Unit 3: Position & Light Transducers

ECE246 — Sensors For Robotics 12 min read

I. Orientation

Robotic sensing converts physical quantities such as displacement, illumination, angular motion, and acceleration into electrical signals that a controller can measure. Position and light transducers are especially important because robot control depends on knowing location, orientation, object presence, and environmental conditions.

Measurement principle: A transducer produces an output related to an input physical quantity; the relationship may be analog, digital, or frequency-based.
Resolution: The smallest input change that can be distinguished, such as (0.1^\circ) for an encoder.
Accuracy: Closeness of a measurement to the true value.
Repeatability: Ability to produce the same result under identical conditions.
Sensitivity: Change in output per unit change in input, for example (2\ \text{mV}/^\circ\text{C}).
Calibration convention: Sensor output must be mapped to physical units using a known reference, offset, and scale factor.
Loading and noise: Sensor impedance, electrical interference, quantization, temperature, and mechanical backlash can affect the measured value.

II. Position Transducers

Position transducers measure linear or angular displacement and provide feedback for robot joints, grippers, and mobile platforms. Their output is used in closed-loop control to compare actual position with commanded position.

A. Position transducers

A position transducer converts displacement into a measurable voltage, resistance, pulse count, or digital data word.

Linear position: Measures displacement (x), commonly in millimetres, using a potentiometer, linear encoder, or linear variable differential transformer.
Angular position: Measures shaft angle (\theta), commonly in degrees or radians, using a rotary potentiometer or encoder.
Absolute measurement: The output directly identifies position after power-up; an absolute encoder may provide a unique digital code for every shaft angle.
Incremental measurement: Position is obtained by accumulating changes from a reference point; power loss generally requires re-homing.
Transfer function: A linear sensor can be represented as
TEXT
```
  y = Kx + b
```
where (y) is sensor output, (K) is sensitivity, (x) is position, and (b) is offset.
Selection factors: Range, resolution, bandwidth, friction, backlash, environmental sealing, and compatibility with the controller determine suitability.

B. Potentiometers

A potentiometer measures position through the change in resistance produced by a sliding or rotating contact called a wiper.

Construction: A resistive track is connected between supply voltage (V_s); the wiper produces output voltage (V_o).
Ideal output: For a uniform track,
TEXT
```
  V_o = V_s (x / L)
```
where (x) is wiper displacement and (L) is total track length.
Angular form: For a shaft angle (\theta) over range (\theta{\max}),

TEXT
V_o = V_s (theta / theta_max)

where (\theta) and (\theta{\max}) use the same angular units.
Advantages: Low cost, simple voltage interfacing, and direct absolute position measurement.
Limitations: Wiper wear, electrical noise, finite life, friction, and limited speed make potentiometers less suitable for high-cycle robot joints.
Loading effect: A low-resistance controller input or external load forms a voltage divider and makes the output nonlinear; a buffer amplifier reduces this error.

C. Optical encoders

Optical encoders use a light source, patterned disk or scale, and photodetectors to determine shaft position or motion.

Incremental quadrature: Two channels, A and B, are phase-shifted by (90^\circ). The sequence A-leading-B indicates one direction, while B-leading-A indicates the reverse.
Position calculation: If (N) counts are recorded for an encoder with (P) pulses per revolution,
TEXT
```
  theta = 2 pi N / (4P)
```
for four-edge quadrature counting; (\theta) is angular position in radians.
Index pulse: A once-per-revolution Z pulse establishes a reference position and supports accurate homing.
Absolute encoder: Multiple tracks or coded patterns provide a unique position word, avoiding accumulated count loss.
Advantages: High resolution, low mechanical contact, good repeatability, and direct digital compatibility.
Limitations: Dust, oil, vibration, missed pulses, and poor alignment can reduce reliability; signal cables require noise control.

D. Interfacing of position transducers

Interfacing converts the raw sensor output into a clean, scaled signal suitable for a robot controller.

Analog interface: A potentiometer output is filtered and connected to an ADC; an (n)-bit ADC with reference (V_{\text{ref}}) has ideal voltage step
TEXT
```
  Delta V = V_ref / (2^n - 1)
```
where (n) is ADC resolution in bits.
Digital interface: Encoder channels connect to interrupt inputs, timer/counter peripherals, or fieldbus modules; hardware counting prevents missed pulses at high speed.
Signal conditioning: Use voltage dividers, buffers, differential receivers, Schmitt triggers, pull-up resistors, and low-pass filters as required.
Calibration: Measure output at known positions, determine gain and offset, and store correction constants in the controller.
Electrical protection: Grounding, shielding, galvanic isolation, and transient suppression protect low-level signals from motor switching noise.

III. Light Transducers

Light transducers detect visible, infrared, ultraviolet, or other optical radiation and convert photon energy into current, voltage, resistance, or multiplied charge.

A. Light transducers

A light transducer produces an electrical response related to incident optical power or illumination.

Photovoltaic response: A photodiode can generate current approximately proportional to incident optical power over a useful range.
Photoconductive response: Illumination changes the conductivity of a material, as in a photoresistor.
Robot uses: Object detection, line following, barcode reading, flame detection, optical communication, and position measurement.
Important quantities: Illuminance is measured in lux, while optical power is measured in watts; the two are not interchangeable without considering spectral response.
Design concerns: Ambient light, wavelength, response time, saturation, dark current, and field of view affect sensor performance.

B. Photo resistors

Photo resistors, or light-dependent resistors (LDRs), change resistance according to illumination.

Operating relationship: Resistance decreases as light intensity increases; the exact relationship is material-dependent and often nonlinear.
Interface circuit: An LDR and fixed resistor form a voltage divider:
TEXT
```
  V_o = V_s R_f / (R_LDR + R_f)
```
where (Rf) is the fixed resistance and (R{\text{LDR}}) is light-dependent resistance.
Advantages: Inexpensive, simple, and sensitive over a broad light range.
Limitations: Slow response, significant temperature dependence, nonlinear output, and poor precision compared with photodiodes.
Application: A robot can detect a bright line or lamp by comparing divider voltage with an ADC threshold, but calibration is needed when ambient illumination changes.

C. Photo diodes & Photocells

Photodiodes and photocells detect light by generating a photocurrent, with photodiodes generally providing faster and more predictable operation.

Photodiode biasing: Reverse bias widens the depletion region and reduces junction capacitance, improving speed; zero-bias photovoltaic operation reduces circuit complexity.
Photocurrent: Over the linear range,
TEXT
```
  I_photo approximately proportional to P_opt
```
where (I{\text{photo}}) is photocurrent and (P{\text{opt}}) is incident optical power.
Transimpedance interface: An op-amp converts current to voltage:
TEXT
```
  V_o = -I_photo R_f
```
where (R_f) is feedback resistance.
Photocell meaning: In robotics, “photocell” may refer broadly to a light-sensitive cell, including a photodiode or LDR; the actual device type should be specified.
Limitations: Dark current, amplifier noise, saturation, and spectral mismatch require filtering and suitable bias selection.

D. Photomultipliers

Photomultipliers detect extremely weak light by multiplying photoelectrons emitted from a photocathode.

Operating sequence: Photons strike a photocathode, emitted electrons are accelerated through dynodes, and secondary emission increases the electron population.
Gain: Total gain may reach approximately (10^6) to (10^8), depending on dynode number and voltage.
Advantages: Exceptional sensitivity, fast response, and low-light detection capability.
Limitations: Requires high voltage, is physically delicate, responds to magnetic fields, and is unsuitable for ordinary bright-light robot sensing.
Application: Photomultipliers are useful in scientific instruments, fluorescence measurement, and specialized radiation or photon-counting systems.

E. Optical array transducers

Optical array transducers combine many light-sensitive elements to obtain spatial information rather than one overall intensity value.

Array structure: A linear array supports scanning across a barcode or edge; a two-dimensional CCD or CMOS array captures an image.
Readout: Pixels are addressed sequentially and converted by ADCs into intensity values.
Robot applications: Vision, line tracking, object recognition, structured-light ranging, and optical flow.
Resolution trade-off: More pixels improve spatial detail but increase data rate, processing demand, and sensitivity to calibration errors.
Calibration requirements: Dark-current subtraction, gain correction, lens distortion correction, and exposure control improve measurement quality.

F. Thermal and photon detectors

Thermal and photon detectors differ in whether radiation is measured through heating or direct photon interaction.

Thermal detectors: Incident radiation raises detector temperature; thermopiles and bolometers can respond over broad wavelengths but are comparatively slow.
Photon detectors: Photodiodes and photomultipliers use photon-generated charge carriers and generally offer faster response.
Comparison:
1. Thermal: Broad spectral response, lower speed, and output linked to temperature rise.
2. Photon: Wavelength-dependent response, high speed, and output linked to photon energy or count.
Robotic selection: Infrared thermopiles suit noncontact temperature measurement, while photodiodes suit fast beam interruption or position detection.

G. Interferometers

Interferometers measure very small displacement by comparing the phase of coherent light beams traveling along different optical paths.

Principle: A beam splitter creates reference and measurement beams; recombination produces intensity fringes dependent on path difference.
Displacement relation: In a simple reflective arrangement, one fringe movement corresponds to displacement
TEXT
```
  d = lambda / 2
```
where (d) is mirror displacement and (\lambda) is light wavelength.
Advantages: Extremely high resolution and excellent repeatability.
Limitations: Requires coherent light, accurate alignment, vibration isolation, and careful interpretation of fringe counts.
Application: Precision robot calibration, linear-stage measurement, and checking positioning accuracy.

IV. Inertial and Mobile-Robot Sensors

These sensors estimate orientation, motion, or travelled distance when direct external position measurements are unavailable.

A. Gyroscopes

A gyroscope measures angular velocity and can estimate orientation by integration.

Measurement model:
TEXT
```
  theta(t) = theta(0) + integral omega(t) dt
```
where (\theta) is angle and (\omega) is angular velocity.
MEMS principle: A vibrating mass experiences Coriolis force when the device rotates; capacitive sensing measures the resulting vibration change.
Main error: Bias and scale-factor errors integrate over time, producing drift.
Correction: Fuse gyro data with accelerometer, magnetometer, encoder, or external position data to bound drift.

B. Inertial Measurement Unit (IMU)

An IMU combines accelerometers and gyroscopes, commonly in a three-axis package, to estimate body motion.

Components: A six-axis IMU contains three accelerometer axes and three gyro axes; a nine-axis unit adds a three-axis magnetometer.
Attitude estimation: Gyro integration provides short-term dynamic response, while gravity measured by accelerometers supplies a long-term pitch and roll reference.
Fusion methods: Complementary filters, Kalman filters, and nonlinear attitude filters combine complementary sensor strengths.
Limitations: Linear acceleration can be confused with gravity, gyro bias causes drift, and vibration requires mechanical or digital filtering.

C. Wheel odometry

Wheel odometry estimates mobile-robot displacement from wheel rotations.

Single-wheel distance:
TEXT
```
  s = r phi
```
where (s) is travelled distance, (r) is wheel radius, and (\phi) is wheel rotation in radians.
Differential drive: For wheel distances (s_R) and (s_L), the approximate heading change is
TEXT
```
  Delta theta = (s_R - s_L) / B
```
where (B) is the distance between wheels.
Advantages: Inexpensive, continuous, and independent of lighting.
Limitations: Wheel slip, unequal diameters, backlash, encoder quantization, and floor irregularities cause cumulative error.

D. Accelerometers

Accelerometers measure specific force, including the effect of gravity, and are used for motion, tilt, vibration, and shock sensing.

Basic relation: For an ideal stationary axis aligned with gravity, the measured magnitude is approximately (9.81\ \text{m/s}^2), or (1g).
Position estimation: Double integration is theoretically possible:
TEXT
```
  v = v_0 + integral a dt
  x = x_0 + integral v dt
```
where (a) is acceleration, (v) velocity, and (x) position.
Drift problem: A small bias, such as (0.01\ \text{m/s}^2), creates rapidly growing velocity and position errors after integration.
Applications: Tilt estimation, collision detection, stabilization, vibration monitoring, and sensor fusion.

V. Contact and Range Sensors

These sensors detect nearby objects or boundaries either through physical contact or emitted radiation.

A. Limit switches

A limit switch is a mechanically actuated binary sensor that signals when a mechanism reaches a defined travel boundary.

Construction: A lever, roller, or plunger operates normally open (NO) or normally closed (NC) contacts.
Interface: A digital input with a pull-up resistor reads a stable logic state; switch bounce is removed through hardware filtering or software debounce.
Applications: Robot homing, end-of-travel protection, gripper closure detection, and emergency interlocking.
Limitations: Mechanical wear, contact bounce, actuation force, and finite positioning repeatability require suitable mounting and redundancy where safety matters.

B. Infrared sensors

Infrared sensors use infrared emission and detection to sense proximity, reflectivity, interruption, or temperature.

Reflective arrangement: An IR LED emits radiation and a photodiode or phototransistor measures returned light; output depends strongly on surface colour and distance.
Break-beam arrangement: An emitter and receiver face one another; an object is detected when it interrupts the beam.
Modulation: Pulsing the emitter at a carrier frequency, such as (38\ \text{kHz}), helps reject sunlight and steady ambient illumination.
Limitations: Black or shiny surfaces, sunlight, cross-talk, and changing geometry can produce false readings.
Applications: Line followers, obstacle detectors, encoders, and object counters.

C. Ultrasonic sensors

Ultrasonic sensors determine distance from the time taken for a sound pulse to travel to an object and return.

Range equation:
TEXT
```
  d = c t / 2
```
where (d) is target distance, (c) is sound speed, approximately (343\ \text{m/s}) at (20^\circ\text{C}), and (t) is round-trip time.
Operation: A transducer transmits a burst, switches to receiving mode, and measures the echo time.
Advantages: Works in darkness, measures several metres in suitable conditions, and is less dependent on visible colour than optical sensors.
Limitations: Soft or angled surfaces absorb or deflect sound; temperature changes alter (c), while multiple echoes and a minimum blind zone complicate measurement.
Robotic use: Obstacle avoidance, wall following, bin-level sensing, and approximate mapping. Sensor placement and time scheduling are needed to prevent cross-talk between multiple units.