How to optimize this example code to run quicker? - arduino

Question

I am currently in the process of learning about, and making a PID controller. I first wrote a program to take data from the accelerometer, and was able to get raw data, but I had no idea on how to write a proper filter to convert the raw data to degrees.
I found an example code with libraries that had a "Quaternian filter" that outputs the raw data in degrees, but it refreshes way too slow to be useful. I did not see any delays in the main code, is there any way I can make it refresh faster?
Here is the main code:
#include <Servo.h>
int myRoll = 0;
/* MPU9250 Basic Example Code
by: Kris Winer
date: April 1, 2014
license: Beerware - Use this code however you'd like. If you
find it useful you can buy me a beer some time.
Modified by Brent Wilkins July 19, 2016
Demonstrate basic MPU-9250 functionality including parameterizing the register
addresses, initializing the sensor, getting properly scaled accelerometer,
gyroscope, and magnetometer data out. Added display functions to allow display
to on breadboard monitor. Addition of 9 DoF sensor fusion using open source
Madgwick and Mahony filter algorithms. Sketch runs on the 3.3 V 8 MHz Pro Mini
and the Teensy 3.1.
SDA and SCL should have external pull-up resistors (to 3.3V).
10k resistors are on the EMSENSR-9250 breakout board.
Hardware setup:
MPU9250 Breakout --------- Arduino
VDD ---------------------- 3.3V
VDDI --------------------- 3.3V
SDA ----------------------- A4
SCL ----------------------- A5
GND ---------------------- GND
*/
#include "quaternionFilters.h"
#include "MPU9250.h"
#define AHRS true // Set to false for basic data read
#define SerialDebug true // Set to true to get Serial output for debugging
// Pin definitions
int intPin = 12; // These can be changed, 2 and 3 are the Arduinos ext int pins
int myLed = 13; // Set up pin 13 led for toggling
Servo myservo;
MPU9250 myIMU;
void setup()
{
myservo.attach(9);
myservo.write(90);
Wire.begin();
// TWBR = 12; // 400 kbit/sec I2C speed
Serial.begin(115200);
// Set up the interrupt pin, its set as active high, push-pull
pinMode(intPin, INPUT);
digitalWrite(intPin, LOW);
pinMode(myLed, OUTPUT);
digitalWrite(myLed, HIGH);
// Read the WHO_AM_I register, this is a good test of communication
byte c = myIMU.readByte(MPU9250_ADDRESS, WHO_AM_I_MPU9250);
Serial.print("MPU9250 "); Serial.print("I AM "); Serial.print(c, HEX);
Serial.print(" I should be "); Serial.println(0x71, HEX);
if (c == 0x73) // WHO_AM_I should always be 0x68
{
Serial.println("MPU9250 is online...");
/*
// Start by performing self test and reporting values
myIMU.MPU9250SelfTest(myIMU.SelfTest);
Serial.print("x-axis self test: acceleration trim within : ");
Serial.print(myIMU.SelfTest[0],1); Serial.println("% of factory value");
Serial.print("y-axis self test: acceleration trim within : ");
Serial.print(myIMU.SelfTest[1],1); Serial.println("% of factory value");
Serial.print("z-axis self test: acceleration trim within : ");
Serial.print(myIMU.SelfTest[2],1); Serial.println("% of factory value");
Serial.print("x-axis self test: gyration trim within : ");
Serial.print(myIMU.SelfTest[3],1); Serial.println("% of factory value");
Serial.print("y-axis self test: gyration trim within : ");
Serial.print(myIMU.SelfTest[4],1); Serial.println("% of factory value");
Serial.print("z-axis self test: gyration trim within : ");
Serial.print(myIMU.SelfTest[5],1); Serial.println("% of factory value");
*/
/* // Calibrate gyro and accelerometers, load biases in bias registers
// myIMU.calibrateMPU9250(myIMU.gyroBias, myIMU.accelBias);
*/
myIMU.initMPU9250();
byte d = myIMU.readByte(AK8963_ADDRESS, WHO_AM_I_AK8963);
/*
// Get magnetometer calibration from AK8963 ROM
// myIMU.initAK8963(myIMU.magCalibration);
// Initialize device for active mode read of magnetometer
*/
} /* if (c == 0x71)
else
{
Serial.print("Could not connect to MPU9250: 0x");
Serial.println(c, HEX);
while(1) ; // Loop forever if communication doesn't happen
}
}
*/
}
void loop(){
// If intPin goes high, all data registers have new data
// On interrupt, check if data ready interrupt
if (myIMU.readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01)
{
myIMU.readAccelData(myIMU.accelCount); // Read the x/y/z adc values
myIMU.getAres();
// Now we'll calculate the accleration value into actual g's
// This depends on scale being set
myIMU.ax = (float)myIMU.accelCount[0]*myIMU.aRes; // - accelBias[0];
myIMU.ay = (float)myIMU.accelCount[1]*myIMU.aRes; // - accelBias[1];
myIMU.az = (float)myIMU.accelCount[2]*myIMU.aRes; // - accelBias[2];
myIMU.readGyroData(myIMU.gyroCount); // Read the x/y/z adc values
myIMU.getGres();
// Calculate the gyro value into actual degrees per second
// This depends on scale being set
myIMU.gx = (float)myIMU.gyroCount[0]*myIMU.gRes;
myIMU.gy = (float)myIMU.gyroCount[1]*myIMU.gRes;
myIMU.gz = (float)myIMU.gyroCount[2]*myIMU.gRes;
myIMU.readMagData(myIMU.magCount); // Read the x/y/z adc values
myIMU.getMres();
// User environmental x-axis correction in milliGauss, should be
// automatically calculated
myIMU.magbias[0] = +470.;
// User environmental x-axis correction in milliGauss TODO axis??
myIMU.magbias[1] = +120.;
// User environmental x-axis correction in milliGauss
myIMU.magbias[2] = +125.;
// Calculate the magnetometer values in milliGauss
// Include factory calibration per data sheet and user environmental
// corrections
// Get actual magnetometer value, this depends on scale being set
myIMU.mx = (float)myIMU.magCount[0]*myIMU.mRes*myIMU.magCalibration[0] -
myIMU.magbias[0];
myIMU.my = (float)myIMU.magCount[1]*myIMU.mRes*myIMU.magCalibration[1] -
myIMU.magbias[1];
myIMU.mz = (float)myIMU.magCount[2]*myIMU.mRes*myIMU.magCalibration[2] -
myIMU.magbias[2];
} // if (readByte(MPU9250_ADDRESS, INT_STATUS) & 0x01)
// Must be called before updating quaternions!
myIMU.updateTime();
// Sensors x (y)-axis of the accelerometer is aligned with the y (x)-axis of
// the magnetometer; the magnetometer z-axis (+ down) is opposite to z-axis
// (+ up) of accelerometer and gyro! We have to make some allowance for this
// orientationmismatch in feeding the output to the quaternion filter. For the
// MPU-9250, we have chosen a magnetic rotation that keeps the sensor forward
// along the x-axis just like in the LSM9DS0 sensor. This rotation can be
// modified to allow any convenient orientation convention. 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, my, mx, mz);
MahonyQuaternionUpdate(myIMU.ax, myIMU.ay, myIMU.az, myIMU.gx*DEG_TO_RAD,
myIMU.gy*DEG_TO_RAD, myIMU.gz*DEG_TO_RAD, myIMU.my,
myIMU.mx, myIMU.mz, myIMU.deltat);
if (!AHRS)
{
myIMU.delt_t = millis() - myIMU.count;
if (myIMU.delt_t > 500)
{
myIMU.count = millis();
digitalWrite(myLed, !digitalRead(myLed)); // toggle led
} // if (myIMU.delt_t > 500)
} // if (!AHRS)
else
{
// Serial print and/or display at 0.5 s rate independent of data rates
myIMU.delt_t = millis() - myIMU.count;
// update LCD once per half-second independent of read rate
if (myIMU.delt_t > 500)
{
// 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, the 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.
myIMU.yaw = atan2(2.0f * (*(getQ()+1) * *(getQ()+2) + *getQ() *
*(getQ()+3)), *getQ() * *getQ() + *(getQ()+1) * *(getQ()+1)
- *(getQ()+2) * *(getQ()+2) - *(getQ()+3) * *(getQ()+3));
myIMU.pitch = -asin(2.0f * (*(getQ()+1) * *(getQ()+3) - *getQ() *
*(getQ()+2)));
myIMU.roll = atan2(2.0f * (*getQg() * *(getQ()+1) + *(getQ()+2) *
*(getQ()+3)), *getQ() * *getQ() - *(getQ()+1) * *(getQ()+1)
- *(getQ()+2) * *(getQ()+2) + *(getQ()+3) * *(getQ()+3));
myIMU.pitch *= RAD_TO_DEG;
myIMU.yaw *= RAD_TO_DEG;
// Declination of SparkFun Electronics (40°05'26.6"N 105°11'05.9"W) is
// 8° 30' E ± 0° 21' (or 8.5°) on 2016-07-19
// - http://www.ngdc.noaa.gov/geomag-web/#declination
myIMU.yaw -= 8.5;
myIMU.roll *= RAD_TO_DEG;
if(SerialDebug)
{
Serial.print(myIMU.yaw, 2);
Serial.print(", ");
Serial.print(myIMU.pitch, 2);
Serial.print(", ");
Serial.println(myIMU.roll, 2);
}
myIMU.count = millis();
myIMU.sumCount = 0;
myIMU.sum = 0;
} // if (myIMU.delt_t > 500)
} // if (AHRS)
myservo.write(myIMU.roll);
}
The libraries are below:
here is quaternionFilters.cpp
// 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 & 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!
#include "quaternionFilters.h"
// These are the free parameters in the Mahony filter and fusion scheme, Kp
// for proportional feedback, Ki for integral
#define Kp 2.0f * 5.0f
#define Ki 0.0f
static float GyroMeasError = PI * (40.0f / 180.0f);
// gyroscope measurement drift in rad/s/s (start at 0.0 deg/s/s)
static float GyroMeasDrift = PI * (0.0f / 180.0f);
// 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.
static float beta = sqrt(3.0f / 4.0f) * GyroMeasError; // Compute beta
// Compute zeta, the other free parameter in the Madgwick scheme usually
// set to a small or zero value
static float zeta = sqrt(3.0f / 4.0f) * GyroMeasDrift;
// Vector to hold integral error for Mahony method
static float eInt[3] = {0.0f, 0.0f, 0.0f};
// Vector to hold quaternion
static float q[4] = {1.0f, 0.0f, 0.0f, 0.0f};
void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat)
{
// short name local variable for readability
float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
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 deltat)
{
// short name local variable for readability
float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];
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;
}
const float * getQ () { return q; }
aaaand .h
#ifndef _QUATERNIONFILTERS_H_
#define _QUATERNIONFILTERS_H_
#include <Arduino.h>
void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy,
float gz, float mx, float my, float mz,
float deltat);
void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy,
float gz, float mx, float my, float mz,
float deltat);
const float * getQ();
#endif // _QUATERNIONFILTERS_H_

Answer 1

That is very difficult.
Calculations with floats are very slowly on 8 bit processors. Try to use int where possible or choose for a 32 bit processor.