A Practitioner’s Protocol for Apples‑to‑Apples Humanoid Energy Tests

Despite daily progress videos and glossy spec sheets, a simple, comparable answer to “how efficient is this humanoid?” remains elusive. Joint‑resolved efficiency maps are rarely public, standardized cost of transport (COT) is almost never reported, and regeneration policies are often opaque. That leaves engineers and buyers guessing at mobility range, thermal limits, and real‑world task performance.

This matters now because architectural choices—from quasi‑direct drive to strain‑wave gears and cycloidal transmissions—directly shape energy use, recoverable braking, and derating under load. Without a shared playbook, claims can’t be weighed on equal footing. This article lays out a practitioner’s protocol to measure and report joint efficiency, COT, and regeneration with confidence.

What follows is a step‑by‑step methodology you can deploy today: what counts as comparable, instrumentation and calibration checklists, a standardized task suite with speeds/terrains/payloads, environmental controls and normalization rules, data products and file formats, control disclosures, and uncertainty/validation procedures. It also includes a publication template, acceptance criteria, and common pitfalls to avoid. Adopt it, and your results will compare apples to apples.

Test philosophy and scope: what counts as comparable

Comparable energy data starts by agreeing on the quantities, the normalization rules, and the context. The protocol focuses on joint‑resolved and system‑level metrics that map directly to task demands and actuator physics.

Key quantities to report

• Joint mechanical‑to‑electrical efficiency η_joint(τ, ω, T): mechanical output power (τ·ω) divided by DC‑bus electrical input power to the joint’s inverter. Publish as maps over torque‑speed envelopes at specified component temperatures, with duty‑cycle and ambient explicitly stated.
• Cost of transport (COT)/specific resistance ε: total electrical energy E consumed divided by m·g·d, normalized by total mass m (robot plus prescribed payload), gravity g, and distance d. Report steady‑state and transient segments separately.
• Torque and power density: actuator‑module peak and continuous ratings (Nm/kg, W/kg) at defined thermal limits. Module includes motor, transmission, sensing, housing, and cooling.
• Backdrivability and reflected inertia: minimum external torque to backdrive at low speed; report reflected inertia and separate Coulomb/viscous friction.
• Regeneration efficiency: fraction of recoverable mechanical energy returned to the DC bus during negative‑work phases (e.g., heel‑strike, downhill, braking), accounting for inverter and battery acceptance.
• Thermal derating and duty‑cycle limits: torque–time envelopes, temperature rise time constants, and controller protections at specified ambient conditions.
• Acoustic noise and maintenance: A‑weighted SPL at 1 m for representative tasks; any disclosed lubrication/inspection intervals and known wear items.

Normalization rules

• Environment: 20 ± 2 °C ambient, 40–60% RH, still air (0.1–0.3 m/s).
• Speeds: level walking at 0.5, 1.0, 1.5 m/s; running at 2.5 m/s where supported.
• Slopes: ±5° and ±10° (or standardized stairs with specified rise/run).
• Surfaces: hard, uneven, and compliant modules of known geometry.
• Payloads: 0, 10, and 20 kg, with standardized, chest‑mounted fixtures.
• Report both gross values and normalized metrics.

Why this framing? Because actuator architectures behave differently across torque‑speed‑temperature space. Low‑ratio quasi‑direct drive and direct drive emphasize transparency, low friction, and effective regeneration; high‑ratio strain‑wave gears trade compactness and precision for friction and hysteresis that penalize low‑speed efficiency and energy recovery. Cycloidal drives often land between these poles with robust efficiency and shock tolerance. Power‑electronics choices also matter: GaN inverters at 48–100 V can materially cut switching losses and improve partial‑load control smoothness, while SiC devices typically shine at higher DC bus voltages.

A crisp line between “comparable” and “not comparable” helps keep results honest:

Category	Comparable when…	Not comparable when…
Efficiency maps	Reported as η_joint(τ, ω, T) at stated temperatures and duty cycles	Aggregated into a single number without torque‑speed context
COT	Normalized by total mass, speed, slope, surface; steady vs transient separated	Reported only as battery SOC change without speed/payload/ambient
Regeneration	DC‑bus energy returned and battery acceptance disclosed	Claimed qualitatively without bus‑side accounting
Thermal limits	Torque–time and temperature‑rise curves at stated ambient conditions	“Continuous torque” stated without ambient and cooling context
Control settings	Controller modes, gains/bandwidth ranges, regen thresholds published	Closed‑box controller with undisclosed policies

Public materials from leading humanoids frequently omit joint efficiency maps, standardized COT, and regeneration fractions—precisely why a shared protocol is needed. This methodology fills that gap by specifying what to measure, how to measure it, and how to publish it so peers can reproduce and compare.

Instrumentation, calibration, and environmental controls

The fidelity of your results is bounded by your sensors and calibration discipline. Treat power, torque, speed, and temperature as first‑class measurements.

Measurement stack (synchronous, low‑latency)

• Electrical power: Measure DC‑bus voltage and current at high rate (≥5 kHz) per actuator group, synchronized with per‑joint inverter telemetry. Validate inverter‑reported currents against calibrated shunts or probes.
• Motion: Capture high‑resolution joint position/velocity (≥16‑bit encoders). Time‑align all signals.
• Torque: Prefer in‑line torque sensors where feasible. If using current‑to‑torque models, calibrate with bench tests and characterize transmission efficiency.
• Thermal: Record motor winding temperatures, transmission housing temperatures, inverter temperatures, plus ambient temperature and airflow.
• Ground interaction: Use IMUs and ground force plates or instrumented insoles to segment gait and identify negative‑work phases.
• Acoustics: Acquire A‑weighted SPL at 1 m in controlled ambient during representative tasks.

Calibration and identification

• Torque sensor calibration and linearity checks before each campaign.
• Electrical: Validate voltage/current instrumentation; document uncertainty.
• Friction and inertia: Perform backdrive tests, plus chirp/PRBS excitation to identify Coulomb/viscous terms and reflected inertia.
• Thermal: Establish temperature rise time constants for motors/transmissions at representative loads.

Environmental controls and normalization

• Maintain 20 ± 2 °C, 40–60% RH, still air (0.1–0.3 m/s). Specify footwear and foot compliance.
• Publish robot mass and inertial properties; document payload mass, position, and inertia.
• Repeat a subset of trials at 30 °C to expose thermal derating differences.

Common instrumentation pitfalls to avoid

• Measuring energy only at the battery terminals without DC‑bus granularity.
• Relying on unvalidated inverter telemetry for current/torque.
• Omitting ambient conditions and airflow, which undermines thermal comparisons.
• Neglecting start/stop transients, which skew COT at short distances.

Standardized task suite and control disclosures

Energy behavior is task‑dependent. The suite below captures steady gaits, transients, impacts, negative work, and high quasi‑static torques—each revealing different aspects of efficiency, regeneration, and thermal behavior.

Standardized task suite

• Level walking: 0.5, 1.0, 1.5 m/s over at least 200 m each, with ≥60 s steady‑state windows. Include separate start/stop trials to isolate transient costs.
• Running: 2.5 m/s over 200 m where supported.
• Slopes/stairs: Ascend/descend standardized stairs (specified rise/run) or 10° slopes, three cycles each.
• Uneven/soft terrain: EUROBENCH‑style uneven floors and compliant mats for 60 m at 1.0 m/s.
• Push recovery: Standardized lateral and sagittal impulses during 1.0 m/s walking and in‑place stance.
• Squatting: 10 repetitions to specified depth and cadence, plus static holds at 50% and 80% of rated continuous knee torque for 30 s.
• Payloads: Repeat 1.0 m/s walking and stairs with 10 kg and 20 kg chest‑mounted payloads using standardized fixtures.

Control disclosures that must accompany results

• Controller modes: Position, torque, and/or impedance control; outline gain ranges and bandwidths.
• Regeneration policy: State whether regen is enabled, including DC‑bus voltage thresholds, current limits, and braking strategies during deceleration or downhill phases.
• Series elasticity: For SEA designs, publish spring parameters and placement; note any energy‑storage policies in cyclic tasks.
• Power electronics: Disclose DC‑bus voltage and whether GaN or SiC devices are used at the inverter stage, since device choice affects switching losses, partial‑load efficiency, and regen behavior.

Why these disclosures? Low‑ratio QDD and DD joints generally exhibit lower friction and reflected inertia, improving energy efficiency, disturbance rejection, and regeneration in dynamic tasks. High‑ratio strain‑wave gears deliver compact precision but raise friction and hysteresis that penalize low‑speed efficiency and energy recovery. Cycloidal transmissions typically offer robust efficiency and shock tolerance. SEA can store/return energy when tuned well, but overly soft configurations can waste energy or limit bandwidth. GaN‑based inverters at typical humanoid bus voltages reduce switching losses and enable higher PWM frequencies for smoother torque and better partial‑load efficiency, while SiC becomes attractive at higher voltages not commonly used in current 48–100 V humanoids.

Data products, file formats, uncertainty, validation, and publication templates

Results must be reproducible and re‑analyzable. Publish raw, time‑synchronized logs and the full chain of derived metrics, with uncertainties and processing scripts.

Minimum data products

• Per‑joint efficiency maps: η_joint(τ, ω, T) from bench dyno tests, validated in situ during tasks. Include friction parameters and backdrivability.
• System‑level COT: By task and speed, with start/steady/stop breakdowns and normalization by total mass.
• Regeneration fractions: Energy returned to the DC bus and the resulting reduction in battery‑side energy draw during negative‑work phases; include inverter and battery charge‑acceptance limits.
• Torque/power density: Actuator‑module peak and continuous figures at defined thermal limits.
• Thermal derating: Torque–temperature curves and time‑to‑limit at specified ambient conditions.
• Acoustic spectra: A‑weighted SPL and spectra during steady 1.0 m/s walking and squatting holds.
• Operating context: Joint torque–velocity histograms per task to show which regions of the efficiency map were exercised.

Open file formats and artifacts

Artifact	Required contents	Preferred formats
Raw logs (time‑sync)	Per‑joint currents/voltages, DC‑bus V/I, positions/velocities, temperatures, IMU, force/pressure, SPL	ROS bag, HDF5
Calibration files	Sensor calibrations, current‑to‑torque maps, thermal calibration	YAML/JSON + PDFs
Derived metrics	COT per segment, regen fractions, efficiency maps, friction parameters	CSV/HDF5 + plots (PNG/SVG)
Processing scripts	Data parsing and computation, with version pins	Open repository (e.g., with README)

Uncertainty and validation

• Quantify uncertainties for electrical power, torque, speed, temperature, SPL. Report methods (e.g., shunt calibration, torque sensor traceability).
• Validate bench‑measured efficiency maps in situ: compare predicted bus energy from joint torques/velocities to measured DC‑bus energy during steady segments.
• Repeatability: At minimum, three repeats per task condition; publish mean and variance for COT and regen fractions.
• Reproducibility: Where possible, cross‑validate on EUROBENCH‑style modules and follow NIST/ASTM test‑method documentation so other labs can replicate.

Publication template and acceptance criteria

Required sections for a complete, publishable package:

• Executive summary: What was measured, under what conditions, and the headline outcomes for COT, regen, and derating.
• Robot and actuator disclosure: Motors, transmissions (type and ratio), SEA parameters, inverter topology/device (GaN/SiC) and DC‑bus voltage, thermal design context.
• Environmental conditions: Ambient temperature, RH, airflow; footwear; surface modules.
• Instrumentation and calibration: Sensors used, rates, synchronization, calibration files, and uncertainties.
• Task suite configuration: Distances, speeds, slopes/stairs, payload definitions, impulses for push recovery, squatting protocols.
• Control and regen policy: Controller modes, gains/bandwidth ranges, regen thresholds and limits.
• Results: Per‑joint efficiency maps; COT by task (start/steady/stop); regeneration fractions; thermal derating curves; acoustic spectra; torque‑velocity histograms.
• Data release: Links to ROS bag/HDF5 logs, calibration files, derived metric bundles, and processing scripts.
• Validation: Bench vs in‑situ cross‑checks, repeats, and uncertainty propagation.
• Deviations: Any departures from the protocol (and rationale), with sensitivity analysis where possible.

Acceptance criteria for apples‑to‑apples comparison:

• All minimum data products present, with uncertainties and calibration artifacts.
• Normalization rules followed (ambient, speeds, slopes, surfaces, payloads), or deviations clearly disclosed.
• DC‑bus‑level energy measurements and regen accounting included.
• Controller and regen policies disclosed with thresholds and limits.
• Repeatability demonstrated; steady‑state windows identified and separated from transients.

Common pitfalls that invalidate comparisons

• Reporting only battery SOC deltas without DC‑bus granularity or environmental context.
• Publishing single‑number “efficiency” without torque‑speed‑temperature maps.
• Skipping controller/regen disclosures; policies can move COT and regen fractions dramatically.
• Ignoring friction characterization; Coulomb vs viscous split matters for low‑speed tasks.
• No thermal derating curves; “continuous torque” is meaningless without ambient and cooling.
• Bundling payload and no‑payload results without proper normalization.

Bringing it all together

• Actuator architecture context: Summarize the transmission and motor choices because they shape loss mechanisms and regeneration potential. Low‑ratio QDD/DD typically deliver better transparency and regen; strain‑wave gears prioritize compactness but pay friction/hysteresis costs; cycloidal drives trade mass/volume for robust efficiency and shock tolerance; SEA can store/return energy when tuned well.
• Power electronics disclosure: State whether inverters use GaN at 48–100 V (often improving partial‑load efficiency and torque smoothness) or SiC at higher voltages, since this affects measured electrical losses and regen acceptance.
• Alignment with shared testbeds: Where available, use EUROBENCH modules and NIST/ASTM‑style method documentation so others can replicate your setup and analysis. 🧪

Conclusion

Energy is destiny for humanoids. Without disciplined, joint‑resolved measurements and standardized tasks, efficiency claims stay anecdotal. A clear protocol—what to measure, how to normalize, what to publish—turns demos into data and comparisons into engineering.

Key takeaways

• Publish per‑joint efficiency maps η_joint(τ, ω, T) with friction/backdrivability and thermal context.
• Report COT by task and segment, normalized by total mass, speed, slope, surface, and payload.
• Measure regeneration at the DC‑bus and disclose inverter/battery acceptance and braking policies.
• Control settings, SEA parameters, and inverter device choices (GaN/SiC) are part of the data, not implementation trivia.
• Release raw logs (ROS bag/HDF5), calibration files, processing scripts, and uncertainties so others can reproduce results.

Next steps for practitioners

• Instrument at the DC‑bus level and validate torque/current calibrations.
• Adopt the standardized task suite and environmental controls; re‑run a subset at 30 °C to expose thermal derating.
• Build and publish efficiency maps, COT, regen fractions, and thermal curves with uncertainty budgets.
• Align with EUROBENCH modules and NIST/ASTM‑style documentation for repeatability and reproducibility.

Looking ahead, organizations that meet these publication standards will enable evidence‑driven selection of actuators, transmissions, and controls. That, in turn, will accelerate the march toward efficient, reliable, and safe humanoid mobility—measured the same way, everywhere.

Sources & References