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welcome to the next video in our series
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explaining how to build your own Arduino
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quadcopter drone in this video we will
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explore how you can measure angles with
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the help of the mpu 6050 gyroscope and
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accelerometer
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which will subsequently be used to
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design a different type of flight
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controller in the previous videos we
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designed a flight controller to
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stabilize the quadcopter based on the
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rotation rates in degrees per second
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this means that you give a rotation rate
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commands to your radio transmitter for
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example if you move the stick and give
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it a pitch rate command of 10 degrees
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per second the quadcopter will pitch 10
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degrees each seconds if you release a
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stick after 6 seconds the pitch rotation
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rate commands will fall back to zero
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degrees per second causing the pitch
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angle of the quadcopter to stop at 60
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degrees however the quadcopter does not
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automatically go back to a level pitch
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angle of zero degrees with this type of
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controller for Pilots this type of
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controller is rather difficult because
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it does not stabilize the quadcopter to
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a level position when releasing the
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sticks to go to such a controller it is
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necessary to give an angle commands for
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example when you give a 45 degree pitch
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command with the Stick of the radio
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transmitter the controller will cause
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the pitch angle of the quadcopter to go
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as quick as possible to 45 degrees when
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you release the stick the pitch angle
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command goes back to 0 degrees and the
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quadcopter's pitch angle goes back to
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zero degrees as well the controller
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which gives you direct control over the
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roll and Pitch angles of your quadcopter
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is often called a stabilized mode
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controller as opposed to a rate or Acro
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mode controller to build a stabilized
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mode controller we first need to be able
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to measure angles correctly a very
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simple approach to measure angles can be
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found by simply integrating the rotation
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rates to get the actual angle remember
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that K holds the number of the current
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iteration and TS is the iteration length
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which is equal to 4 milliseconds in a
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250 Hertz Loop if you were discretizing
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integral for using the Arduino codes
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you would need to add the rotation rate
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multiplied by the iteration length to
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the angle of the previous iteration in
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order to get the angle of the current
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iteration if that sounds too simple to
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be true that's unfortunately because it
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is this approach has two major problems
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you keep dragging all measurement errors
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from previous iterations with you
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causing the calculated angle to drift
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very fast another issue is a change of
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angles during your movement suppress the
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quadcopter is flying with a constant
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pitch angle of 45 degrees when you are
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around the z-axis without any pitch
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rotation rate around the y-axis the
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pitch angle will nonetheless decrease or
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increase because the y-axis changes its
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direction as well this is equally true
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for the rule rotation rate that is why
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you need to use a totally different
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approach for measuring angles and for
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which you will use the accelerometer
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built in your mpu 6050 as the name
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implies the accelerometer measures the
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acceleration of the sensor along the X Y
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and Z directions from basic physics you
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remember that we experience a
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gravitational acceleration and anywhere
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on Earth and that this gravitational
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acceleration is equal to the
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gravitational constant 1G or 9.81 meters
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per square seconds this means that when
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you let your mpu 6050 sensor lie flat on
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a table without moving it the
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measurement of the acceleration along
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the zip direction or x z is equal to 1G
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the acceleration along the X and Y axis
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will be zero in this case similarly when
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you position the sensor such that one of
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the other axis lies perpendicular to the
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surface of the table the corresponding
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acceleration is also equal to 1g of
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course any other direction not along one
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of the three main axes will result in a
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non-zero acceleration value for all
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three directions through some clever
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mathematical equations this
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accelerometer property will enable you
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to calculate the exact Rule and Pitch
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angles of your quadcopter let's assume
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you roll around the x-axis until you
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reach the angle Theta rule to visualize
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this transformation a box bounded by the
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X Y and Z directions is sketched on the
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screen from your basic trigonometry
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knowledge you know that the tangent of
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the angle of a triangle is equal to the
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length of the opposite side divided by
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the length of the adhesion side in case
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of the angle Theta rule the length of
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the opposite side is equal to the
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acceleration in the y direction the
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length of the adjacent side can be
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calculated by the Pythagoras who finally
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giving you the equation to calculate the
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roll angle from the accelerometer values
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a similar strategy and reasoning can be
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applied for the pitch angles giving you
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a second equation to calculate the pitch
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angle from the accelerometer values and
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that's it
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you are now able to calculate the rule
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and Pitch angles from the accelerometer
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values now you need to transform this to
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a working code for this part you only
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need your TNC and mpu6050 and you can
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choose to test the code on a breadboard
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or directly on your assembled quadcopter
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we will take the code from the gyroscope
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derived in Parts 4 and 5 and add the
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necessary lines to read the
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accelerometer values first Define the
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accelerometer and roll and Pitch
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variables next start a function that
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will extract the signals from the
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mpu6050 and switch on the low pass
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filter seen in Project 4. now you need
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to configure the accelerometer outputs
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according to the mpu6050 register map
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the accelerometer configuration settings
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are stored in register 1C for this
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project you will choose a full-scale
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range of 8 G which corresponds to a
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value for the AFS scl setting of two or
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a 0 for B3 and a 1 4 bit 4. the other
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bits can be set to zero which gives a
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binary representation of 16 or a
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hexadecimal value of 10. the values of
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the accelerometer are located in the
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registers with hexadecimal numbers 3B
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240. start writing to address 0 times 3B
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to indicate the first register and
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request 6 bytes from the address of the
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sensor 0 times 68 the accelerometer
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measurements are spread out over 3 times
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2 registers with each 8 Bits repeat the
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same code for all accelerometer
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directions next configure the gyroscope
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output as seen in part 4 and extract the
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rotation rates to convert the
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accelerometer measurements from LSB to G
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remember that you configured the AFS scl
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setting to an LSB sensitivity of 4096
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LSB per G to get the measurements in G
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just divide the measurement in LSB by
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4096 LSB per g at the start of this part
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you learned how to calculate the roll
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and Pitch angles from the accelerometer
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values you can use these equations at
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this point but take into accounts that
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are acting hence calculated by Arduino
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returns a result in radians not in
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degrees to convert the angles from
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radians to degrees just divide the
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results by P divided by 180. start a
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communication with the gyroscope as seen
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in part 4 and print the accelerometer
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values now upload The Code by connecting
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the TNC to your computer and pressing
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the upload button in the Arduino IDE
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open the serial Monitor and watch the
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acceleration measurements in the X Y and
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Z directions on the screen you will see
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that the acceleration in the set
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direction is almost equal to 1G because
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the mpu6050 is lying flat on the table
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now tilt the sensor vertically in the y
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direction
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notice that the acceleration in the y
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direction
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becomes almost equal to 1 while the Z
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Direction goes back to zero repeat this
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for the X Direction
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calibration is once again necessary to
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correct these values as they are not
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exactly equal to one in the different
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directions this calibration needs to be
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done manually and will be different for
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each sensor just abstract or add the
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difference between the actual values of
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the accelerometer and one in lines 36 to
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38 of the codes and we check that the
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acceleration values in all three
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directions are equal to one G when
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tilting the mpu 6050
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now that you have calibrated the
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accelerometer replace the lines in the
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loop parts of the codes to print the
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roll and pitch angle and upload the code
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again instead of looking at the serial
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monitor we will use the serial plotter
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to visualize the roll and Pitch angles
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first you will roll the accelerometer in
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the positive direction up to an angle of
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30 degrees the accelerometer values are
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very responsive and very accurate repeat
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this movement and subsequently perform a
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two positive and one negative pitch
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movement as well the results are
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excellent and very accurate
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when the sensor is level again the roll
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and Pitch angles are nearing zero
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however a problem appears when the
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accelerometer experiences vibrations
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which are inevitable when flying a
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quadcopter due to the presence and
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influence of the moving Motors let's
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simulate these Vibrations by hand you
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will notice a very sharp Peaks and drops
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in the measured pitch and roll angles
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because the amplitude of these
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vibrations will increase a lot during
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flight it is not feasible to build a
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good controller based on the
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accelerometer measurements because they
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are heavily disturbed by these
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vibrations integrating the rotation
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rates to obtain the angles is also
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possible and straightforward as we saw
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in the first part of this video this
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rotation rate measurements are not
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sensible to vibrations however you get
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an ever increasing error because you
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will add all measurement error first
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when integrating to obtain the angle the
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graph on the screen shows the
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measurements of the angle through
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rotation rate integration and
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accelerometer trigonometry for a
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stationary sensor and illustrates the
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ever increasing error with rotation rate
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integration and the sensitivity to
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vibrations with accelerometer
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measurements it is clear that the two
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methods of measuring and calculating
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angles are not suitable for a flight
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controller and that we will need a
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different solution in the next video
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I will show you how you can combine both
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measurements and get rid of their
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individual disadvantages by using a
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Kalman filter
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thank you for watching this video don't
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forget to subscribe if you like the
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series and remember that you can find
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all tutorials on YouTube and the full
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code on GitHub
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the manual which contains all
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expectations is available as well on
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GitHub if you need some more information
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thanks for watching and see you next
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time
