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Arduino/MPU6050/AdafruitMotorShieldV2: script hangs/freezes when turn on motors

I'm a newby to robotics and electronics in general, so please don't assume I tried anything you might think is obvious.

I'm trying to create a cart which will basically run around by itself (simple AI routines to avoid obstacles, go from pt. A to pt. B around corners, follow lines, etc.). I'm putting together an Adafruit Arduino Uno R3 with the Adafruit Motor Shield v2 and an MPU-6050. I'm using the "breadboard" on the Motor Shield for the circuitry, soldering everything there.

I can get all the pieces working independently with their own scripts: the Motor Shield drives the 4 motors as expected using the Adafruit library; I'm using the "JRowberg" library for the MPU-6050, and started with the example MPU6050_DMP6.ino, which works fine as long as the cart motors are turned off. My only changes in the example script below are motor startup and some simple motor commands.

As long as I leave the switch which powers the motors off, everything seems fine: it outputs to the Serial window continuously with Euler data which, I assume, is correct. However, a few seconds after I turn on the power to the motors (and the wheels start turning), it just hangs/freezes: the output to the Serial window stops (sometimes in mid-line), and the wheels keep turning at the speed of their last change. Sometimes I see "FIFO overflow" errors, but not always. Sometimes I see "nan" for some of the floating point values before it hangs, but not always.

Some things I've tried, all of which changed noting: * I've swapped out the MPU-6050 board for another from the same manufacturer. * I've tried moving the MPU-6050 away from the motors using a ribbon cable. * I've changed the I2C clock using JRowber's advice (a change in a .h file and changing the value of the TWBR variable), but I don't think I've tried all possible values. * I've changed the speed of the MotorShield in the AFMS.begin() command, although, again, there are probably other values I haven't tried, and I'm not sure how in-sync this and the TWBR value need to be.

And some other things, all to no avail.

Below is an example script which fails for me:

#include "I2Cdev.h"
#include "MPU6050_6Axis_MotionApps20.h"
// is used in I2Cdev.h
#if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE
    #include "Wire.h"
#endif
#include "Adafruit_MotorShield.h"
#include "utility/Adafruit_PWMServoDriver.h"

#define DEBUG 1

MPU6050 mpu;
#define OUTPUT_READABLE_EULER

#define LED_PIN 13
bool blinkState = false;

bool dmpReady = false;  // set true if DMP init was successful
uint8_t mpuIntStatus;   // holds actual interrupt status byte from MPU
uint8_t devStatus;      // return status after each device operation (0 = success, !0  = error)
uint16_t packetSize;    // expected DMP packet size (default is 42 bytes)
uint16_t fifoCount;     // count of all bytes currently in FIFO
uint8_t fifoBuffer[64]; // FIFO storage buffer

Quaternion q;           // [w, x, y, z]         quaternion container
VectorInt16 aa;         // [x, y, z]            accel sensor measurements
VectorInt16 aaReal;     // [x, y, z]            gravity-free accel sensor measurements
VectorInt16 aaWorld;    // [x, y, z]            world-frame accel sensor measurements
VectorFloat gravity;    // [x, y, z]            gravity vector
float euler[3];         // [psi, theta, phi]    Euler angle container
float ypr[3];           // [yaw, pitch, roll]   yaw/pitch/roll container and gravity vector

uint8_t teapotPacket[14] = { '$', 0x02, 0,0, 0,0, 0,0, 0,0, 0x00, 0x00, '\r', '\n' };

Adafruit_MotorShield AFMS = Adafruit_MotorShield(); 
#define NUM_MOTORS 4
#define MOTOR_FL 0
#define MOTOR_FR 1
#define MOTOR_RR 2
#define MOTOR_RL 3
Adafruit_DCMotor *myMotors[NUM_MOTORS] =  {
  AFMS.getMotor(1),
  AFMS.getMotor(2),
  AFMS.getMotor(3),
  AFMS.getMotor(4),
};

#define CHANGE_SPEED_TIME 500
long changeSpeedMillis = 0;
int curSpeed = 30;

volatile bool mpuInterrupt = false;     // indicates whether MPU interrupt pin has gone high
void dmpDataReady() {
    mpuInterrupt = true;
}

void setup() {
    #if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE
        Wire.begin();
        TWBR = 24; // 400kHz I2C clock (200kHz if CPU is 8MHz)
    #elif I2CDEV_IMPLEMENTATION == I2CDEV_BUILTIN_FASTWIRE
        Fastwire::setup(400, true);
    #endif

    Serial.begin(115200);
    while (!Serial); // wait for Leonardo enumeration, others continue immediately

    // start the motor shield.
      AFMS.begin();  // create with the default frequency 1.6KHz
//    AFMS.begin(4000);  // OR with a different frequency, say 4KHz
    // kill all the motors.
    myMotors[MOTOR_FL]->run(BRAKE);
    myMotors[MOTOR_FL]->setSpeed(0);  
    myMotors[MOTOR_FR]->run(BRAKE);
    myMotors[MOTOR_FR]->setSpeed(0);  
    myMotors[MOTOR_RR]->run(BRAKE);
    myMotors[MOTOR_RR]->setSpeed(0);  
    myMotors[MOTOR_RL]->run(BRAKE);
    myMotors[MOTOR_RL]->setSpeed(0);
    Serial.println("Motor Shield ready!");

    Serial.println(F("Initializing I2C devices..."));
    mpu.initialize();

    // verify connection
    Serial.println(F("Testing device connections..."));
    Serial.println(mpu.testConnection() ? F("MPU6050 connection successful") :     F("MPU6050 connection failed"));

    // wait for ready
    Serial.println(F("\nSend any character to begin DMP programming and demo: "));
    while (Serial.available() && Serial.read()); // empty buffer
    while (!Serial.available());                 // wait for data
    while (Serial.available() && Serial.read()); // empty buffer again

    // load and configure the DMP
    Serial.println(F("Initializing DMP..."));
    devStatus = mpu.dmpInitialize();

    // supply your own gyro offsets here, scaled for min sensitivity
    mpu.setXGyroOffset(220);
    mpu.setYGyroOffset(76);
    mpu.setZGyroOffset(-85);
    mpu.setZAccelOffset(1788); // 1688 factory default for my test chip

    // make sure it worked (returns 0 if so)
    if (devStatus == 0) {
        // turn on the DMP, now that it's ready
        Serial.println(F("Enabling DMP..."));
        mpu.setDMPEnabled(true);

        // enable Arduino interrupt detection
        Serial.println(F("Enabling interrupt detection (Arduino external interrupt 0)..."));
        attachInterrupt(0, dmpDataReady, RISING);
        mpuIntStatus = mpu.getIntStatus();

        // set our DMP Ready flag so the main loop() function knows it's okay to use it
        Serial.println(F("DMP ready! Waiting for first interrupt..."));
        dmpReady = true;

        // get expected DMP packet size for later comparison
        packetSize = mpu.dmpGetFIFOPacketSize();
    } else {
        // ERROR!
        // 1 = initial memory load failed
        // 2 = DMP configuration updates failed
        // (if it's going to break, usually the code will be 1)
        Serial.print(F("DMP Initialization failed (code "));
        Serial.print(devStatus);
        Serial.println(F(")"));
    }

    // configure LED for output
    pinMode(LED_PIN, OUTPUT);
}

void loop() {
    // if programming failed, don't try to do anything
    if (!dmpReady) return;

    // wait for MPU interrupt or extra packet(s) available
    while (!mpuInterrupt && fifoCount < packetSize) {
      // as per Vulpo's post.
      delay(10);
      if (millis() > changeSpeedMillis) {
            curSpeed += 20;
            if (curSpeed > 256) {
              curSpeed = 30;
            }
            Serial.print("changing speed to: ");
            Serial.println(curSpeed);
            myMotors[MOTOR_FL]->run(FORWARD);
            myMotors[MOTOR_FL]->setSpeed(curSpeed);
            myMotors[MOTOR_FR]->run(FORWARD);
            myMotors[MOTOR_FR]->setSpeed(curSpeed);
            myMotors[MOTOR_RR]->run(FORWARD);
            myMotors[MOTOR_RR]->setSpeed(curSpeed);
            myMotors[MOTOR_RL]->run(FORWARD);
            myMotors[MOTOR_RL]->setSpeed(curSpeed);

            changeSpeedMillis = millis() + CHANGE_SPEED_TIME;
      }
    }

    // reset interrupt flag and get INT_STATUS byte
    mpuInterrupt = false;
    mpuIntStatus = mpu.getIntStatus();

    // get current FIFO count
    fifoCount = mpu.getFIFOCount();

    // check for overflow (this should never happen unless our code is too inefficient)
    if ((mpuIntStatus & 0x10) || fifoCount == 1024) {
        // reset so we can continue cleanly
        mpu.resetFIFO();
        Serial.println(F("FIFO overflow!"));

    // otherwise, check for DMP data ready interrupt (this should happen frequently)
    } else if (mpuIntStatus & 0x02) {
        // wait for correct available data length, should be a VERY short wait
        while (fifoCount < packetSize) fifoCount = mpu.getFIFOCount();

        // read a packet from FIFO
        mpu.getFIFOBytes(fifoBuffer, packetSize);

        // track FIFO count here in case there is > 1 packet available
        // (this lets us immediately read more without waiting for an interrupt)
        fifoCount -= packetSize;

        #ifdef OUTPUT_READABLE_EULER
            // display Euler angles in degrees
            mpu.dmpGetQuaternion(&q, fifoBuffer);
            mpu.dmpGetEuler(euler, &q);
            Serial.print("euler\t");
            Serial.print(euler[0] * 180/M_PI);
            Serial.print("\t");
            Serial.print(euler[1] * 180/M_PI);
            Serial.print("\t");
            Serial.println(euler[2] * 180/M_PI);
        #endif

        // blink LED to indicate activity
        blinkState = !blinkState;
        digitalWrite(LED_PIN, blinkState);
    }
}

Have you considered that your troubles are caused by interference from the currents flowing into your motors? If your motors are DC brush, then more interference may be radiated from the brushes back into your various wires. As a first step, perhaps let only one motor work and see if hangups diminish in frequency (although, to be sure, you need a 'scope onto a few wires carrying logic signals.

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