Robo India presents theory and working principles of Inertia Measuring unit (IMU), gyroscope, accelerometer and Kalman Filter. It is an important controlling part of unmanned Arial vehicles (UAV) We have named it as evaluation of dynamics. We welcome all of your views and queries, we are found at- website: http://roboindia.com mail- info@roboindia.com

1. Evaluation of Dynamics
Robo India
www.roboindia.com

2. Introduction
The study of the causes of motion and changes
in motion is Dynamics.
Our points of concern of Dynamics:
Acceleration.
Angular velocity.
Position and Orientation.

3. Required Instruments
The evaluation procedure will require following
instruments/devices.
1. Accelerometer
2. Gyroscope
3. Inertial Measuring Unit

4. Accelerometer | Introduction
Accelerometer is a device that measures
acceleration with respect to gravity free space
reference (free fall reference).
A typical concept of accelerometer

5. Draw backs of typical accelerometer
• It would be more complex for multiple axis.
• Measurement would be more complex.
• Difficult to fit in applications.
• Maintenance would be high.
Micro Electro Mechanical System (MEMS)
accelerometer sensors overcome all such
limitations.

6. MEMS Accelerometer
MEMS accelerometer are very tiny
electromechanical sensors that gives output in
electronic form(i.e. voltage/current) .
Types of MEMS accelerometers:
• Capacitive
• Piezoelectric
• Piezoresistive etc.

7. Capacitive Accelerometer
In capacitive accelerometer micro-machined silicon
material is used. The distance between these
materials varies with the acceleration faced by the
accelerometer that causes to change the
capacitance which leads to change output voltage.
The particular output voltage defines a particular
acceleration.
Out put can be:
1. Analogue
2. Digital

8. Useful Terminologies
• Output: accelerometer sensor gives voltage output that
indicates the acceleration faced by the sensor in terms of g
(acceleration due to gravity (g) = 9.81 m/sec2).
• Sensitivity: The rate of change in output voltage with the
acceleration. (Unit: mV / g)
• Ratiometricity: It means a linear relation between output
voltage and sensitivity with respect to change in applied
supply voltage.
• Zero g (0g): standard output voltage that represents a
gravity free space, means the accelerometer is facing no
acceleration.

9. Capacitive Accelerometer | Concept

10. Acceleration Measurement

11. Measurement of angle & acceleration
R = √ ( Accx
2 + Accy
2 + Accz
2)
Ax = cos-1(Accx / R)
Ay = cos-1(Accy / R)
Az = cos-1(Accz / R)
Where:
Vx, Vy, Vz : Output for respective axis
ACC x, ACCy, ACCz : Acceleraton of respective axis
R : Resultant Vector
A x, Ay, Az : Angle about respective axis

12. Application of Accelerometers
• Engineering: to detect acceleration, engine testing, air
bag operations, breaking system and various industrial
applications.
• Robotics: Motion sensing, hand held devices to save
battery consumption.
• 3D-Gamming: Tilt & motion sensor
• Cell phones / PDA : Screen orientation, gamming sensor,
image stability
• Navigation and dead reckoning: e-compass
• Laptop PCs, HDD audio and video player: Free fall
detects to prevent data damaging in Hard Disk Drives
(HDD).

13. Gyroscope
Gyroscope is a device that resists to change its position, its
position doesn’t change with the changes occurs in
external surroundings. This property helps extremely in
determining the angular velocity for the balancing,
landing, turning and taking off of air-vehicles.

14. MEMS Gyroscope
Electronic(MEMS) gyroscope sensors are different from
the traditional and mechanical gyroscopes. A very tiny IC
(Plastic Land Grid Array, LGA package) does the same work
and gives output in the desired manner, which makes the
electronic gyroscope very easy to use in automation.
MEMS Gyroscope works on the Coriolis force concept. A
driving mass is kept in continuous oscillating movement,
the driving mass acts as sensing element and reacts to the
applied angular velocity. The whole arrangement is made
up by the integration of actuators and accelerometers on
a micro-machined chip.

15. Measuring Gyro output
Angular velocities:
Ωx = (Vx-V0)/Sensitivity 0/sec
Ωy = (Vy-V0)/Sensitivity 0/sec
Ωz = (Vz-V0)/Sensitivity 0/sec
Where:
Vx , Vy & Vz :Output voltages for X,Y and Z axis.
Ωx , Ωy & Ωz :Angular velocities about X, Y & Z axis
x, 𝒙′ : new and old position
𝑻 − 𝑻′ : Time difference
Position:
𝒙 = 𝒙′ + 𝜴 (𝑻 − 𝑻′)

16. Application of Gyroscope
• Spaceship
• Ship / and motor boats
• Airplanes
• Unmanned air vehicles
• Racing cars
• Gamming consoles
• Robotics
• Dead reckoning (vehicle navigation)
• Motion sensing in mobile phones and PDA’s

17. Inertial Measuring Unit (IMU)
Inertial Measuring Units are the integration of
Accelerometers and Gyroscopes that measures velocity,
orientation, acceleration, angular velocity and
gravitational force.
• Why IMU?
• Advantages of IMU
• Requirement of filter

18. Kalman Filter
Kalman Filter was proposed by Hungarian-American
engineer Rudolf Emil Kalman. Kalman Filter is a
mathematical estimation algorithm that involves a wide
range of processes and applications.
The Kalman Filter has main
function of combining the
measurement of time series
data of the same variables but
from the different sensors and
to forecast the state. It predicts
the state and corrects it.

19. Kalman Filter

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