Unit 1: Measurements in Robotics - Subjective Questions

Sensor: A sensor is a device that detects a physical quantity such as temperature, distance, force, light, or acceleration and produces a corresponding measurable output.

Transducer: A transducer converts energy from one form into another. In instrumentation, it usually converts a physical quantity into an electrical signal.

Relationship: A sensor is often the sensing element of a transducer. The sensor detects the physical phenomenon, while the transducer converts the detected phenomenon into a usable signal.

Examples:

• An ultrasonic distance sensor detects reflected sound waves and converts the time of flight into an electrical distance signal.
• A thermistor senses temperature by changing its electrical resistance.
• A strain gauge converts mechanical strain into a change in resistance.
• An encoder converts rotary motion into electrical pulses.

The measurement process in robotics generally consists of the following stages:

• Physical phenomenon: A quantity such as position, velocity, force, or temperature exists in the robot or its environment.
• Sensing: The sensing element responds to the physical quantity.
• Transduction: The response is converted into an electrical signal, such as voltage, current, resistance, or frequency.
• Signal conditioning: The signal is amplified, filtered, linearized, or isolated.
• Analog-to-digital conversion: An ADC converts the conditioned analog signal into digital data.
• Processing: A controller interprets the measurement and may compensate for calibration errors.
• Decision and actuation: The control algorithm uses the information to generate commands for motors or other actuators.

This chain allows a robot to observe its state and environment and respond appropriately.

Sensors can be classified in several ways:

• Based on the measured quantity: Position, velocity, acceleration, force, torque, temperature, proximity, vision, and tactile sensors.
• Based on output: Analog sensors provide continuously varying outputs, whereas digital sensors provide discrete values or digital codes.
• Based on contact: Contact sensors physically touch the object, while non-contact sensors such as ultrasonic and infrared sensors measure without contact.
• Based on energy requirement: Active sensors emit energy into the environment, while passive sensors detect naturally available energy.
• Based on reference: Absolute sensors measure a quantity relative to a fixed reference, while incremental sensors measure changes from a previous position.
• Based on function: Proprioceptive sensors measure the robot's internal state, while exteroceptive sensors measure external objects or environmental conditions.
• Based on operating principle: Sensors may be resistive, capacitive, inductive, optical, magnetic, piezoelectric, or thermal.

The terms describe different sensor characteristics:

• Accuracy: The closeness of a measured value to the true value. A highly accurate sensor has a small measurement error.
• Precision: The ability to produce nearly identical readings when the same quantity is measured repeatedly.
• Resolution: The smallest change in the input that can be detected by the sensor.
• Sensitivity: The ratio of change in output to change in input, expressed as .
• Range: The minimum-to-maximum interval of input values over which the sensor operates within its specifications.

A sensor can be precise but inaccurate if its readings are repeatable but consistently offset from the true value. Similarly, high sensitivity does not necessarily mean high accuracy.

Measurement errors are the differences between the measured value and the true value. Important sources include:

• Systematic error: A repeatable error caused by calibration offset, gain error, or incorrect sensor characteristics.
• Random error: An unpredictable variation caused by electrical noise, environmental fluctuations, or internal device uncertainty.
• Environmental error: Error due to temperature, humidity, vibration, electromagnetic interference, or illumination.
• Loading error: The sensor changes the quantity being measured, thereby affecting the measurement.
• Quantization error: Error introduced when a continuous signal is represented by finite digital levels.
• Hysteresis error: Different outputs occur for the same input depending on whether the input is increasing or decreasing.
• Drift: A gradual change in output over time even when the input remains constant.
• Nonlinearity: Deviation of the sensor response from the ideal straight-line relationship.

Errors can cause inaccurate robot localization, unstable control, poor trajectory tracking, and unsafe operation.

For repeated measurements , the average value is

Averaging can reduce the influence of random error, but it does not remove a systematic bias unless the bias is known and compensated.

Static characteristics describe sensor behavior when the input is constant or changes very slowly. They include:

• Accuracy
• Precision
• Sensitivity
• Resolution
• Linearity
• Hysteresis
• Repeatability
• Range

Dynamic characteristics describe the response to time-varying inputs. They include:

• Response time
• Time constant
• Rise time
• Settling time
• Bandwidth
• Natural frequency
• Damping ratio

Static characteristics are important when a robot must measure a steady position or force accurately. Dynamic characteristics are essential when the robot moves quickly or responds to changing objects. A sensor with poor response time may introduce delays and cause instability in a feedback control system.

A smart sensor combines sensing, processing, communication, and diagnostic functions in one system. Its typical architecture contains:

• Sensing element: Detects the physical quantity.
• Transduction element: Converts the physical response into an electrical signal.
• Analog signal-conditioning circuit: Provides amplification, filtering, linearization, and offset correction.
• Analog-to-digital converter: Converts the conditioned signal into digital data.
• Processor or microcontroller: Performs calibration, compensation, data processing, diagnostics, and decision-making.
• Memory: Stores calibration constants, sensor identification data, and configuration settings.
• Communication interface: Sends data to a robot controller through interfaces such as I2C, SPI, CAN, UART, or Ethernet.
• Power-management unit: Regulates and distributes power to the sensor and electronics.

The architecture enables local processing and makes the sensor more adaptable, reliable, and easier to integrate into robotic systems.

A smart sensor is a sensor integrated with signal-conditioning electronics, a processor, memory, and often a communication interface. It can process and interpret its own measurements before transmitting them.

Compared with a conventional sensor, a smart sensor can provide:

• Automatic calibration and compensation for temperature or drift.
• Digital filtering and noise reduction.
• Linearization of a nonlinear sensor response.
• Self-testing and fault diagnosis.
• Local data conversion and feature extraction.
• Standardized digital communication.
• Storage of identification and calibration information.
• Improved interoperability with robot controllers.

A conventional sensor generally produces a raw analog output and depends on external circuits for amplification, conversion, calibration, and processing.

Calibration is the process of comparing a sensor's output with a known reference and determining the correction required to obtain accurate measurements.

A typical process is:

• Select a reference standard with accuracy better than the sensor being calibrated.
• Apply several known input values across the sensor's operating range.
• Record the corresponding sensor outputs.
• Plot or calculate the relationship between input and output.
• Determine offset, sensitivity, gain, nonlinearity, and hysteresis.
• Store a correction equation, lookup table, or calibration coefficients.
• Verify the calibrated sensor using additional reference points.

A calibration curve may be represented by

where is the gain or sensitivity and is the offset. Calibration records should include the sensor identity, date, reference equipment, environmental conditions, measured data, correction values, and next calibration interval.

• One-point calibration: A known input is applied and the output offset is corrected. It is suitable when the sensor has a reliable factory gain and the main error is zero offset.

• Two-point calibration: Two known inputs, usually near the lower and upper limits, are applied. Both offset and gain are estimated. For an approximately linear sensor, the calibration equation can be written as

  where is the measured output, is the estimated gain, and is the offset.

• Multipoint calibration: Several reference inputs are applied across the operating range. The data can be fitted using a polynomial, piecewise-linear model, or lookup table. It is appropriate for sensors with significant nonlinearity or high accuracy requirements.

Two-point calibration is common for linear sensors, while multipoint calibration is preferred for precision robotic measurement systems.

Assume that the sensor output varies linearly with the input:

For the two calibration points:

Subtracting the first equation from the second gives:

Substituting this value into the first equation gives:

Therefore, the calibrated output model is

If the measured output must be converted back to the input estimate, the inverse calibration equation is

This method corrects both the offset and the gain of an approximately linear sensor.

• Linearity: The degree to which the sensor's input-output relationship follows an ideal straight line. Nonlinearity is often expressed as a percentage of full-scale output.

• Hysteresis: The difference in output for the same input when the input is approached from increasing and decreasing directions. It may result from mechanical friction, magnetic effects, or material properties.

• Repeatability: The ability of a sensor to provide the same output when the same input is applied repeatedly under identical conditions.

• Reproducibility: The ability to provide consistent results when measurement conditions change, such as the operator, time, location, or measurement equipment.

These characteristics are important because a robot may perform repeated motions under changing environmental and operating conditions. Poor hysteresis or repeatability can produce inconsistent positioning and force-control results.

The loading effect occurs when connecting a sensor or measuring instrument changes the physical system being measured. As a result, the measured value differs from the original value.

For example, a voltage sensor with finite input resistance connected to a circuit draws current and changes the circuit voltage. In robotics, a force sensor may alter the mechanical stiffness or mass distribution of an end-effector.

Causes include:

• Finite electrical input impedance.
• Sensor mass or mechanical stiffness.
• Friction and backlash in position measurement mechanisms.
• Heat generated by the sensor.
• Physical contact with the measured object.

Methods of reduction:

• Use sensors with high electrical input impedance.
• Use signal buffers and instrumentation amplifiers.
• Select low-mass and mechanically compliant sensors where appropriate.
• Use non-contact sensing methods.
• Include the sensor's effect in the system model and calibration procedure.

Signal conditioning converts a raw sensor output into a signal suitable for processing, transmission, or control. It improves compatibility, accuracy, and reliability.

Major operations include:

• Amplification: Increases a weak signal so that it uses the available ADC range effectively.
• Attenuation: Reduces a signal that is too large for the following circuit.
• Buffering: Prevents the next circuit from loading the sensor.
• Filtering: Removes unwanted frequency components and noise.
• Linearization: Converts a nonlinear sensor response into an approximately linear output.
• Level shifting: Adds or removes a DC offset to match circuit input limits.
• Isolation: Prevents ground loops and protects low-voltage electronics from high-voltage sections.
• Excitation: Supplies a stable voltage or current to passive sensors such as strain gauges.
• Multiplexing and sample-and-hold: Allow multiple signals to share an ADC and maintain a stable value during conversion.

Proper conditioning is necessary before analog-to-digital conversion and controller processing.

An instrumentation amplifier is a precision differential amplifier designed to amplify the voltage difference between two input terminals while rejecting common-mode voltage.

Its important features are:

• High input impedance, which minimizes loading of the sensor.
• High common-mode rejection ratio, which suppresses signals appearing equally on both input lines.
• Low offset voltage and low drift.
• Adjustable and accurately controlled gain.
• Good compatibility with bridge circuits.

A simplified relationship is

where is the differential gain. Force sensors and strain gauges often use Wheatstone bridges that produce very small differential voltages in the presence of a larger common-mode voltage. An instrumentation amplifier amplifies the small useful difference while rejecting much of the unwanted common-mode signal.

Noise is an unwanted random or deterministic disturbance that is superimposed on the useful sensor signal. It reduces measurement quality and can cause incorrect control decisions.

Common types and sources include:

• Thermal noise: Produced by random motion of charge carriers in resistive components.
• Shot noise: Caused by the discrete nature of electric charge in electronic devices.
• Flicker noise: Low-frequency electronic noise associated with semiconductor devices.
• Quantization noise: Introduced when an ADC maps continuous amplitudes to discrete levels.
• Electromagnetic interference: Caused by motors, switching power supplies, wireless devices, and nearby cables.
• Mechanical noise: Produced by vibration, friction, backlash, and shocks.
• Environmental noise: Includes changes in temperature, light, acoustic energy, and air movement.

Noise may appear as voltage fluctuations, incorrect pulses, unstable readings, or errors in estimated position and velocity.

• Low-pass filter: Passes low-frequency components and attenuates high-frequency components. It is used to smooth noisy position, force, or temperature signals.

• High-pass filter: Passes high-frequency components and attenuates low-frequency components. It can remove slow drift or DC offsets and detect rapid changes.

• Band-pass filter: Passes a selected range of frequencies while attenuating frequencies below and above that range. It is useful when the useful signal is concentrated in a known frequency band.

• Notch filter: Strongly attenuates a narrow frequency band while passing most other frequencies. It is used to suppress a known interference frequency, such as a mechanical resonance or power-line component.

The filter must be selected according to the signal bandwidth and control requirements. Excessive filtering can introduce delay and reduce the robot's responsiveness.

A commonly used first-order discrete-time low-pass filter is

where:

• is the current sensor measurement.
• is the filtered output.
• is the previous filtered output.
• is the smoothing factor, with .

The current measurement contributes a fraction , while the previous output contributes a fraction . If is large, the filter responds quickly but removes less noise. If is small, the output is smoother but responds more slowly to real changes.

For a sampling interval and an approximate time constant , a common selection is

The filter is useful for noisy sensor data, but its delay must be considered in feedback control applications.

The sampling theorem states that a continuous signal with maximum frequency must be sampled at a frequency satisfying

where is the sampling frequency. The minimum theoretical sampling frequency, , is called the Nyquist rate.

Aliasing occurs when a signal is sampled too slowly. High-frequency components then appear as false lower-frequency components in the sampled data. In robotics, aliasing may cause incorrect estimates of vibration, velocity, position, or motor behavior.

Aliasing can be prevented by:

• Sampling at a sufficiently high frequency.
• Applying an analog anti-aliasing low-pass filter before the ADC.
• Limiting the bandwidth of the sensor and signal-conditioning circuit.
• Using synchronized sampling when several sensors are combined.
• Avoiding frequencies near half the sampling frequency.

Once aliasing has occurred during sampling, it cannot generally be removed by digital filtering.