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Arduino 9dof
/*****************************************************************
LSM9DS0_AHRS.ino
SFE_LSM9DS0 Library AHRS Data Fusion Example Code
Jim Lindblom @ SparkFun Electronics
Original Creation Date: February 18, 2014
https://github.com/sparkfun/LSM9DS0_Breakout
Modified by Kris Winer, April 4, 2014
The LSM9DS0 is a versatile 9DOF sensor. It has a built-in
accelerometer, gyroscope, and magnetometer. Very cool! Plus it
functions over either SPI or I2C.
This Arduino sketch utilizes Jim Lindblom's SFE_LSM9DS0 library to generate the basic sensor data
for use in two sensor fusion algorithms becoming increasingly popular with DIY quadcopter and robotics engineers.
Like the original LSM9SD0_simple.ino sketch, it'll demo the following:
* How to create a LSM9DS0 object, using a constructor (global
variables section).
* How to use the begin() function of the LSM9DS0 class.
* How to read the gyroscope, accelerometer, and magnetometer
using the readGryo(), readAccel(), readMag() functions and the
gx, gy, gz, ax, ay, az, mx, my, and mz variables.
* How to calculate actual acceleration, rotation speed, magnetic
field strength using the calcAccel(), calcGyro() and calcMag()
functions.
In addition, the sketch will demo:
* How to check for data updates using interrupts
* How to display output at a rate different from the sensor data update and fusion filter update rates
* How to specify the accelerometer anti-aliasing (low-pass) filter rate
* How to use the data from the LSM9DS0 to fuse the sensor data into a quaternion representation of the sensor frame
orientation relative to a fixed Earth frame providing absolute orientation information for subsequent use.
* An example of how to use the quaternion data to generate standard aircraft orientation data in the form of
Tait-Bryan angles representing the sensor yaw, pitch, and roll angles suitable for any vehicle stablization control application.
Hardware setup: This library supports communicating with the
LSM9DS0 over either I2C or SPI. If you're using I2C, these are
the only connections that need to be made:
LSM9DS0 --------- Arduino
SCL ---------- SCL (A5 on older 'Duinos')
SDA ---------- SDA (A4 on older 'Duinos')
VDD ------------- 3.3V
GND ------------- GND
DRDYG-------------4 (gyro data ready interrupt, can be any digital pin)
INTX1-------------3 (accelerometer data ready interrupt, can be any digital pin)
INTX2-------------2 (magnetometer data ready interrupt, can be any digital pin)
(CSG, CSXM, SDOG, and SDOXM should all be pulled high jumpers on
the breakout board will do this for you.)
If you're using SPI, here is an example hardware setup:
LSM9DS0 --------- Arduino
CSG -------------- 9
CSXM ------------- 10
SDOG ------------- 12
SDOXM ------------ 12 (tied to SDOG)
SCL -------------- 13
SDA -------------- 11
VDD -------------- 3.3V
GND -------------- GND
The LSM9DS0 has a maximum voltage of 3.6V. Make sure you power it
off the 3.3V rail! And either use level shifters between SCL
and SDA or just use a 3.3V Arduino Pro.
In addition, this sketch uses a Nokia 5110 48 x 84 pixel display which requires
digital pins 5 - 9 described below. If using SPI you might need to press one of the A0 - A3 pins
into service as a digital input instead.
Development environment specifics:
IDE: Arduino 1.0.5
Hardware Platform: Arduino Pro 3.3V/8MHz
LSM9DS0 Breakout Version: 1.0
This code is beerware. If you see me (or any other SparkFun
employee) at the local, and you've found our code helpful, please
buy us a round!
Distributed as-is; no warranty is given.
*****************************************************************/
// The SFE_LSM9DS0 requires both the SPI and Wire libraries.
// Unfortunately, you'll need to include both in the Arduino
// sketch, before including the SFE_LSM9DS0 library.
#include <SPI.h> // Included for SFE_LSM9DS0 library
#include <Wire.h>
#include <SFE_LSM9DS0.h>
///////////////////////
// Example I2C Setup //
///////////////////////
// Comment out this section if you're using SPI
// SDO_XM and SDO_G are both grounded, so our addresses are:
#define LSM9DS0_XM 0x1D // Would be 0x1E if SDO_XM is LOW
#define LSM9DS0_G 0x6B // Would be 0x6A if SDO_G is LOW
// Create an instance of the LSM9DS0 library called `dof` the
// parameters for this constructor are:
// [SPI or I2C Mode declaration],[gyro I2C address],[xm I2C add.]
LSM9DS0 dof(MODE_I2C, LSM9DS0_G, LSM9DS0_XM);
///////////////////////////////
// Interrupt Pin Definitions //
///////////////////////////////
const byte INT1XM = 2; // INT1XM tells us when accel data is ready
const byte INT2XM = 3; // INT2XM tells us when mag data is ready
const byte DRDYG = 4; // DRDYG tells us when gyro data is ready
// global constants for 9 DoF fusion and AHRS (Attitude and Heading Reference System)
#define GyroMeasError PI * (40.0f / 180.0f) // gyroscope measurement error in rads/s (shown as 3 deg/s)
#define GyroMeasDrift PI * (0.0f / 180.0f) // gyroscope measurement drift in rad/s/s (shown as 0.0 deg/s/s)
// There is a tradeoff in the beta parameter between accuracy and response speed.
// In the original Madgwick study, beta of 0.041 (corresponding to GyroMeasError of 2.7 degrees/s) was found to give optimal accuracy.
// However, with this value, the LSM9SD0 response time is about 10 seconds to a stable initial quaternion.
// Subsequent changes also require a longish lag time to a stable output, not fast enough for a quadcopter or robot car!
// By increasing beta (GyroMeasError) by about a factor of fifteen, the response time constant is reduced to ~2 sec
// I haven't noticed any reduction in solution accuracy. This is essentially the I coefficient in a PID control sense;
// the bigger the feedback coefficient, the faster the solution converges, usually at the expense of accuracy.
// In any case, this is the free parameter in the Madgwick filtering and fusion scheme.
#define beta sqrt(3.0f / 4.0f) * GyroMeasError // compute beta
#define zeta sqrt(3.0f / 4.0f) * GyroMeasDrift // compute zeta, the other free parameter in the Madgwick scheme usually set to a small or zero value
float pitch, yaw, roll, heading;
float deltat = 0.0f; // integration interval for both filter schemes
uint16_t lastUpdate = 0; // used to calculate integration interval
uint16_t now = 0; // used to calculate integration interval
float ax, ay, az, gx, gy, gz, mx, my, mz; // variables to hold latest sensor data values
float q[4] = {1.0f, 0.0f, 0.0f, 0.0f}; // vector to hold quaternion
// packet structure for InvenSense teapot demo
uint8_t teapotPacket[14] = { '$', 0x02, 0,0, 0,0, 0,0, 0,0, 0x00, 0x00, '\r', '\n' };
void setup()
{
Serial.begin(115200); // Start serial at 115200 bps
// Set up interrupt pins as inputs:
pinMode(INT1XM, INPUT);
pinMode(INT2XM, INPUT);
pinMode(DRDYG, INPUT);
// begin() returns a 16-bit value which includes both the gyro
// and accelerometers WHO_AM_I response. You can check this to
// make sure communication was successful.
uint16_t status = dof.begin();
Serial.print("LSM9DS0 WHO_AM_I's returned: 0x");
Serial.println(status, HEX);
Serial.println("Should be 0x49D4");
Serial.println();
// Set data output ranges; choose lowest ranges for maximum resolution
// Accelerometer scale can be: A_SCALE_2G, A_SCALE_4G, A_SCALE_6G, A_SCALE_8G, or A_SCALE_16G
dof.setAccelScale(dof.A_SCALE_2G);
// Gyro scale can be: G_SCALE__245, G_SCALE__500, or G_SCALE__2000DPS
dof.setGyroScale(dof.G_SCALE_245DPS);
// Magnetometer scale can be: M_SCALE_2GS, M_SCALE_4GS, M_SCALE_8GS, M_SCALE_12GS
dof.setMagScale(dof.M_SCALE_2GS);
// Set output data rates
// Accelerometer output data rate (ODR) can be: A_ODR_3125 (3.225 Hz), A_ODR_625 (6.25 Hz), A_ODR_125 (12.5 Hz), A_ODR_25, A_ODR_50,
// A_ODR_100, A_ODR_200, A_ODR_400, A_ODR_800, A_ODR_1600 (1600 Hz)
dof.setAccelODR(dof.A_ODR_100); // Set accelerometer update rate at 100 Hz
// Accelerometer anti-aliasing filter rate can be 50, 194, 362, or 763 Hz
// Anti-aliasing acts like a low-pass filter allowing oversampling of accelerometer and rejection of high-frequency spurious noise.
// Strategy here is to effectively oversample accelerometer at 100 Hz and use a 50 Hz anti-aliasing (low-pass) filter frequency
// to get a smooth ~150 Hz filter update rate
dof.setAccelABW(dof.A_ABW_50); // Choose lowest filter setting for low noise
// Gyro output data rates can be: 95 Hz (bandwidth 12.5 or 25 Hz), 190 Hz (bandwidth 12.5, 25, 50, or 70 Hz)
// 380 Hz (bandwidth 20, 25, 50, 100 Hz), or 760 Hz (bandwidth 30, 35, 50, 100 Hz)
dof.setGyroODR(dof.G_ODR_190_BW_125); // Set gyro update rate to 190 Hz with the smallest bandwidth for low noise
// Magnetometer output data rate can be: 3.125 (ODR_3125), 6.25 (ODR_625), 12.5 (ODR_125), 25, 50, or 100 Hz
dof.setMagODR(dof.M_ODR_125); // Set magnetometer to update every 80 ms
}
void loop()
{
if(digitalRead(DRDYG)) { // When new gyro data is ready
dof.readGyro(); // Read raw gyro data
gx = dof.calcGyro(dof.gx); // Convert to degrees per seconds
gy = dof.calcGyro(dof.gy);
gz = dof.calcGyro(dof.gz);
}
if(digitalRead(INT1XM)) { // When new accelerometer data is ready
dof.readAccel(); // Read raw accelerometer data
ax = dof.calcAccel(dof.ax); // Convert to g's
ay = dof.calcAccel(dof.ay);
az = dof.calcAccel(dof.az);
}
if(digitalRead(INT2XM)) { // When new magnetometer data is ready
dof.readMag(); // Read raw magnetometer data
mx = dof.calcMag(dof.mx); // Convert to Gauss
my = dof.calcMag(dof.my);
mz = dof.calcMag(dof.mz);
}
now = micros();
deltat = ((now - lastUpdate)/1000000.0f); // set integration time by time elapsed since last filter update
lastUpdate = now;
// Sensors x- and y-axes are aligned but magnetometer z-axis (+ down) is opposite to z-axis (+ up) of accelerometer and gyro!
// This is ok by aircraft orientation standards!
// Pass gyro rate as rad/s
MadgwickQuaternionUpdate(ax, ay, az, gx*PI/180.0f, gy*PI/180.0f, gz*PI/180.0f, mx, my, mz);
// Define output variables from updated quaternion---these are Tait-Bryan angles, commonly used in aircraft orientation.
// In this coordinate system, the positive z-axis is down toward Earth.
// Yaw is the angle between Sensor x-axis and Earth magnetic North (or true North if corrected for local declination),
// looking down on the sensor positive yaw is counterclockwise.
// Pitch is angle between sensor x-axis and Earth ground plane, toward the Earth is positive, up toward the sky is negative.
// Roll is angle between sensor y-axis and Earth ground plane, y-axis up is positive roll.
// These arise from the definition of the homogeneous rotation matrix constructed from quaternions.
// Tait-Bryan angles as well as Euler angles are non-commutative; that is, to get the correct orientation the rotations must be
// applied in the correct order which for this configuration is yaw, pitch, and then roll.
// For more see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles which has additional links.
//yaw = atan2(2.0f * (q[1] * q[2] + q[0] * q[3]), q[0] * q[0] + q[1] * q[1] - q[2] * q[2] - q[3] * q[3]);
//pitch = -asin(2.0f * (q[1] * q[3] - q[0] * q[2]));
//roll = atan2(2.0f * (q[0] * q[1] + q[2] * q[3]), q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3]);
//pitch *= 180.0f / PI;
//yaw *= 180.0f / PI;
//roll *= 180.0f / PI;
// display quaternion values in InvenSense Teapot demo format:
teapotPacket[2] = q[0];
teapotPacket[3] = q[0];
teapotPacket[4] = q[1];
teapotPacket[5] = q[1];
teapotPacket[6] = q[2];
teapotPacket[7] = q[2];
teapotPacket[8] = q[3];
teapotPacket[9] = q[3];
Serial.write(teapotPacket, 14);
teapotPacket[11]++; // packetCount, loops at 0xFF on purpose
//Serial.print(yaw, 2);
//Serial.print(", ");
//Serial.print(pitch, 2);
//Serial.print(", ");
//Serial.println(roll, 2);
// With ODR settings of 400 Hz, 380 Hz, and 25 Hz for the accelerometer, gyro, and magnetometer, respectively,
// the filter is updating at a ~125 Hz rate using the Madgwick scheme and ~165 Hz using the Mahony scheme
// even though the display refreshes at only 2 Hz.
// The filter update rate can be increased by reducing the rate of data reading. The optimal implementation is
// one which balances the competing rates so they are about the same; that is, the filter updates the sensor orientation
// at about the same rate the data is changing. Of course, other implementations are possible. One might consider
// updating the filter at twice the average new data rate to allow for finite filter convergence times.
// The filter update rate is determined mostly by the mathematical steps in the respective algorithms,
// the processor speed (8 MHz for the 3.3V Pro Mini), and the sensor ODRs, especially the magnetometer ODR:
// smaller ODRs for the magnetometer produce the above rates, maximum magnetometer ODR of 100 Hz produces
// filter update rates of ~110 and ~135 Hz for the Madgwick and Mahony schemes, respectively.
// This is presumably because the magnetometer read takes longer than the gyro or accelerometer reads.
// With low ODR settings of 100 Hz, 95 Hz, and 6.25 Hz for the accelerometer, gyro, and magnetometer, respectively,
// the filter is updating at a ~150 Hz rate using the Madgwick scheme and ~200 Hz using the Mahony scheme.
// These filter update rates should be fast enough to maintain accurate platform orientation for
// stabilization control of a fast-moving robot or quadcopter. Compare to the update rate of 200 Hz
// produced by the on-board Digital Motion Processor of Invensense's MPU6050 6 DoF and MPU9150 9DoF sensors.
// The 3.3 V 8 MHz Pro Mini is doing pretty well!
}
// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
{
float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability
float norm;
float hx, hy, _2bx, _2bz;
float s1, s2, s3, s4;
float qDot1, qDot2, qDot3, qDot4;
// Auxiliary variables to avoid repeated arithmetic
float _2q1mx;
float _2q1my;
float _2q1mz;
float _2q2mx;
float _4bx;
float _4bz;
float _2q1 = 2.0f * q1;
float _2q2 = 2.0f * q2;
float _2q3 = 2.0f * q3;
float _2q4 = 2.0f * q4;
float _2q1q3 = 2.0f * q1 * q3;
float _2q3q4 = 2.0f * q3 * q4;
float q1q1 = q1 * q1;
float q1q2 = q1 * q2;
float q1q3 = q1 * q3;
float q1q4 = q1 * q4;
float q2q2 = q2 * q2;
float q2q3 = q2 * q3;
float q2q4 = q2 * q4;
float q3q3 = q3 * q3;
float q3q4 = q3 * q4;
float q4q4 = q4 * q4;
// Normalise accelerometer measurement
norm = sqrt(ax * ax + ay * ay + az * az);
if (norm == 0.0f) return; // handle NaN
norm = 1.0f/norm;
ax *= norm;
ay *= norm;
az *= norm;
// Normalise magnetometer measurement
norm = sqrt(mx * mx + my * my + mz * mz);
if (norm == 0.0f) return; // handle NaN
norm = 1.0f/norm;
mx *= norm;
my *= norm;
mz *= norm;
// Reference direction of Earth's magnetic field
_2q1mx = 2.0f * q1 * mx;
_2q1my = 2.0f * q1 * my;
_2q1mz = 2.0f * q1 * mz;
_2q2mx = 2.0f * q2 * mx;
hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
_2bx = sqrt(hx * hx + hy * hy);
_2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
_4bx = 2.0f * _2bx;
_4bz = 2.0f * _2bz;
// Gradient decent algorithm corrective step
s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4); // normalise step magnitude
norm = 1.0f/norm;
s1 *= norm;
s2 *= norm;
s3 *= norm;
s4 *= norm;
// Compute rate of change of quaternion
qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
// Integrate to yield quaternion
q1 += qDot1 * deltat;
q2 += qDot2 * deltat;
q3 += qDot3 * deltat;
q4 += qDot4 * deltat;
norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion
norm = 1.0f/norm;
q[0] = q1 * norm;
q[1] = q2 * norm;
q[2] = q3 * norm;
q[3] = q4 * norm;
}
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