Unit 3: Electrical and Electronics Elements

ECE244 — Elements Of Robotics 10 min read

I. Orientation — Electrical energy, motion, sensing, and control

Robotic systems convert electrical energy into controlled mechanical motion, measure physical conditions through sensors, and use embedded controllers to make decisions. The central chain is power source → driver → actuator → mechanism, with sensor feedback → controller closing the control loop.

Energy conversion: Motors convert electrical power into torque and speed; sensors convert physical variables into electrical signals.
Voltage and current: Voltage (V) is electrical potential difference in volts; current (I) is charge flow in amperes.
Power relationship: Electrical power is
[
P=VI
]
where (P) is power in watts.
Feedback principle: A controller compares desired output with measured output and adjusts actuator input.
Signal convention: Analog signals vary continuously, while digital signals use discrete logic levels such as (0) and (1).
Practical assumptions: Components must remain within rated voltage, current, temperature, speed, and mechanical-load limits.

II. Electromechanical Actuators — Motors that produce motion

Motors are actuators that generate rotational motion through electromagnetic interaction. Selection depends on required torque, speed, positioning accuracy, efficiency, cost, and control complexity.

A. DC motors

A DC motor produces continuous rotation when direct current creates electromagnetic torque between its stator field and rotor conductors.

Construction: Common parts include permanent magnets or field windings, an armature, commutator, and brushes.
Operating relation: Motor torque is approximately
[
T=K_t I
]
where (T) is torque in N·m, (K_t) is the torque constant, and (I) is armature current.
Speed control: Pulse-width modulation (PWM) changes average applied voltage; a 60% duty cycle ideally applies about (0.6V_s), where (V_s) is supply voltage.
Advantages: DC motors are inexpensive, simple to control, and suitable for wheels, fans, pumps, and small robotic joints.
Limitations: Brushes wear, electrical noise is produced, and open-loop speed varies with load; an encoder is needed for accurate feedback.

B. Servo motors

A servo motor is a motor combined with feedback and control electronics to achieve a commanded position, speed, or torque.

Closed-loop action: The controller minimizes error
[
e(t)=r(t)-y(t)
]
where (r(t)) is the reference position and (y(t)) is measured position.
Typical hobby servo: A three-wire servo commonly uses power, ground, and a PWM command; a pulse near 1.5 ms often represents the center position, though exact limits vary.
Components: A servo includes a motor, reduction gears, position sensor, amplifier, and internal controller.
Applications: Robot arms, steering mechanisms, camera mounts, and grippers use servos when controlled angular position is required.
Limitations: Gear backlash, limited rotation range, stall-current heating, and inadequate torque can reduce performance.

C. Stepper motors

A stepper motor rotates in discrete angular increments as its stator phases are energized in sequence.

Step angle: If a motor has (N_s) steps per revolution,
[
\theta_s=\frac{360^\circ}{N_s}
]
where (\theta_s) is the step angle.
Control: A driver receives pulse and direction signals; each pulse commands one step or microstep.
Strengths: Steppers provide simple position control without an encoder and produce high holding torque at low speed.
Weaknesses: They may lose steps under excessive load or acceleration, and current remains significant while holding position.
Applications: 3D printers, CNC axes, linear stages, and indexing mechanisms use steppers for predictable incremental movement.

D. Brushless DC motors (BLDC)

A BLDC motor uses electronic commutation instead of brushes and a mechanical commutator.

Construction: Permanent magnets are normally placed on the rotor, while three-phase windings are placed on the stator.
Commutation: A controller energizes phases in sequence using Hall sensors, an encoder, or sensorless back-EMF detection.
Advantages: BLDC motors offer high efficiency, long service life, low maintenance, and high power-to-weight ratio.
Control quantity: Three-phase inverter switches regulate winding currents; electrical commutation frequency increases with rotor speed.
Applications and limits: Drones, electric vehicles, cooling fans, and collaborative robots benefit from BLDC motors, but their drivers and control algorithms are more complex than those of brushed DC motors.

III. Motor Interface and Feedback — Drivers and measurement

Actuators require power electronics to switch current safely and sensors to report actual motion. These elements connect low-power controller signals to high-power mechanical behavior.

A. Motor drivers

A motor driver is a power-electronic interface that supplies the current and voltage required by a motor while accepting low-power control commands.

H-bridge: Four switches allow a DC motor to run forward, reverse, brake, or coast; reversing polarity reverses rotation.
PWM control: The duty ratio
[
D=\frac{t{\text{on}}}{T}
]
where (t{\text{on}}) is switch-on time and (T) is PWM period, controls average motor voltage.
Protection: Drivers commonly include overcurrent, thermal shutdown, undervoltage lockout, and flyback paths for inductive current.
Motor matching: A driver must tolerate the motor’s nominal voltage, continuous current, peak or stall current, and switching frequency.
BLDC operation: A three-phase inverter, often using MOSFETs, independently switches the motor phases according to rotor position.

B. Encoders

An encoder measures shaft position or rotation and converts it into electrical pulses or digital data for feedback control.

Incremental encoder: Produces A and B quadrature channels; the phase order indicates direction, while pulse count indicates relative displacement.
Absolute encoder: Provides a unique digital code for each shaft angle, retaining position information after power loss.
Resolution: An encoder rated at 1,000 pulses per revolution gives an angular interval of (0.36^\circ) per pulse before quadrature processing.
Feedback use: Position error can be converted into motor commands, allowing speed regulation, trajectory tracking, and detection of stalled motion.
Limitations: Missed counts, electrical noise, mounting misalignment, and backlash can cause measured position to differ from actual tool position.

IV. Electrical Energy Systems — Power supply and storage

Power systems must provide stable voltage and sufficient current while protecting electronics and actuators from faults.

A. Power supply systems

A power supply system converts, regulates, distributes, and protects electrical energy for the robot.

Main stages: A system may contain a battery or mains input, fuse, switch, DC-DC converter, regulator, motor bus, and logic-voltage rail.
Voltage regulation: A buck converter reduces voltage efficiently; a boost converter increases it; a linear regulator is simple but dissipates excess power as heat.
Sizing relation: Required supply power should exceed
[
P{\text{req}}\geq \frac{\sum P{\text{loads}}}{\eta}
]
where (\eta) is conversion efficiency.
Distribution: Motors should have suitable wiring, grounding, decoupling capacitors, and sometimes a separate logic supply to limit noise.
Protection: Fuses, reverse-polarity protection, current limiting, thermal monitoring, and emergency-stop circuits reduce hazard and component damage.

B. Batteries

A battery stores chemical energy and supplies portable electrical power to the robot.

Capacity: Battery energy is approximately
[
E=V{\text{nom}}C
]
where (E) is watt-hours, (V{\text{nom}}) is nominal voltage, and (C) is capacity in ampere-hours.
Common chemistries: Lithium-ion and lithium-polymer cells have high energy density; nickel-metal hydride is more tolerant but heavier; lead-acid is inexpensive but bulky.
Discharge rating: A 2 Ah battery rated at 10C can theoretically deliver 20 A under specified conditions.
Battery management: Lithium batteries require cell balancing, overcharge protection, over-discharge protection, and temperature monitoring.
Practical limits: Actual runtime decreases with high current, cold temperature, aging, conversion loss, and peak motor loads.

V. Robotic Sensing — Detecting environment and state

Sensors provide measurements needed for navigation, safety, manipulation, and control. Sensor choice depends on range, resolution, response time, environmental conditions, and interface.

A. Basic sensors

Basic sensors detect variables such as light, temperature, acceleration, magnetic field, and sound.

Temperature: A thermistor changes resistance with temperature; an ADC converts its voltage-divider output into a digital value.
Light: An LDR or photodiode changes electrical behavior with illumination and can support line following or object detection.
Inertial measurement: Accelerometers measure linear acceleration in (\text{m/s}^2); gyroscopes measure angular rate in rad/s or degrees/s.
Magnetic sensing: Hall-effect sensors detect magnetic fields and can identify gear teeth, rotor position, or end-stop magnets.
Selection concern: Sensor range and resolution must match the task; a narrow-range sensor can saturate when the physical input exceeds its limits.

B. Proximity sensors

Proximity sensors detect nearby objects without requiring physical contact.

Inductive type: Detects conductive metal through changes in an electromagnetic field; it is reliable in dusty industrial environments but does not detect plastic well.
Capacitive type: Detects changes in capacitance and can sense plastic, liquid, or metal, though humidity and material variation affect readings.
Ultrasonic type: Sends a sound pulse and measures echo time:
[
d=\frac{vt}{2}
]
where (d) is distance, (v) is sound speed, and (t) is round-trip time.
Infrared type: Uses emitted or reflected infrared light; ambient light, surface color, and reflectivity influence measurement.
Applications: Proximity sensors support collision avoidance, object presence detection, limit detection, and automatic gripping.

C. Position sensors

Position sensors measure linear or angular location of a robot link, joint, wheel, or end effector.

Potentiometer: A wiper produces voltage proportional to shaft position over its mechanical range; it is inexpensive but wears mechanically.
Encoder: Incremental and absolute encoders provide digital position information, as described by pulse count or an angle code.
Linear sensor: A linear potentiometer, magnetic scale, or linear encoder measures translation in millimeters.
Reference requirement: Incremental systems generally need homing against a limit switch because pulse counts alone do not define absolute position after startup.
Error sources: Quantization, backlash, offset, misalignment, and calibration error reduce positional accuracy.

D. Force sensors

Force sensors measure applied force, load, pressure, or torque so that a robot can interact safely with objects.

Strain gauge: Mechanical deformation changes resistance; a Wheatstone bridge converts small resistance changes into a differential voltage.
Load cell: A calibrated strain-gauge structure measures force, commonly in newtons or kilograms-force.
Tactile sensing: Pressure-sensitive materials or arrays detect contact location and distribution in grippers and robotic fingers.
Torque relation: For a known lever arm,
[
\tau=Fr
]
where (\tau) is torque in N·m, (F) is force in newtons, and (r) is perpendicular distance in meters.
Limitations: Hysteresis, temperature drift, overload, mounting stress, and calibration quality affect force accuracy.

VI. Signal conditioning — Making sensor signals usable

Signal conditioning prepares raw sensor outputs for reliable processing by amplification, filtering, isolation, conversion, or linearization.

Amplification: An instrumentation amplifier increases a small differential signal while rejecting common-mode voltage; gain is (G=V{\text{out}}/V{\text{in}}).
Filtering: A low-pass filter reduces high-frequency noise; for a first-order RC filter,
[
f_c=\frac{1}{2\pi RC}
]
where (f_c) is cutoff frequency, (R) resistance, and (C) capacitance.
ADC conversion: An (n)-bit ADC with reference (V{\text{ref}}) has ideal voltage resolution
[
\Delta V=\frac{V{\text{ref}}}{2^n}.
]
Other operations: Voltage dividers adapt ranges, bridge circuits measure resistance changes, isolation protects logic, and linearization maps nonlinear readings to physical units.
Design caution: Filtering reduces noise but introduces delay; excessive delay can destabilize fast motor-control loops.

VII. Introduction to embedded controllers — Local computation and control

An embedded controller is a dedicated computing unit, commonly a microcontroller, that reads inputs, executes control logic, and drives outputs in real time.

Core components: A microcontroller typically contains a CPU, Flash program memory, RAM, GPIO, timers, PWM units, ADCs, communication peripherals, and interrupt hardware.

Control cycle: A basic loop is:

TEXT

  initialize hardware
  repeat:
      read sensors
      condition signals
      compute control output
      update motor driver
      monitor faults

Interfaces: UART, I²C, SPI, CAN, and USB connect controllers to sensors, drivers, displays, and other controllers.
Timing: Timer interrupts provide fixed sampling intervals; a 1 kHz loop samples every 1 ms, supporting responsive control when computation finishes within that interval.
Control implementation: Proportional control uses
[
u=K_p e
]
where (u) is actuator command, (K_p) is proportional gain, and (e) is measured error.
Reliability: Watchdogs, brownout detection, limit checks, emergency stops, and fail-safe output states prevent software faults from creating dangerous motion.