Student Project Inquiry(Building a Self Balancing robot)
The MPU6050 is an I2C device.  By default the Arduino uses the internal pullup resistors in the IO pins for the pullups on the I2C bus.

This is bad - it makes the I2C bus very susceptible to noise, and motors are very noisy devices.

You need to make sure you have appropriate pullup resistors on the I2C bus (3.3KΩ is good) and keep the I2C wires as short as you reasonably can.

Also keeping power sources as separate as possible is essential.  Don't be tempted to use the 5V power from the Arduino to power your motors - you must use an external power source, or the motors will cause havoc with the microcontroller circuitry and communications.