case air reboot, this can cause problem. But this is very unlikely happen.
if(bFilterInit == false) {
NonlinearSO3AHRSinit(ax,ay,az,mx,my,mz);
bFilterInit = true;
}
//! If magnetometer measurement is available, use it.
if(!((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f))) {
float hx, hy, hz, bx, bz;
float halfwx, halfwy, halfwz;
// Normalise magnetometer measurement
// Will sqrt work better? PX4 system is powerful enough?
recipNorm = invSqrt(mx * mx + my * my + mz * mz);
mx *= recipNorm;
my *= recipNorm;
mz *= recipNorm;
// Reference direction of Earth's magnetic field
hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
hz = 2.0f * mx * (q1q3 - q0q2) + 2.0f * my * (q2q3 + q0q1) + 2.0f * mz * (0.5f - q1q1 - q2q2);
bx = sqrt(hx * hx + hy * hy);
bz = hz;
// Estimated direction of magnetic field
halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);
// Error is sum of cross product between estimated direction and measured direction of field vectors
halfex += (my * halfwz - mz * halfwy);
halfey += (mz * halfwx - mx * halfwz);
halfez += (mx * halfwy - my * halfwx);
}
// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
float halfvx, halfvy, halfvz;
// Normalise accelerometer measurement
recipNorm = invSqrt(ax * ax + ay * ay + az * az);
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
// Estimated direction of gravity and magnetic field
halfvx = q1q3 - q0q2;
halfvy = q0q1 + q2q3;
halfvz = q0q0 - 0.5f + q3q3;
// Error is sum of cross product between estimated direction and measured direction of field vectors
halfex += ay * halfvz - az * halfvy;
halfey += az * halfvx - ax * halfvz;
halfez += ax * halfvy - ay * halfvx;
}
// Apply feedback only when valid data has been gathered from the accelerometer or magnetometer
if(halfex != 0.0f && halfey != 0.0f && halfez != 0.0f) {
// Compute and apply integral feedback if enabled
if(twoKi > 0.0f) {
gyro_bias[0] += twoKi * halfex * dt; // integral error scaled by Ki
gyro_bias[1] += twoKi * halfey * dt;
gyro_bias[2] += twoKi * halfez * dt;
// apply integral feedback
gx += gyro_bias[0];
gy += gyro_bias[1];
gz += gyro_bias[2];
}
else {
gyro_bias[0] = 0.0f; // prevent integral windup
gyro_bias[1] = 0.0f;
gyro_bias[2] = 0.0f;
}
// Apply proportional feedback
gx += twoKp * halfex;
gy += twoKp * halfey;
gz += twoKp * halfez;
}
//! Integrate rate of change of quaternion
#if 0
gx *= (0.5f * dt); // pre-multiply common factors
gy *= (0.5f * dt);
gz *= (0.5f * dt);
#endif
// Time derivative of quaternion. q_dot = 0.5*q\otimes omega.
//! q_k = q_{k-1} + dt*\dot{q}
//! \dot{q} = 0.5*q \otimes P(\omega)
dq0 = 0.5f*(-q1 * gx - q2 * gy - q3 * gz);
dq1 = 0.5f*(q0 * gx + q2 * gz - q3 * gy);
dq2 = 0.5f*(q0 * gy - q1 * gz + q3 * gx);
dq3 = 0.5f*(q0 * gz + q1 * gy - q2 * gx);
q0 += dt*dq0;
q1 += dt*dq1;
q2 += dt*dq2;
q3 += dt*dq3;
// Normalise quaternion
recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
// Auxiliary variables to avoid repeated arithmetic
q0q0 = q0 * q0;
q0q1 = q0 * q1;
q0q2 = q0 * q2;
q0q3 = q0 * q3;
q1q1 = q1 * q1;
q1q2 = q1 * q2;
q1q3 = q1 * q3;
q2q2 = q2 * q2;
q2q3 = q2 * q3;
q3q3 = q3 * q3;
}
/*
* Nonliner complementary filter on SO(3), attitude estimator main function.
*
* Estimates the attitude once started.
*
* @param argc number of commandline arguments (plus command name)
* @param argv strings containing the arguments
*/
int attitude_estimator_so3_thread_main(int argc, char *argv[])
{
//! Time constant
float dt = 0.005f;
/* output euler angles */
float euler[3] = {0.0f, 0.0f, 0.0f};
/* Initialization */
float Rot_matrix[9] = {1.f, 0.0f, 0.0f, 0.0f, 1.f, 0.0f, 0.0f, 0.0f, 1.f }; /**< init: identity matrix */
float acc[3] = {0.0f, 0.0f, 0.0f};
float gyro[3] = {0.0f, 0.0f, 0.0f};
float mag[3] = {0.0f, 0.0f, 0.0f};
warnx("main thread started");
struct sensor_combined_s raw;
memset(&raw, 0, sizeof(raw));
//! Initialize attitude vehicle uORB message.
struct vehicle_attitude_s att;
memset(&att, 0, sizeof(att));
struct vehicle_control_mode_s control_mode;
memset(&control_mode, 0, sizeof(control_mode));
uint64_t last_data = 0;
uint64_t last_measurement = 0;
/* subscribe to raw data */
int sub_raw = orb_subscribe(ORB_ID(sensor_combined));
/* rate-limit raw data updates to 333 Hz (sensors app publishes at 200, so this is just paranoid) */
orb_set_interval(sub_raw, 3);
/* subscribe to param changes */
int sub_params = orb_subscribe(ORB_ID(parameter_update));
/* subscribe to control mode */
int sub_control_mode = orb_subscribe(ORB_ID(vehicle_control_mode));
/* advertise attitude */
//orb_advert_t pub_att = orb_advertise(ORB_ID(vehicle_attitude), &att);
//orb_advert_t att_pub = -1;
orb_advert_t att_pub = orb_advertise(ORB_ID(vehicle_attitude), &att);
int loopcounter = 0;
thread_running = true;
// XXX write this out to perf regs
/* keep track of sensor updates */
uint64_t sensor_last_timestamp[3] = {0, 0, 0};
struct attitude_estimator_so3_params so3_comp_params;
struct attitude_estimator_so3_param_handles so3_comp_param_handles;
/* initialize parameter handles */
parameters_init(&so3_comp_param_handles);
parameters_update(&so3_comp_param_handles, &so3_comp_params);
uint64_t start_time = hrt_absolute_time();
bool initialized = false;
bool state_initialized = false;
float gyro_offsets[3] = { 0.0f, 0.0f, 0.0f };
unsigned offset_count = 0;
/* register the perf counter */
perf_counter_t so3_comp_loop_perf = perf_alloc(PC_ELAPSED, "attitude_estimator_so3");
/* Main loop*/
while (!thread_should_exit) {
struct pollfd fds[2];
fds[0].fd = sub_raw;
fds[0].events = POLLIN;
fds[1].fd = sub_params;
fds[1].events = POLLIN;
int ret = poll(fds, 2, 1000);
if (ret < 0) {
/* XXX this is seriously bad - should be an emergency */
} else if (ret == 0) {
/* check if we're in HIL - not getting sensor data is fine then */
orb_copy(ORB_ID(vehicle_control_mode), sub_control_mode, &control_mode);
if (!control_mode.flag_system_hil_enabled) {
warnx("WARNING: Not getting sensors - sensor app running?");
}
} else {
/* only update parameters if they changed */
if (fds[1].revents & POLLIN) {
/* read from param to clear updated flag */
struct parameter_update_s update;
orb_copy(ORB_ID(parameter_update), sub_params, &update);
/* update parameters */
parameters_update(&so3_comp_param_handles, &so3_comp_params);
}
/* only run filter if sensor values changed */
if (fds[0].revents & POLLIN) {
/* get latest measurements */
orb_copy(ORB_ID(sensor_combined), sub_raw, &raw);
if (!initialized) {
gyro_offsets[0] += raw.gyro_rad_s[0];
gyro_offsets[1] += raw.gyro_rad_s[1];
gyro_offsets[2] += raw.gyro_rad_s[2];
offset_count++;
if (hrt_absolute_time() > start_time + 3000000l) {
initialized = true;
gyro_offsets[0] /= offset_count;
gyro_offsets[1] /= offset_count;
gyro_offsets[2] /= offset_count;
warnx("gyro initialized, offsets: %.5f %.5f %.5f", (double)gyro_offsets[0], (double)gyro_offsets[1], (double)gyro_offsets[2]);
}
} else {
perf_begin(so3_comp_loop_perf);
/* Calculate data time difference in seconds */
dt = (raw.timestamp - last_measurement) / 1000000.0f;
last_measurement = raw.timestamp;
/* Fill in gyro measurements */
if (sensor_last_timestamp[0] != raw.timestamp) {
sensor_last_timestamp[0] = raw.timestamp;
}
gyro[0] = raw.gyro_rad_s[0] - gyro_offsets[0];
gyro[1] = raw.gyro_rad_s[1] - gyro_offsets[1];
gyro[2] = raw.gyro_rad_s[2] - gyro_offsets[2];
/* update accelerometer measurements */
if (sensor_last_timestamp[1] != raw.accelerometer_timestamp) {
sensor_last_timestamp[1] = raw.accelerometer_timestamp;
}
acc[0] = raw.accelerometer_m_s2[0];
acc[1] = raw.accelerometer_m_s2[1];
acc[2] = raw.accelerometer_m_s2[2];
/* update magnetometer measurements */
if (sensor_last_timestamp[2] != raw.magnetometer_timestamp) {
sensor_last_timestamp[2] = raw.magnetometer_timestamp;
}
mag[0] = raw.magnetometer_ga[0];
mag[1] = raw.magnetometer_ga[1];
mag[2] = raw.magnetometer_ga[2];
/* initialize with good values once we have a reasonable dt estimate */
if (!state_initialized && dt < 0.05f && dt > 0.001f) {
state_initialized = true;
warnx("state initialized");
}
/* do not execute the filter if not initialized */
if (!state_initialized) {
continue;
}
// NOTE : Accelerometer is reversed.
// Because proper mount of PX4 will give you a reversed accelerometer readings.
NonlinearSO3AHRSupdate(gyro[0], gyro[1], gyro[2],
-acc[0], -acc[1], -acc[2],
mag[0], mag[1], mag[2],
so3_comp_params.Kp,
so3_comp_params.Ki,
dt);
// Convert q->R, This R converts inertial frame to body frame.
Rot_matrix[0] = q0q0 + q1q1 - q2q2 - q3q3;// 11
Rot_matrix[1] = 2.f * (q1*q2 + q0*q3); // 12
Rot_matrix[2] = 2.f * (q1*q3 - q0*q2); // 13
Rot_matrix[3] = 2.f * (q1*q2 - q0*q3); // 21
Rot_matrix[4] = q0q0 - q1q1 + q2q2 - q3q3;// 22
Rot_matrix[5] = 2.f * (q2*q3 + q0*q1); // 23
Rot_matrix[6] = 2.f * (q1*q3 + q0*q2); // 31
Rot_matrix[7] = 2.f * (q2*q3 - q0*q1); // 32
Rot_matrix[8] = q0q0 - q1q1 - q2q2 + q3q3;// 33
//1-2-3 Representation.
//Equation (290)
//Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors, James Diebel.
// Existing PX4 EKF code was generated by MATLAB which uses coloum major order matrix.
euler[0] = atan2f(Rot_matrix[5], Rot_matrix[8]); //! Roll
euler[1] = -asinf(Rot_matrix[2]); //! Pitch
euler[2] = atan2f(Rot_matrix[1], Rot_matrix[0]); //! Yaw
/* swap values for next iteration, check for fatal inputs */
if (isfinite(euler[0]) && isfinite(euler[1]) && isfinite(euler[2])) {
// Publish only finite euler angles
att.roll = euler[0] - so3_comp_params.roll_off;
att.pitch = euler[1] - so3_comp_params.pitch_off;
att.yaw = euler[2] - so3_comp_params.yaw_off;
} else {
/* due to inputs or numerical failure the output is invalid, skip it */
// Due to inputs or numerical failure the output is invalid
warnx("infinite euler angles, rotation matrix:");
warnx("%.3f %.3f %.3f", (double)Rot_matrix[0], (double)Rot_matrix[1], (double)Rot_matrix[2]);
warnx("%.3f %.3f %.3f", (double)Rot_matrix[3], (double)Rot_matrix[4], (double)Rot_matrix[5]);
warnx("%.3f %.3f %.3f", (double)Rot_matrix[6], (double)Rot_matrix[7], (double)Rot_matrix[8]);
// Don't publish anything
continue;
}
if (last_data > 0 && raw.timestamp > last_data + 12000) {
warnx("sensor data missed");
}
last_data = raw.timestamp;
/* send out */
att.timestamp = raw.timestamp;
// Quaternion
att.q[0] = q0;
att.q[1] = q1;
att.q[2] = q2;
att.q[3] = q3;
att.q_valid = true;
// Euler angle rate. But it needs to be investigated again.
/*
att.rollspeed = 2.0f*(-q1*dq0 + q0*dq1 - q3*dq2 + q2*dq3);
att.pitchspeed = 2.0f*(-q2*dq0 + q3*dq1 + q0*dq2 - q1*dq3);
att.yawspeed = 2.0f*(-q3*dq0 -q2*dq1 + q1*dq2 + q0*dq3);
*/
att.rollspeed = gyro[0];
att.pitchspeed = gyro[1];
att.yawspeed = gyro[2];
att.rollacc = 0;
att.pitchacc = 0;
att.yawacc = 0;
/* TODO: Bias estimation required */
memcpy(&att.rate_offsets, &(gyro_bias), sizeof(att.rate_offsets));
/* copy rotation matrix */
memcpy(&att.R, Rot_matrix, sizeof(float)*9);
att.R_valid = true;
// Publish
if (att_pub > 0) {
orb_publish(ORB_ID(vehicle_attitude), att_pub, &att);
} else {
warnx("NaN in roll/pitch/yaw estimate!");
orb_advertise(ORB_ID(vehicle_attitude), &att);
}
perf_end(so3_comp_loop_perf);
}
}
}
loopcounter++;
}
thread_running = false;
return 0;
}