Panusorn Chinsakuljaroen
imu for l432kc
MPU9250.h
- Committer:
- sunninety1
- Date:
- 2018-12-05
- Revision:
- 3:4a1bc31c360f
File content as of revision 3:4a1bc31c360f:
#ifndef MPU9250_H
#define MPU9250_H
#include "mbed.h"
#include "math.h"
// See also MPU-9250 Register Map and Descriptions, Revision 4.0, RM-MPU-9250A-00, Rev. 1.4, 9/9/2013 for registers not listed in
// above document; the MPU9250 and MPU9150 are virtually identical but the latter has a different register map
//
//Magnetometer Registers
#define AK8963_ADDRESS 0x0C<<1
#define WHO_AM_I_AK8963 0x00 // should return 0x48
#define INFO 0x01
#define AK8963_ST1 0x02 // data ready status bit 0
#define AK8963_XOUT_L 0x03 // data
#define AK8963_XOUT_H 0x04
#define AK8963_YOUT_L 0x05
#define AK8963_YOUT_H 0x06
#define AK8963_ZOUT_L 0x07
#define AK8963_ZOUT_H 0x08
#define AK8963_ST2 0x09 // Data overflow bit 3 and data read error status bit 2
#define AK8963_CNTL 0x0A // Power down (0000), single-measurement (0001), self-test (1000) and Fuse ROM (1111) modes on bits 3:0
#define AK8963_ASTC 0x0C // Self test control
#define AK8963_I2CDIS 0x0F // I2C disable
#define AK8963_ASAX 0x10 // Fuse ROM x-axis sensitivity adjustment value
#define AK8963_ASAY 0x11 // Fuse ROM y-axis sensitivity adjustment value
#define AK8963_ASAZ 0x12 // Fuse ROM z-axis sensitivity adjustment value
#define SELF_TEST_X_GYRO 0x00
#define SELF_TEST_Y_GYRO 0x01
#define SELF_TEST_Z_GYRO 0x02
/*#define X_FINE_GAIN 0x03 // [7:0] fine gain
#define Y_FINE_GAIN 0x04
#define Z_FINE_GAIN 0x05
#define XA_OFFSET_H 0x06 // User-defined trim values for accelerometer
#define XA_OFFSET_L_TC 0x07
#define YA_OFFSET_H 0x08
#define YA_OFFSET_L_TC 0x09
#define ZA_OFFSET_H 0x0A
#define ZA_OFFSET_L_TC 0x0B */
#define SELF_TEST_X_ACCEL 0x0D
#define SELF_TEST_Y_ACCEL 0x0E
#define SELF_TEST_Z_ACCEL 0x0F
#define SELF_TEST_A 0x10
#define XG_OFFSET_H 0x13 // User-defined trim values for gyroscope
#define XG_OFFSET_L 0x14
#define YG_OFFSET_H 0x15
#define YG_OFFSET_L 0x16
#define ZG_OFFSET_H 0x17
#define ZG_OFFSET_L 0x18
#define SMPLRT_DIV 0x19
#define CONFIG 0x1A
#define GYRO_CONFIG 0x1B
#define ACCEL_CONFIG 0x1C
#define ACCEL_CONFIG2 0x1D
#define LP_ACCEL_ODR 0x1E
#define WOM_THR 0x1F
#define MOT_DUR 0x20 // Duration counter threshold for motion interrupt generation, 1 kHz rate, LSB = 1 ms
#define ZMOT_THR 0x21 // Zero-motion detection threshold bits [7:0]
#define ZRMOT_DUR 0x22 // Duration counter threshold for zero motion interrupt generation, 16 Hz rate, LSB = 64 ms
#define FIFO_EN 0x23
#define I2C_MST_CTRL 0x24
#define I2C_SLV0_ADDR 0x25
#define I2C_SLV0_REG 0x26
#define I2C_SLV0_CTRL 0x27
#define I2C_SLV1_ADDR 0x28
#define I2C_SLV1_REG 0x29
#define I2C_SLV1_CTRL 0x2A
#define I2C_SLV2_ADDR 0x2B
#define I2C_SLV2_REG 0x2C
#define I2C_SLV2_CTRL 0x2D
#define I2C_SLV3_ADDR 0x2E
#define I2C_SLV3_REG 0x2F
#define I2C_SLV3_CTRL 0x30
#define I2C_SLV4_ADDR 0x31
#define I2C_SLV4_REG 0x32
#define I2C_SLV4_DO 0x33
#define I2C_SLV4_CTRL 0x34
#define I2C_SLV4_DI 0x35
#define I2C_MST_STATUS 0x36
#define INT_PIN_CFG 0x37
#define INT_ENABLE 0x38
#define DMP_INT_STATUS 0x39 // Check DMP interrupt
#define INT_STATUS 0x3A
#define ACCEL_XOUT_H 0x3B
#define ACCEL_XOUT_L 0x3C
#define ACCEL_YOUT_H 0x3D
#define ACCEL_YOUT_L 0x3E
#define ACCEL_ZOUT_H 0x3F
#define ACCEL_ZOUT_L 0x40
#define TEMP_OUT_H 0x41
#define TEMP_OUT_L 0x42
#define GYRO_XOUT_H 0x43
#define GYRO_XOUT_L 0x44
#define GYRO_YOUT_H 0x45
#define GYRO_YOUT_L 0x46
#define GYRO_ZOUT_H 0x47
#define GYRO_ZOUT_L 0x48
#define EXT_SENS_DATA_00 0x49
#define EXT_SENS_DATA_01 0x4A
#define EXT_SENS_DATA_02 0x4B
#define EXT_SENS_DATA_03 0x4C
#define EXT_SENS_DATA_04 0x4D
#define EXT_SENS_DATA_05 0x4E
#define EXT_SENS_DATA_06 0x4F
#define EXT_SENS_DATA_07 0x50
#define EXT_SENS_DATA_08 0x51
#define EXT_SENS_DATA_09 0x52
#define EXT_SENS_DATA_10 0x53
#define EXT_SENS_DATA_11 0x54
#define EXT_SENS_DATA_12 0x55
#define EXT_SENS_DATA_13 0x56
#define EXT_SENS_DATA_14 0x57
#define EXT_SENS_DATA_15 0x58
#define EXT_SENS_DATA_16 0x59
#define EXT_SENS_DATA_17 0x5A
#define EXT_SENS_DATA_18 0x5B
#define EXT_SENS_DATA_19 0x5C
#define EXT_SENS_DATA_20 0x5D
#define EXT_SENS_DATA_21 0x5E
#define EXT_SENS_DATA_22 0x5F
#define EXT_SENS_DATA_23 0x60
#define MOT_DETECT_STATUS 0x61
#define I2C_SLV0_DO 0x63
#define I2C_SLV1_DO 0x64
#define I2C_SLV2_DO 0x65
#define I2C_SLV3_DO 0x66
#define I2C_MST_wait_ms_CTRL 0x67
#define SIGNAL_PATH_RESET 0x68
#define MOT_DETECT_CTRL 0x69
#define USER_CTRL 0x6A // Bit 7 enable DMP, bit 3 reset DMP
#define PWR_MGMT_1 0x6B // Device defaults to the SLEEP mode
#define PWR_MGMT_2 0x6C
#define DMP_BANK 0x6D // Activates a specific bank in the DMP
#define DMP_RW_PNT 0x6E // Set read/write pointer to a specific start address in specified DMP bank
#define DMP_REG 0x6F // Register in DMP from which to read or to which to write
#define DMP_REG_1 0x70
#define DMP_REG_2 0x71
#define FIFO_COUNTH 0x72
#define FIFO_COUNTL 0x73
#define FIFO_R_W 0x74
#define WHO_AM_I_MPU9250 0x75 // Should return 0x71
#define XA_OFFSET_H 0x77
#define XA_OFFSET_L 0x78
#define YA_OFFSET_H 0x7A
#define YA_OFFSET_L 0x7B
#define ZA_OFFSET_H 0x7D
#define ZA_OFFSET_L 0x7E
// Using the MSENSR-9250 breakout board, ADO is set to 0
// Seven-bit device address is 110100 for ADO = 0 and 110101 for ADO = 1
//mbed uses the eight-bit device address, so shift seven-bit addresses left by one!
#define ADO 0
#if ADO
#define MPU9250_ADDRESS 0x69<<1 // Device address when ADO = 1
#else
#define MPU9250_ADDRESS 0x68<<1 // Device address when ADO = 0
#endif
// Set initial input parameters
enum Ascale {
AFS_2G = 0,
AFS_4G,
AFS_8G,
AFS_16G
};
enum Gscale {
GFS_250DPS = 0,
GFS_500DPS,
GFS_1000DPS,
GFS_2000DPS
};
enum Mscale {
MFS_14BITS = 0, // 0.6 mG per LSB
MFS_16BITS // 0.15 mG per LSB
};
uint8_t Ascale = AFS_2G; // AFS_2G, AFS_4G, AFS_8G, AFS_16G
uint8_t Gscale = GFS_250DPS; // GFS_250DPS, GFS_500DPS, GFS_1000DPS, GFS_2000DPS
uint8_t Mscale = MFS_16BITS; // MFS_14BITS or MFS_16BITS, 14-bit or 16-bit magnetometer resolution
uint8_t Mmode = 0x06; // Either 8 Hz 0x02) or 100 Hz (0x06) magnetometer data ODR
float aRes, gRes, mRes; // scale resolutions per LSB for the sensors
//Set up I2C, (SDA,SCL)
I2C i2c(D4, D5);
DigitalOut myled(LED1);
// Pin definitions
int intPin = 12; // These can be changed, 2 and 3 are the Arduinos ext int pins
int16_t accelCount[3]; // Stores the 16-bit signed accelerometer sensor output
int16_t gyroCount[3]; // Stores the 16-bit signed gyro sensor output
int16_t magCount[3]; // Stores the 16-bit signed magnetometer sensor output
float magCalibration[3] = {0, 0, 0}, magbias[3] = {0, 0, 0}; // Factory mag calibration and mag bias
float gyroBias[3] = {0, 0, 0}, accelBias[3] = {0, 0, 0}; // Bias corrections for gyro and accelerometer
float ax, ay, az, gx, gy, gz, mx, my, mz; // variables to hold latest sensor data values
int16_t tempCount; // Stores the real internal chip temperature in degrees Celsius
float temperature;
float SelfTest[6];
int delt_t = 0; // used to control display output rate
int count = 0; // used to control display output rate
// parameters for 6 DoF sensor fusion calculations
float PI = 3.14159265358979323846f;
float GyroMeasError = PI * (60.0f / 180.0f); // gyroscope measurement error in rads/s (start at 60 deg/s), then reduce after ~10 s to 3
float beta = sqrt(3.0f / 4.0f) * GyroMeasError; // compute beta
float GyroMeasDrift = PI * (1.0f / 180.0f); // gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
float 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
#define Kp 2.0f * 5.0f // these are the free parameters in the Mahony filter and fusion scheme, Kp for proportional feedback, Ki for integral
#define Ki 0.0f
float pitch, yaw, roll;
float deltat = 0.0f; // integration interval for both filter schemes
int lastUpdate = 0, firstUpdate = 0, Now = 0; // used to calculate integration interval // used to calculate integration interval
float q[4] = {1.0f, 0.0f, 0.0f, 0.0f}; // vector to hold quaternion
float eInt[3] = {0.0f, 0.0f, 0.0f}; // vector to hold integral error for Mahony method
class MPU9250 {
protected:
public:
//===================================================================================================================
//====== Set of useful function to access acceleratio, gyroscope, and temperature data
//===================================================================================================================
void writeByte(uint8_t address, uint8_t subAddress, uint8_t data)
{
char data_write[2];
data_write[0] = subAddress;
data_write[1] = data;
i2c.write(address, data_write, 2, 0);
}
char readByte(uint8_t address, uint8_t subAddress)
{
char data[1]; // `data` will store the register data
char data_write[1];
data_write[0] = subAddress;
i2c.write(address, data_write, 1, 1); // no stop
i2c.read(address, data, 1, 0);
return data[0];
}
void readBytes(uint8_t address, uint8_t subAddress, uint8_t count, uint8_t * dest)
{
char data[14];
char data_write[1];
data_write[0] = subAddress;
i2c.write(address, data_write, 1, 1); // no stop
i2c.read(address, data, count, 0);
for(int ii = 0; ii < count; ii++) {
dest[ii] = data[ii];
}
}
void getMres() {
switch (Mscale)
{
// Possible magnetometer scales (and their register bit settings) are:
// 14 bit resolution (0) and 16 bit resolution (1)
case MFS_14BITS:
mRes = 10.0*4219.0/8190.0; // Proper scale to return milliGauss
break;
case MFS_16BITS:
mRes = 10.0*4219.0/32760.0; // Proper scale to return milliGauss
break;
}
}
void getGres() {
switch (Gscale)
{
// Possible gyro scales (and their register bit settings) are:
// 250 DPS (00), 500 DPS (01), 1000 DPS (10), and 2000 DPS (11).
// Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
case GFS_250DPS:
gRes = 250.0/32768.0;
break;
case GFS_500DPS:
gRes = 500.0/32768.0;
break;
case GFS_1000DPS:
gRes = 1000.0/32768.0;
break;
case GFS_2000DPS:
gRes = 2000.0/32768.0;
break;
}
}
void getAres() {
switch (Ascale)
{
// Possible accelerometer scales (and their register bit settings) are:
// 2 Gs (00), 4 Gs (01), 8 Gs (10), and 16 Gs (11).
// Here's a bit of an algorith to calculate DPS/(ADC tick) based on that 2-bit value:
case AFS_2G:
aRes = 2.0/32768.0;
break;
case AFS_4G:
aRes = 4.0/32768.0;
break;
case AFS_8G:
aRes = 8.0/32768.0;
break;
case AFS_16G:
aRes = 16.0/32768.0;
break;
}
}
void readAccelData(int16_t * destination)
{
uint8_t rawData[6]; // x/y/z accel register data stored here
readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]); // Read the six raw data registers into data array
destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
}
void readGyroData(int16_t * destination)
{
uint8_t rawData[6]; // x/y/z gyro register data stored here
readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]); // Read the six raw data registers sequentially into data array
destination[0] = (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
destination[1] = (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
destination[2] = (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
}
void readMagData(int16_t * destination)
{
uint8_t rawData[7]; // x/y/z gyro register data, ST2 register stored here, must read ST2 at end of data acquisition
if(readByte(AK8963_ADDRESS, AK8963_ST1) & 0x01) { // wait for magnetometer data ready bit to be set
readBytes(AK8963_ADDRESS, AK8963_XOUT_L, 7, &rawData[0]); // Read the six raw data and ST2 registers sequentially into data array
uint8_t c = rawData[6]; // End data read by reading ST2 register
if(!(c & 0x08)) { // Check if magnetic sensor overflow set, if not then report data
destination[0] = (int16_t)(((int16_t)rawData[1] << 8) | rawData[0]); // Turn the MSB and LSB into a signed 16-bit value
destination[1] = (int16_t)(((int16_t)rawData[3] << 8) | rawData[2]) ; // Data stored as little Endian
destination[2] = (int16_t)(((int16_t)rawData[5] << 8) | rawData[4]) ;
}
}
}
int16_t readTempData()
{
uint8_t rawData[2]; // x/y/z gyro register data stored here
readBytes(MPU9250_ADDRESS, TEMP_OUT_H, 2, &rawData[0]); // Read the two raw data registers sequentially into data array
return (int16_t)(((int16_t)rawData[0]) << 8 | rawData[1]) ; // Turn the MSB and LSB into a 16-bit value
}
void resetMPU9250() {
// reset device
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
wait(0.1);
}
void initAK8963(float * destination)
{
// First extract the factory calibration for each magnetometer axis
uint8_t rawData[3]; // x/y/z gyro calibration data stored here
writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer
wait(0.01);
writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x0F); // Enter Fuse ROM access mode
wait(0.01);
readBytes(AK8963_ADDRESS, AK8963_ASAX, 3, &rawData[0]); // Read the x-, y-, and z-axis calibration values
destination[0] = (float)(rawData[0] - 128)/256.0f + 1.0f; // Return x-axis sensitivity adjustment values, etc.
destination[1] = (float)(rawData[1] - 128)/256.0f + 1.0f;
destination[2] = (float)(rawData[2] - 128)/256.0f + 1.0f;
writeByte(AK8963_ADDRESS, AK8963_CNTL, 0x00); // Power down magnetometer
wait(0.01);
// Configure the magnetometer for continuous read and highest resolution
// set Mscale bit 4 to 1 (0) to enable 16 (14) bit resolution in CNTL register,
// and enable continuous mode data acquisition Mmode (bits [3:0]), 0010 for 8 Hz and 0110 for 100 Hz sample rates
writeByte(AK8963_ADDRESS, AK8963_CNTL, Mscale << 4 | Mmode); // Set magnetometer data resolution and sample ODR
wait(0.01);
}
void initMPU9250()
{
// Initialize MPU9250 device
// wake up device
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Clear sleep mode bit (6), enable all sensors
wait(0.1); // wait_ms 100 ms for PLL to get established on x-axis gyro; should check for PLL ready interrupt
// get stable time source
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01); // Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
// Configure Gyro and Accelerometer
// Disable FSYNC and set accelerometer and gyro bandwidth to 44 and 42 Hz, respectively;
// DLPF_CFG = bits 2:0 = 010; this sets the sample rate at 1 kHz for both
// Maximum wait_ms is 4.9 ms which is just over a 200 Hz maximum rate
writeByte(MPU9250_ADDRESS, CONFIG, 0x03);
// Set sample rate = gyroscope output rate/(1 + SMPLRT_DIV)
writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x04); // Use a 200 Hz rate; the same rate set in CONFIG above
// Set gyroscope full scale range
// Range selects FS_SEL and AFS_SEL are 0 - 3, so 2-bit values are left-shifted into positions 4:3
uint8_t c = readByte(MPU9250_ADDRESS, GYRO_CONFIG);
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, c | Gscale << 3); // Set full scale range for the gyro
// Set accelerometer configuration
c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG);
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0xE0); // Clear self-test bits [7:5]
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c & ~0x18); // Clear AFS bits [4:3]
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, c | Ascale << 3); // Set full scale range for the accelerometer
// Set accelerometer sample rate configuration
// It is possible to get a 4 kHz sample rate from the accelerometer by choosing 1 for
// accel_fchoice_b bit [3]; in this case the bandwidth is 1.13 kHz
c = readByte(MPU9250_ADDRESS, ACCEL_CONFIG2);
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c & ~0x0F); // Clear accel_fchoice_b (bit 3) and A_DLPFG (bits [2:0])
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, c | 0x03); // Set accelerometer rate to 1 kHz and bandwidth to 41 Hz
// The accelerometer, gyro, and thermometer are set to 1 kHz sample rates,
// but all these rates are further reduced by a factor of 5 to 200 Hz because of the SMPLRT_DIV setting
// Configure Interrupts and Bypass Enable
// Set interrupt pin active high, push-pull, and clear on read of INT_STATUS, enable I2C_BYPASS_EN so additional chips
// can join the I2C bus and all can be controlled by the Arduino as master
writeByte(MPU9250_ADDRESS, INT_PIN_CFG, 0x22);
writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x01); // Enable data ready (bit 0) interrupt
}
// Function which accumulates gyro and accelerometer data after device initialization. It calculates the average
// of the at-rest readings and then loads the resulting offsets into accelerometer and gyro bias registers.
void calibrateMPU9250(float * dest1, float * dest2)
{
uint8_t data[12]; // data array to hold accelerometer and gyro x, y, z, data
uint16_t ii, packet_count, fifo_count;
int32_t gyro_bias[3] = {0, 0, 0}, accel_bias[3] = {0, 0, 0};
// reset device, reset all registers, clear gyro and accelerometer bias registers
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x80); // Write a one to bit 7 reset bit; toggle reset device
wait(0.1);
// get stable time source
// Set clock source to be PLL with x-axis gyroscope reference, bits 2:0 = 001
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x01);
writeByte(MPU9250_ADDRESS, PWR_MGMT_2, 0x00);
wait(0.2);
// Configure device for bias calculation
writeByte(MPU9250_ADDRESS, INT_ENABLE, 0x00); // Disable all interrupts
writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00); // Disable FIFO
writeByte(MPU9250_ADDRESS, PWR_MGMT_1, 0x00); // Turn on internal clock source
writeByte(MPU9250_ADDRESS, I2C_MST_CTRL, 0x00); // Disable I2C master
writeByte(MPU9250_ADDRESS, USER_CTRL, 0x00); // Disable FIFO and I2C master modes
writeByte(MPU9250_ADDRESS, USER_CTRL, 0x0C); // Reset FIFO and DMP
wait(0.015);
// Configure MPU9250 gyro and accelerometer for bias calculation
writeByte(MPU9250_ADDRESS, CONFIG, 0x01); // Set low-pass filter to 188 Hz
writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00); // Set sample rate to 1 kHz
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00); // Set gyro full-scale to 250 degrees per second, maximum sensitivity
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00); // Set accelerometer full-scale to 2 g, maximum sensitivity
uint16_t gyrosensitivity = 131; // = 131 LSB/degrees/sec
uint16_t accelsensitivity = 16384; // = 16384 LSB/g
// Configure FIFO to capture accelerometer and gyro data for bias calculation
writeByte(MPU9250_ADDRESS, USER_CTRL, 0x40); // Enable FIFO
writeByte(MPU9250_ADDRESS, FIFO_EN, 0x78); // Enable gyro and accelerometer sensors for FIFO (max size 512 bytes in MPU-9250)
wait(0.04); // accumulate 40 samples in 80 milliseconds = 480 bytes
// At end of sample accumulation, turn off FIFO sensor read
writeByte(MPU9250_ADDRESS, FIFO_EN, 0x00); // Disable gyro and accelerometer sensors for FIFO
readBytes(MPU9250_ADDRESS, FIFO_COUNTH, 2, &data[0]); // read FIFO sample count
fifo_count = ((uint16_t)data[0] << 8) | data[1];
packet_count = fifo_count/12;// How many sets of full gyro and accelerometer data for averaging
for (ii = 0; ii < packet_count; ii++) {
int16_t accel_temp[3] = {0, 0, 0}, gyro_temp[3] = {0, 0, 0};
readBytes(MPU9250_ADDRESS, FIFO_R_W, 12, &data[0]); // read data for averaging
accel_temp[0] = (int16_t) (((int16_t)data[0] << 8) | data[1] ) ; // Form signed 16-bit integer for each sample in FIFO
accel_temp[1] = (int16_t) (((int16_t)data[2] << 8) | data[3] ) ;
accel_temp[2] = (int16_t) (((int16_t)data[4] << 8) | data[5] ) ;
gyro_temp[0] = (int16_t) (((int16_t)data[6] << 8) | data[7] ) ;
gyro_temp[1] = (int16_t) (((int16_t)data[8] << 8) | data[9] ) ;
gyro_temp[2] = (int16_t) (((int16_t)data[10] << 8) | data[11]) ;
accel_bias[0] += (int32_t) accel_temp[0]; // Sum individual signed 16-bit biases to get accumulated signed 32-bit biases
accel_bias[1] += (int32_t) accel_temp[1];
accel_bias[2] += (int32_t) accel_temp[2];
gyro_bias[0] += (int32_t) gyro_temp[0];
gyro_bias[1] += (int32_t) gyro_temp[1];
gyro_bias[2] += (int32_t) gyro_temp[2];
}
accel_bias[0] /= (int32_t) packet_count; // Normalize sums to get average count biases
accel_bias[1] /= (int32_t) packet_count;
accel_bias[2] /= (int32_t) packet_count;
gyro_bias[0] /= (int32_t) packet_count;
gyro_bias[1] /= (int32_t) packet_count;
gyro_bias[2] /= (int32_t) packet_count;
if(accel_bias[2] > 0L) {accel_bias[2] -= (int32_t) accelsensitivity;} // Remove gravity from the z-axis accelerometer bias calculation
else {accel_bias[2] += (int32_t) accelsensitivity;}
// Construct the gyro biases for push to the hardware gyro bias registers, which are reset to zero upon device startup
data[0] = (-gyro_bias[0]/4 >> 8) & 0xFF; // Divide by 4 to get 32.9 LSB per deg/s to conform to expected bias input format
data[1] = (-gyro_bias[0]/4) & 0xFF; // Biases are additive, so change sign on calculated average gyro biases
data[2] = (-gyro_bias[1]/4 >> 8) & 0xFF;
data[3] = (-gyro_bias[1]/4) & 0xFF;
data[4] = (-gyro_bias[2]/4 >> 8) & 0xFF;
data[5] = (-gyro_bias[2]/4) & 0xFF;
/// Push gyro biases to hardware registers
/* writeByte(MPU9250_ADDRESS, XG_OFFSET_H, data[0]);
writeByte(MPU9250_ADDRESS, XG_OFFSET_L, data[1]);
writeByte(MPU9250_ADDRESS, YG_OFFSET_H, data[2]);
writeByte(MPU9250_ADDRESS, YG_OFFSET_L, data[3]);
writeByte(MPU9250_ADDRESS, ZG_OFFSET_H, data[4]);
writeByte(MPU9250_ADDRESS, ZG_OFFSET_L, data[5]);
*/
dest1[0] = (float) gyro_bias[0]/(float) gyrosensitivity; // construct gyro bias in deg/s for later manual subtraction
dest1[1] = (float) gyro_bias[1]/(float) gyrosensitivity;
dest1[2] = (float) gyro_bias[2]/(float) gyrosensitivity;
// Construct the accelerometer biases for push to the hardware accelerometer bias registers. These registers contain
// factory trim values which must be added to the calculated accelerometer biases; on boot up these registers will hold
// non-zero values. In addition, bit 0 of the lower byte must be preserved since it is used for temperature
// compensation calculations. Accelerometer bias registers expect bias input as 2048 LSB per g, so that
// the accelerometer biases calculated above must be divided by 8.
int32_t accel_bias_reg[3] = {0, 0, 0}; // A place to hold the factory accelerometer trim biases
readBytes(MPU9250_ADDRESS, XA_OFFSET_H, 2, &data[0]); // Read factory accelerometer trim values
accel_bias_reg[0] = (int16_t) ((int16_t)data[0] << 8) | data[1];
readBytes(MPU9250_ADDRESS, YA_OFFSET_H, 2, &data[0]);
accel_bias_reg[1] = (int16_t) ((int16_t)data[0] << 8) | data[1];
readBytes(MPU9250_ADDRESS, ZA_OFFSET_H, 2, &data[0]);
accel_bias_reg[2] = (int16_t) ((int16_t)data[0] << 8) | data[1];
uint32_t mask = 1uL; // Define mask for temperature compensation bit 0 of lower byte of accelerometer bias registers
uint8_t mask_bit[3] = {0, 0, 0}; // Define array to hold mask bit for each accelerometer bias axis
for(ii = 0; ii < 3; ii++) {
if(accel_bias_reg[ii] & mask) mask_bit[ii] = 0x01; // If temperature compensation bit is set, record that fact in mask_bit
}
// Construct total accelerometer bias, including calculated average accelerometer bias from above
accel_bias_reg[0] -= (accel_bias[0]/8); // Subtract calculated averaged accelerometer bias scaled to 2048 LSB/g (16 g full scale)
accel_bias_reg[1] -= (accel_bias[1]/8);
accel_bias_reg[2] -= (accel_bias[2]/8);
data[0] = (accel_bias_reg[0] >> 8) & 0xFF;
data[1] = (accel_bias_reg[0]) & 0xFF;
data[1] = data[1] | mask_bit[0]; // preserve temperature compensation bit when writing back to accelerometer bias registers
data[2] = (accel_bias_reg[1] >> 8) & 0xFF;
data[3] = (accel_bias_reg[1]) & 0xFF;
data[3] = data[3] | mask_bit[1]; // preserve temperature compensation bit when writing back to accelerometer bias registers
data[4] = (accel_bias_reg[2] >> 8) & 0xFF;
data[5] = (accel_bias_reg[2]) & 0xFF;
data[5] = data[5] | mask_bit[2]; // preserve temperature compensation bit when writing back to accelerometer bias registers
// Apparently this is not working for the acceleration biases in the MPU-9250
// Are we handling the temperature correction bit properly?
// Push accelerometer biases to hardware registers
/* writeByte(MPU9250_ADDRESS, XA_OFFSET_H, data[0]);
writeByte(MPU9250_ADDRESS, XA_OFFSET_L, data[1]);
writeByte(MPU9250_ADDRESS, YA_OFFSET_H, data[2]);
writeByte(MPU9250_ADDRESS, YA_OFFSET_L, data[3]);
writeByte(MPU9250_ADDRESS, ZA_OFFSET_H, data[4]);
writeByte(MPU9250_ADDRESS, ZA_OFFSET_L, data[5]);
*/
// Output scaled accelerometer biases for manual subtraction in the main program
dest2[0] = (float)accel_bias[0]/(float)accelsensitivity;
dest2[1] = (float)accel_bias[1]/(float)accelsensitivity;
dest2[2] = (float)accel_bias[2]/(float)accelsensitivity;
}
// Accelerometer and gyroscope self test; check calibration wrt factory settings
void MPU9250SelfTest(float * destination) // Should return percent deviation from factory trim values, +/- 14 or less deviation is a pass
{
uint8_t rawData[6] = {0, 0, 0, 0, 0, 0};
uint8_t selfTest[6];
int16_t gAvg[3], aAvg[3], aSTAvg[3], gSTAvg[3];
float factoryTrim[6];
uint8_t FS = 0;
writeByte(MPU9250_ADDRESS, SMPLRT_DIV, 0x00); // Set gyro sample rate to 1 kHz
writeByte(MPU9250_ADDRESS, CONFIG, 0x02); // Set gyro sample rate to 1 kHz and DLPF to 92 Hz
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 1<<FS); // Set full scale range for the gyro to 250 dps
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG2, 0x02); // Set accelerometer rate to 1 kHz and bandwidth to 92 Hz
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 1<<FS); // Set full scale range for the accelerometer to 2 g
for( int ii = 0; ii < 200; ii++) { // get average current values of gyro and acclerometer
readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]); // Read the six raw data registers into data array
aAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
aAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
aAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]); // Read the six raw data registers sequentially into data array
gAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
gAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
gAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
}
for (int ii =0; ii < 3; ii++) { // Get average of 200 values and store as average current readings
aAvg[ii] /= 200;
gAvg[ii] /= 200;
}
// Configure the accelerometer for self-test
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0xE0); // Enable self test on all three axes and set accelerometer range to +/- 2 g
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0xE0); // Enable self test on all three axes and set gyro range to +/- 250 degrees/s
wait_ms(25); // wait_ms a while to let the device stabilize
for( int ii = 0; ii < 200; ii++) { // get average self-test values of gyro and acclerometer
readBytes(MPU9250_ADDRESS, ACCEL_XOUT_H, 6, &rawData[0]); // Read the six raw data registers into data array
aSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
aSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
aSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
readBytes(MPU9250_ADDRESS, GYRO_XOUT_H, 6, &rawData[0]); // Read the six raw data registers sequentially into data array
gSTAvg[0] += (int16_t)(((int16_t)rawData[0] << 8) | rawData[1]) ; // Turn the MSB and LSB into a signed 16-bit value
gSTAvg[1] += (int16_t)(((int16_t)rawData[2] << 8) | rawData[3]) ;
gSTAvg[2] += (int16_t)(((int16_t)rawData[4] << 8) | rawData[5]) ;
}
for (int ii =0; ii < 3; ii++) { // Get average of 200 values and store as average self-test readings
aSTAvg[ii] /= 200;
gSTAvg[ii] /= 200;
}
// Configure the gyro and accelerometer for normal operation
writeByte(MPU9250_ADDRESS, ACCEL_CONFIG, 0x00);
writeByte(MPU9250_ADDRESS, GYRO_CONFIG, 0x00);
wait_ms(25); // wait_ms a while to let the device stabilize
// Retrieve accelerometer and gyro factory Self-Test Code from USR_Reg
selfTest[0] = readByte(MPU9250_ADDRESS, SELF_TEST_X_ACCEL); // X-axis accel self-test results
selfTest[1] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_ACCEL); // Y-axis accel self-test results
selfTest[2] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_ACCEL); // Z-axis accel self-test results
selfTest[3] = readByte(MPU9250_ADDRESS, SELF_TEST_X_GYRO); // X-axis gyro self-test results
selfTest[4] = readByte(MPU9250_ADDRESS, SELF_TEST_Y_GYRO); // Y-axis gyro self-test results
selfTest[5] = readByte(MPU9250_ADDRESS, SELF_TEST_Z_GYRO); // Z-axis gyro self-test results
// Retrieve factory self-test value from self-test code reads
factoryTrim[0] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[0] - 1.0) )); // FT[Xa] factory trim calculation
factoryTrim[1] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[1] - 1.0) )); // FT[Ya] factory trim calculation
factoryTrim[2] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[2] - 1.0) )); // FT[Za] factory trim calculation
factoryTrim[3] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[3] - 1.0) )); // FT[Xg] factory trim calculation
factoryTrim[4] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[4] - 1.0) )); // FT[Yg] factory trim calculation
factoryTrim[5] = (float)(2620/1<<FS)*(pow( 1.01 , ((float)selfTest[5] - 1.0) )); // FT[Zg] factory trim calculation
// Report results as a ratio of (STR - FT)/FT; the change from Factory Trim of the Self-Test Response
// To get percent, must multiply by 100
for (int i = 0; i < 3; i++) {
destination[i] = 100.0*((float)(aSTAvg[i] - aAvg[i]))/factoryTrim[i]; // Report percent differences
destination[i+3] = 100.0*((float)(gSTAvg[i] - gAvg[i]))/factoryTrim[i+3]; // Report percent differences
}
}
// 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;
}
// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
// measured ones.
void MahonyQuaternionUpdate(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, bx, bz;
float vx, vy, vz, wx, wy, wz;
float ex, ey, ez;
float pa, pb, pc;
// Auxiliary variables to avoid repeated arithmetic
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; // use reciprocal for division
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; // use reciprocal for division
mx *= norm;
my *= norm;
mz *= norm;
// Reference direction of Earth's magnetic field
hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
bx = sqrt((hx * hx) + (hy * hy));
bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
// Estimated direction of gravity and magnetic field
vx = 2.0f * (q2q4 - q1q3);
vy = 2.0f * (q1q2 + q3q4);
vz = q1q1 - q2q2 - q3q3 + q4q4;
wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);
// Error is cross product between estimated direction and measured direction of gravity
ex = (ay * vz - az * vy) + (my * wz - mz * wy);
ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
if (Ki > 0.0f)
{
eInt[0] += ex; // accumulate integral error
eInt[1] += ey;
eInt[2] += ez;
}
else
{
eInt[0] = 0.0f; // prevent integral wind up
eInt[1] = 0.0f;
eInt[2] = 0.0f;
}
// Apply feedback terms
gx = gx + Kp * ex + Ki * eInt[0];
gy = gy + Kp * ey + Ki * eInt[1];
gz = gz + Kp * ez + Ki * eInt[2];
// Integrate rate of change of quaternion
pa = q2;
pb = q3;
pc = q4;
q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
// Normalise quaternion
norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
norm = 1.0f / norm;
q[0] = q1 * norm;
q[1] = q2 * norm;
q[2] = q3 * norm;
q[3] = q4 * norm;
}
};
#endif