Non linear “heading degree relation”
Hi,
I tried to follow Chris his suggestions (@ his reply Now we’re getting somewhere”). First I put the robot with its front towards south and rotated it 360 degrees. On the monitor, I saw no linear relation between the headings and I decided to do an experiment.
I drew a “degree distribution grid” on a sheet of paper and placed the robot in the centre heading south (heading = 180).
Then I rotated the robot 45 degrees clockwise and noted the headings in the “degree grid”.
I repeated that (4 times) until the robot was back at its starting position.
See picture for results.
It seems that turning “above the center line” per quarter results in a “heading difference” of 60 degrees. And “below the center line” of 120 degrees.
How can this be explained?
And how to get a linear degree distribution?
For the sake of completeness, I added the executed code below
Thanks in advance for your reactions.
Puzzled regards, Ko
/* LSM303DLH Example Code
by: Jim Lindblom
SparkFun Electronics
date: 9/6/11
license: Creative commons share-alike v3.0
Summary:
Show how to calculate level and tilt-compensated heading using
the snazzy LSM303DLH 3-axis magnetometer/3-axis accelerometer.
Firmware:
You can set the accelerometer’s full-scale range by setting
the SCALE constant to either 2, 4, or 8. This value is used
in the initLSM303() function. For the most part, all other
registers in the LSM303 will be at their default value.
Use the LSM303_write() and LSM303_read() functions to write
to and read from the LSM303’s internal registers.
Use getLSM303_accel() and getLSM303_mag() to get the acceleration
and magneto values from the LSM303. You’ll need to pass each of
those functions an array, where the data will be stored upon
return from the void.
getHeading() calculates a heading assuming the sensor is level.
A float between 0 and 360 is returned. You need to pass it a
array with magneto values.
getTiltHeading() calculates a tilt-compensated heading.
A float between 0 and 360 degrees is returned. You need
to pass this function both a magneto and acceleration array.
Headings are calculated as specified in AN3192:
http://www.sparkfun.com/datasheets/Sensors/Magneto/Tilt%20Compensated%20Compass.pdf
Hardware:
I’m using SparkFun’s LSM303 breakout. Only power and the two
I2C lines are connected:
LSM303 Breakout ---------- Arduino
Vin 5V
GND GND
SDA A4
SCL A5
/
#include <Wire.h>
#include <math.h>
#define SCALE 2 // accel full-scale, should be 2, 4, or 8
/ LSM303 Address definitions /
#define LSM303_MAG 0x1E // assuming SA0 grounded
#define LSM303_ACC 0x18 // assuming SA0 grounded
#define X 0
#define Y 1
#define Z 2
/ LSM303 Register definitions /
#define CTRL_REG1_A 0x20
#define CTRL_REG2_A 0x21
#define CTRL_REG3_A 0x22
#define CTRL_REG4_A 0x23
#define CTRL_REG5_A 0x24
#define HP_FILTER_RESET_A 0x25
#define REFERENCE_A 0x26
#define STATUS_REG_A 0x27
#define OUT_X_L_A 0x28
#define OUT_X_H_A 0x29
#define OUT_Y_L_A 0x2A
#define OUT_Y_H_A 0x2B
#define OUT_Z_L_A 0x2C
#define OUT_Z_H_A 0x2D
#define INT1_CFG_A 0x30
#define INT1_SOURCE_A 0x31
#define INT1_THS_A 0x32
#define INT1_DURATION_A 0x33
#define CRA_REG_M 0x00
#define CRB_REG_M 0x01
#define MR_REG_M 0x02
#define OUT_X_H_M 0x03
#define OUT_X_L_M 0x04
#define OUT_Y_H_M 0x05
#define OUT_Y_L_M 0x06
#define OUT_Z_H_M 0x07
#define OUT_Z_L_M 0x08
#define SR_REG_M 0x09
#define IRA_REG_M 0x0A
#define IRB_REG_M 0x0B
#define IRC_REG_M 0x0C
/ Global variables /
int accel[3]; // we’ll store the raw acceleration values here
int mag[3]; // raw magnetometer values stored here
float realAccel[3]; // calculated acceleration values here
void setup()
{
Serial.begin(9600); // Serial is used for debugging
Wire.begin(); // Start up I2C, required for LSM303 communication
initLSM303(SCALE); // Initialize the LSM303, using a SCALE full-scale range
}
void loop()
{
getLSM303_accel(accel); // get the acceleration values and store them in the accel array
while(!(LSM303_read(SR_REG_M) & 0x01))
; // wait for the magnetometer readings to be ready
getLSM303_mag(mag); // get the magnetometer values, store them in mag
//printValues(mag, accel); // print the raw accel and mag values, good debugging
for (int i=0; i<3; i++)
realAccel[i] = accel[i] / pow(2, 15) * SCALE; // calculate real acceleration values, in units of g
/ print both the level, and tilt-compensated headings below to compare /
Serial.print(getHeading(mag), 3); // this only works if the sensor is level
Serial.print("\t\t"); // print some tabs
Serial.println(getTiltHeading(mag, realAccel), 3); // see how awesome tilt compensation is?!
delay(100); // delay for serial readability
}
void initLSM303(int fs)
{
LSM303_write(0x27, CTRL_REG1_A); // 0x27 = normal power mode, all accel axes on
if ((fs==8)||(fs==4))
LSM303_write((0x00 | (fs-fs/2-1)<<4), CTRL_REG4_A); // set full-scale
else
LSM303_write(0x00, CTRL_REG4_A);
LSM303_write(0x14, CRA_REG_M); // 0x14 = mag 30Hz output rate
LSM303_write(0x00, MR_REG_M); // 0x00 = continouous conversion mode
}
void printValues(int * magArray, int * accelArray)
{
/ print out mag and accel arrays all pretty-like /
Serial.print(accelArray[X], DEC);
Serial.print("\t");
Serial.print(accelArray[Y], DEC);
Serial.print("\t");
Serial.print(accelArray[Z], DEC);
Serial.print("\t\t");
Serial.print(magArray[X], DEC);
Serial.print("\t");
Serial.print(magArray[Y], DEC);
Serial.print("\t");
Serial.print(magArray[Z], DEC);
Serial.println();
}
float getHeading(int * magValue)
{
// see section 1.2 in app note AN3192
float heading = 180atan2(magValue[Y], magValue[X])/PI; // assume pitch, roll are 0
if (heading <0)
heading += 360;
return heading;
}
float getTiltHeading(int * magValue, float * accelValue)
{
// see appendix A in app note AN3192
float pitch = asin(-accelValue[X]);
float roll = asin(accelValue[Y]/cos(pitch));
float xh = magValue[X] * cos(pitch) + magValue[Z] * sin(pitch);
float yh = magValue[X] * sin(roll) * sin(pitch) + magValue[Y] * cos(roll) - magValue[Z] * sin(roll) * cos(pitch);
float zh = -magValue[X] * cos(roll) * sin(pitch) + magValue[Y] * sin(roll) + magValue[Z] * cos(roll) * cos(pitch);
float heading = 180 * atan2(yh, xh)/PI;
if (yh >= 0)
return heading;
else
return (360 + heading);
}
void getLSM303_mag(int * rawValues)
{
Wire.beginTransmission(LSM303_MAG);
Wire.send(OUT_X_H_M);
Wire.endTransmission();
Wire.requestFrom(LSM303_MAG, 6);
for (int i=0; i<3; i++)
rawValues[i] = (Wire.receive() << 8) | Wire.receive();
}
void getLSM303_accel(int * rawValues)
{
rawValues[Z] = ((int)LSM303_read(OUT_X_L_A) << 8) | (LSM303_read(OUT_X_H_A));
rawValues[X] = ((int)LSM303_read(OUT_Y_L_A) << 8) | (LSM303_read(OUT_Y_H_A));
rawValues[Y] = ((int)LSM303_read(OUT_Z_L_A) << 8) | (LSM303_read(OUT_Z_H_A));
// had to swap those to right the data with the proper axis
}
byte LSM303_read(byte address)
{
byte temp;
if (address >= 0x20)
Wire.beginTransmission(LSM303_ACC);
else
Wire.beginTransmission(LSM303_MAG);
Wire.send(address);
if (address >= 0x20)
Wire.requestFrom(LSM303_ACC, 1);
else
Wire.requestFrom(LSM303_MAG, 1);
while(!Wire.available())
;
temp = Wire.receive();
Wire.endTransmission();
return temp;
}
void LSM303_write(byte data, byte address)
{
if (address >= 0x20)
Wire.beginTransmission(LSM303_ACC);
else
Wire.beginTransmission(LSM303_MAG);
Wire.send(address);
Wire.send(data);
Wire.endTransmission();
}
in order to determine the needed directions for “guiding” the Rover motors to the free space in the room (direction the Rover was driving AND direction of the greatest free space I want the Rover tot direct to).