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Sensors in humanoid robots

Joint torque, contact force, winding temperature and battery temperature: the measurements behind balance and safe actuation, the sensors that make them, and the calculations they need.

Measurement map

Measured quantityTypical sensorSignalCalculator here
Joint torqueStrain-gauge torque sensor, full bridge, on the output side of the gearboxmV/V bridgeStrain gauge bridge calculator
Rated output of a torque or force sensorFull bridge specified in mV/V at rated loadmV/V bridgeLoad cell output calculator
Resolution of the bridge signalAmplifier and converter inside the sensorCodesADC resolution calculator
Foot and wrist contact forceSix-axis force/torque sensor (several strain-gauge bridges)mV/V per bridge, digitised in the sensorLoad cell output calculator
Motor winding temperatureNTC thermistor or PT1000 in the statorResistanceNTC thermistor calculator
Winding temperature, PT1000 on thin leadsPT1000, two-wire through the limb harnessResistanceRTD lead-wire error calculator
Battery cell and pack temperatureNTC 10 kΩ on cells and busbarsResistance, read by the battery management systemNTC thermistor calculator
Hydraulic or pneumatic pressure (hydraulic actuators, grippers)Pressure transmitter4–20 mA or ratiometric voltagePressure unit converter
Vibration and impact of the structureMEMS accelerometer (also inside the IMU)Digital, in gVibration converter
Sealing of actuators and connectorsEnclosure rating on the datasheetIP codeIP rating decoder
Amplifier gain for a torque bridgeInstrumentation amplifier ahead of the convertermV/V bridge to voltsInstrumentation amplifier gain calculator
Joint angle and speedAbsolute encoder, magnetic or opticalDigitalnone on this site
Body attitudeInertial measurement unit: accelerometers and gyroscopesDigitalnone on this site

Where the sensors sit

A humanoid robot is a chain of electric actuators carrying its own weight. Each joint needs to know its position, the torque it delivers and how hot it is; the feet and wrists need to know the forces at the contact; the battery needs to know the temperature of its cells. Position comes from encoders and attitude from an inertial measurement unit, both digital devices with their own processing. The rest are classic analogue measurements: strain-gauge bridges and resistance thermometers, the same physics as a weighing system or a motor protection circuit, packed into much less space.

Torque and force: strain-gauge bridges

Joint torque sensors and six-axis force/torque sensors are elastic bodies carrying strain gauges wired as Wheatstone bridges. Their output is specified like a load cell: millivolts of signal per volt of excitation at rated load. A bridge rated 2 mV/V and excited with 5 V gives 10 mV at full scale, so a joint working at 30 % of its rated torque produces 3 mV, and one part in a thousand of full scale is 10 µV. That is why the amplifier and converter sit inside the sensor or right beside it: a signal of this size does not survive a trip through a moving cable harness next to motor phases.

The load cell output calculator does this arithmetic for any rated output, excitation and load. The strain gauge bridge calculator goes one step back, from the strain in the gauges to the bridge output, and the ADC resolution calculator shows what the converter behind the bridge can resolve: with 18 noise-free bits and a gain of 128, a 10 mV bridge signal for 100 N is resolved to about 0.0015 N. It treats one bridge at a time. The matrix that separates the six components of a force/torque sensor and removes crosstalk comes from the manufacturer’s calibration and is not something a general calculator can reproduce.

Where the torque sensor sits matters as much as its rating. Measured on the output side of the gearbox, the signal includes what the link really delivers; measured on the motor side, gearbox friction and backlash sit between the sensor and the load.

Temperature: windings and cells

Motor windings are protected by a sensor embedded in the stator, usually an NTC thermistor or a PT1000. Both are read as a resistance. A common 10 kΩ, β = 3950 K thermistor falls to about 1270 Ω at 80 °C and 698 Ω at 100 °C by the Beta model; a PT1000 reads 1460.68 Ω at 120 °C. The NTC calculator and the PT100 / PT1000 calculator convert in both directions.

The choice between the two is partly about wiring. Inside a limb the sensor is usually connected with two thin wires, and their resistance adds to the reading. With 3 m of 0.205 mm² (AWG 24) copper, a two-wire PT1000 reads about 0.13 °C high at 80 °C; a PT100 on the same wires reads about 1.3 °C high, ten times worse, because its resistance changes ten times less per degree. The RTD lead-wire error calculator shows this for any length and conductor. A 10 kΩ thermistor is less sensitive still to lead resistance, at the price of a strongly non-linear curve and wider tolerance between parts.

Battery packs use the same 10 kΩ thermistors on cells and busbars. The Beta value differs between parts (3435 K and 3950 K are both common), and using the wrong one shifts the reading by several degrees away from 25 °C, so take it from the datasheet of the fitted part.

What a calculator cannot tell you

The numbers above are sensor-level conversions. They say nothing about the dynamics that make these measurements hard in a robot: bandwidth of the torque loop, thermal lag between the winding and its sensor, drift of a strain-gauge bridge with temperature, or the fusion of encoder and inertial data. For encoders, inertial units, tactile skins and vision there is no tool on this site.

Sealing is worth a separate check. An actuator or connector rated IP67 has passed a temporary-immersion test, which does not by itself include the water-jet tests of IP65 and IP66; the IP rating decoder explains which rating covers which.

Updated October 11, 2026

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