Robotics Sensors and Actuators

Answer

Correct Option: (i) Magnetic Angular Rate and Gravity

Explanation

MARG = Magnetic, Angular Rate, and Gravity sensor.

Components:

• M = Magnetometer (magnetic field, heading)
• A = Angular Rate = Gyroscope (angular velocity)
• R = Rate (redundant) - sometimes expanded as Magnetic
• G = Gravity = Accelerometer (gravity vector)

MARG = 9-DOF IMU: 3-axis magnetometer + 3-axis gyro + 3-axis accelerometer. Used for orientation estimation (AHRS) via sensor fusion (complementary / Kalman).

Other expansions (Magnitude, Resistance) are incorrect.

Final Answer

Magnetic Angular Rate and Gravity → Option (i).

Answer

Correct Option: (iii) Forward and inverse direction (tachometer with quadrature measures bidirectional speed)

Explanation

Tachometer encoder (incremental / quadrature) measures rotational speed and direction.

• Quadrature (A/B channels) 90° out of phase → via phase lead/lag determines forward vs reverse and counts pulses → speed $\omega = \Delta\text{pulses}/\Delta t$.
• False pulse: Noise, not speed type.
• Single revolution in multiple track: Absolute encoder (Gray code), measures absolute angle, not tachometric speed.
• Exact position: Position encoder, not tachometer.

Tachogenerator gives analog voltage ∝ speed, but quadrature encoder gives digital bidirectional speed.

Final Answer

Forward and inverse direction speed (bidirectional) → Option (iii).

Answer

Correct Option: (ii) 5

Explanation

Encoder resolution: $\text{Resolution} = \frac{360°}{2^{n}}$ where $n$ = number of tracks (bits).

Given resolution $= 11.25°$:

$$2^{n} = \frac{360}{11.25} = 32$$

$$n = \log_2 32 = 5$$

Final Answer

5 tracks → Option (ii) (32 positions).

Answer

1. What is Optical Encoder?

Device that converts rotary/linear position to digital pulses via light interruption. Resolution $=360°/2^n$ where $n$ tracks.

2. How It Works

LED → Code disk (opaque/transparent sectors) → Photodetector. Rotation interrupts beam → pulses count = angle, quadrature phase → direction.

• Incremental: Tracks A/B 90° shifted → pulses, index Z. Count pulses $\Delta N$ → angle $\theta = \Delta N \times$ resolution.
• Absolute: $n$ concentric tracks Gray code → unique $n$-bit word per position, no homing.

3. Types

Type	Principle	Output
Incremental (quadrature)	Two tracks A/B	Pulses + direction
Absolute	$n$-track Gray	Absolute $n$-bit code
Linear	Strip scale	Linear position
Rotary	Disk	Angle

4. Advantages

• High resolution ($0.1°$), accuracy.
• Non-contact (no wear vs potentiometer).
• Digital output directly to controller.
• Fast response.

5. Disadvantages

• Incremental loses position on power-off (needs homing).
• Dust/light contamination sensitive.
• Costlier than potentiometer for low resolution.

6. Applications

• Robot joint feedback, servo motors.
• CNC, 3D printer, conveyor positioning.
• Mobile odometry.

Final Answer

Optical encoder = light-interruption position sensor; counts pulses (incremental) or reads Gray code (absolute); high-resolution non-contact feedback for robot joints/CNC, needs homing for incremental.

Answer

1. What is Accelerometer?

Sensor measuring linear acceleration (m/s²) including gravity, via inertia. Output = acceleration vector.

2. How It Works

Proof mass $m$ suspended by spring. Acceleration $a$ → force $F=ma$ displaces mass $x=F/k$ → displacement → transduction.

• Capacitive MEMS: Movable plate between fixed plates, $C=\epsilon A/d$, $d$ changes with $a$.
• Piezoresistive: Strain gauge on cantilever.
• Piezoelectric: Charge on crystal.

3. Types

Type	Principle	Range
Capacitive MEMS	$C$ change	±2g to ±16g
Piezoresistive	$R$ change	High-g shock
Piezoelectric	$Q$	Vibration only
Thermal	Convection	Low-g

4. Advantages

• Measures tilt (gravity component) + vibration.
• Small MEMS, low power.
• 3-axis available.

5. Disadvantages

• Measures $a+g$ → needs fusion to get orientation.
• Drift, noise, temperature sensitive.
• Cannot measure constant velocity.

6. Applications

• IMU for robot/drone stabilization.
• Tilt sensing, fall detection.
• Vibration monitoring, impact detection.
• Smartphone auto-rotate, step counting.

Final Answer

Accelerometer = proof-mass inertia sensor $F=ma$ → $C/R/Q$ change; types MEMS capacitive/piezoresistive; advantages tilt+vibration sensing, used in IMU and motion tracking.

Answer

Potentiometer

Definition: Variable resistor with wiper, converts linear/angular position to voltage.

Construction: Resistive track (carbon/conductive plastic/wire) + wiper sliding, 3 terminals: two ends + wiper.

Working: Supply $V_{ref}$ across track, wiper voltage $V_o = V_{ref} \cdot (x/L)$, $x$ position. Linear pot $V\propto x$, rotary $V\propto\theta$.

Advantages: Cheap, simple, absolute (no homing), low power.

Disadvantages: Contact wear, friction, limited resolution, noise, limited life, loading.

Applications: Robot joint position feedback (low-cost), joystick, volume control, calibration.

Final: Potentiometer $V_o=V_{ref}x/L$ cheap absolute position but wear.

Answer

Gyroscope

Definition: Sensor measuring angular velocity (°/s) and orientation via angular momentum.

Principle: Coriolis effect on vibrating mass: $F_c = -2m\omega \times v$. MEMS tuning fork vibrates, rotation induces secondary vibration amplitude ∝ $\omega$.

Types:

Type	Principle
MEMS vibratory	Coriolis on tuning fork
Optical (FOG)	Sagnac interferometer
Mechanical	Spinning rotor

Advantages: Measures angular rate, drift compensation with accelerometer (IMU).

Disadvantages: Drift integrates to angle error, temperature sensitive, cost for optical.

Applications: Drone stabilization, robot orientation, IMU, camera gimbal, navigation.

Final: Gyroscope Coriolis $\omega$ sensor, types MEMS/FOG, used for angular rate in IMU with drift.

Answer

2D and 3D Velocity Measurement

2D Velocity: Vector $\vec{v}=(v_x,v_y)$ in plane. Methods:

• Wheel odometry: $v = \omega r$, two wheels → $v_x, \omega_z$.
• Optical flow: Camera estimates $(u,v)$ pixel/frame → $v_{world}$.
• 2D LIDAR Doppler: Frequency shift $\Delta f = 2v/\lambda$.
• IMU + GPS: Integrate $a_x,a_y$.

3D Velocity: $\vec{v}=(v_x,v_y,v_z)$.

• 3D optical flow / stereo vision: Depth $Z$ via disparity, $v_z = \Delta Z/\Delta t$.
• Doppler LIDAR / Radar: 3D $f_d$.
• IMU 6-DOF: Accelerometer + gyro fusion (Kalman) → $v_{3D}$.
• VIO: Visual-Inertial Odometry.

Comparison:

Feature	2D	3D
Sensors	Encoders, 2D LIDAR, single camera	Stereo camera, 3D LIDAR, IMU
Complexity	Low	High
Applications	Mobile base, AGV	Drone, manipulator

Final: 2D = planar $(v_x,v_y)$ via odometry/optical flow, 3D adds $v_z$ via stereo/Doppler/IMU fusion.