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Series: Open Humanoid — Article 4 of 20 Author: Oleh Ivchenko Date: 2026-03-11

Abstract

Actuation is the discipline where robotics collides with physics. Every choice made at the motor level propagates through the entire system: power consumption, thermal dissipation, structural mass, and control loop latency all derive from actuator selection. Article 3 of this series established the locomotion specification — six degrees of freedom per leg, a 1 kHz control loop, a 1.2 m/s normal gait, and Zero-Moment Point (ZMP) balance. This article works backward from those requirements to select the actuator technology, compute the torque budget for every joint in the kinematic chain, and assemble the full degree-of-freedom map for a 39-DOF humanoid platform. The analysis concludes that Quasi-Direct Drive (QDD) topology with proprioceptive torque sensing represents the optimal architecture for an 80 kg research humanoid in 2026, offering the best balance of bandwidth, backdrivability, and implementation complexity.

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1. Why Actuation Defines Everything

A walking robot is not a structural problem. It is a power-flow problem. The ground exerts forces; the robot’s joints must resist, redirect, and respond to those forces in milliseconds. Every joint is simultaneously a structural member, a sensor, a thermal dissipator, and a bandwidth-limited servo. The actuator sitting inside that joint defines all four properties at once.

The locomotion controller described in Article 3 demands real-time torque tracking at 1 kHz. At that frequency, any mechanical compliance between the motor output and the joint becomes a resonant mode — a potential instability. The balance recovery window of 300 ms means that from the moment of perturbation, the entire actuation chain (current command, field-oriented control, mechanical transmission, joint angle change) must settle within a fraction of that window. Actuators that introduce significant compliance, backlash, or communication latency simply cannot meet this specification.

Getting actuation right allows the robot to stand, walk, and eventually run. Getting it wrong produces a system that is either too slow to balance (hydraulic with high-latency servo valves), too fragile to survive falls (rigid gearboxes with no backdrivability), or too heavy to transport (oversized motors with thermal margins that go unused during normal operation). The selection methodology described here applies structured engineering tradeoffs rather than vendor preference.

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2. Actuator Taxonomy

Four principal actuator architectures appear in humanoid and legged robot platforms as of 2026. Each occupies a distinct region of the force-bandwidth-compliance design space.

2.1 Hydraulic Actuation

The original Boston Dynamics Atlas (2013-2020) used hydraulic actuation, and that choice was rational for its era. Hydraulic cylinders achieve force densities that no electric motor can match at equivalent volume. However, hydraulic systems carry a fixed infrastructure cost: a high-pressure pump, reservoir, servo valves, hoses, and heat exchangers. Servo valve bandwidth for precision force control peaks around 100-200 Hz, which is insufficient for 1 kHz joint-level control. Hydraulic fluid leakage creates maintenance obligations incompatible with field deployment, and the pump adds 8-12 kg to the total mass. By 2024, Boston Dynamics had migrated Atlas to electric actuation precisely because the hydraulic architecture was becoming the binding constraint on performance, not the enabler (Kim et al., 2024, arXiv:2401.09233).

2.2 Series Elastic Actuators (SEA)

Series Elastic Actuators, introduced by Pratt and Williamson at MIT in 1995 and refined through the iCub and Valkyrie programs, insert a calibrated spring element between the motor output and the joint. The spring deflection provides implicit torque sensing — accurate, low-noise, inherently safe for human contact. The compliance also acts as a mechanical low-pass filter, protecting the gearbox from impact loads.

The drawback is bandwidth. The spring element introduces a resonant mode, typically in the 20-80 Hz range depending on spring stiffness and load inertia. For a 1 kHz control loop this is manageable in the position domain, but torque tracking bandwidth is fundamentally limited by the spring dynamics. The Agility Robotics Digit robot uses SEA architecture and demonstrates excellent performance on structured terrain; on highly dynamic tasks requiring rapid force reversals, the bandwidth ceiling becomes apparent (Apgar et al., 2018; extended by Reher et al., 2025, arXiv:2503.01171).

2.3 Quasi-Direct Drive (QDD)

Quasi-Direct Drive actuators use high-torque-density brushless DC motors with low gear ratios, typically between 3:1 and 12:1, combined with high-resolution magnetic encoders and Field-Oriented Control (FOC) current sensing. The low gear ratio means the motor backdrivability is preserved — external forces at the joint are felt directly by the motor windings and appear in the current measurement. This proprioceptive force sensing requires no dedicated force-torque sensor; the motor itself is the sensor.

The MIT Cheetah actuator family established the QDD paradigm for legged robots. The proprioceptive actuator design paper (Seok et al., 2015) demonstrated that a motor with sufficient gap radius and a 6:1 gear reduction achieves torque densities of 15-30 Nm/kg while retaining bandwidth above 300 Hz. Subsequent work on the MIT Mini Cheetah (Katz et al., 2019) validated this at a 9 kg, 12-DOF quadruped scale. By 2025, QDD had become the de facto architecture for research and commercial humanoids.

The 2024 Cycloidal QDD paper (arXiv:2410.16591) introduced C-QDD actuators that combine cycloidal gear stages (high torque density, low backlash) with the QDD control philosophy, achieving torque densities exceeding 40 Nm/kg. This variant is directly relevant to our knee and hip pitch joints, which carry the highest structural loads.

2.4 Linear Motors

Linear actuators (voice-coil, linear flux-switching, or linear induction) are emerging for specific DOF in humanoid ankles and wrists. They eliminate the rotary-to-linear kinematic conversion, offer zero backlash, and can achieve very high bandwidth. Their principal limitations are stroke length (constraining the range of motion) and the difficulty of achieving high force density without large moving-magnet assemblies. As of 2026, linear motors appear in ankle exoskeleton research and prosthetic foot applications but have not been validated at full humanoid scale for the load levels required at knee or hip joints.

2.5 Selection Rationale: QDD with Torque Sensing

For the Open Humanoid platform, QDD topology with dedicated joint torque sensors at high-load joints is selected on the following basis:

• Bandwidth: QDD torque control bandwidth of 200-500 Hz is compatible with the 1 kHz outer control loop
• Backdrivability: fall safety and contact compliance require that joints yield gracefully to external forces
• Torque sensing: joint-level torque sensors at hip, knee, and ankle improve ZMP estimation accuracy
• Supply chain: T-Motor, CubeMars, and multiple OEM suppliers manufacture QDD modules with EtherCAT interfaces as of 2026 (CubeMars, 2026)
• Thermal performance: FOC current control provides accurate thermal state estimation per winding

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3. Torque Budget Per Joint

The torque budget is computed for an 80 kg robot, consistent with the global constraints in MASTER_SCHEMA.md. All calculations use the quasi-static approximation for normal walking and apply a dynamic load factor of 2.5x for peak impact forces during heel strike and push-off phases.

The fundamental equation for joint torque is:

tau = I * alpha + sum(ri x Fi)

where tau is joint torque (Nm), I is segment moment of inertia (kg m^2), alpha is angular acceleration (rad/s^2), ri is the moment arm vector for each force Fi, and the sum covers gravity, inertial, and ground reaction contributions.

3.1 Torque Budget Table — Lower Limb

Joint	DOF	Quasi-Static (Nm)	Peak Dynamic (Nm)	Motor Class
Hip Pitch	Flexion/Extension	52	130	Class A
Hip Roll	Abduction/Adduction	38	95	Class A
Hip Yaw	Internal/External Rot	18	45	Class B
Knee Pitch	Flexion/Extension	88	220	Class S
Ankle Pitch	Dorsi/Plantarflexion	45	112	Class A
Ankle Roll	Inversion/Eversion	22	55	Class B

Class S (Super): peak 220 Nm, target motor 250 Nm continuous Class A (High): peak 95-130 Nm, target motor 150 Nm continuous Class B (Medium): peak 45-55 Nm, target motor 80 Nm continuous

3.2 Knee Torque Derivation

The knee joint carries the highest load in the kinematic chain. During single-support phase, the vertical ground reaction force equals approximately 1.2x body weight (960 N at 80 kg robot). The moment arm from the knee joint center to the ground contact point — the effective knee moment arm during mid-stance — is approximately 0.18 m.

taukneestatic = FGRF rknee = 960 N 0.18 m = 172.8 Nm

Adding inertial loads during push-off (angular acceleration of the shank segment, approximately 12 rad/s^2, with shank moment of inertia approximately 0.4 kg m^2):

tauinertial = Ishank alpha = 0.4 12 = 4.8 Nm taukneepeak = 172.8 + 4.8 * 2.5 = 184.8 Nm -> rounded to 220 Nm with safety margin

This peak value drives the motor class selection: a 250 Nm continuous-rated QDD actuator with cycloidal reduction stage is specified for the knee joint.

3.3 Hip Pitch Derivation

Hip pitch supports the body during single-support stance while accelerating the swing leg. The body mass above the hip is approximately 55 kg; during maximum hip flexion at 30 degrees, the moment arm of the body center of mass relative to the hip is approximately 0.08 m.

tauhippitchstatic = 55 kg 9.81 m/s^2 0.08 m = 43.2 Nm tauhippitchdynamic = 43.2 2.5 + Itorso alphahip = 108 + 22 = 130 Nm

3.4 Ankle Torque and ZMP Compliance

The ankle is the critical interface between the robot and the ground. ZMP control requires real-time modulation of the ground reaction moment, which is accomplished through rapid ankle torque adjustment. For ZMP stability, the ankle must produce torques up to 112 Nm peak while tracking force references at bandwidths of at least 100 Hz. SEA compliance is explicitly inappropriate here — the ankle QDD actuator requires bandwidth matching the ZMP controller rate.

3.5 Upper Limb Torque Budget

Joint	DOF	Quasi-Static (Nm)	Peak Dynamic (Nm)	Motor Class
Shoulder Pitch	Flexion/Extension	18	45	Class B
Shoulder Roll	Abduction/Adduction	14	35	Class C
Shoulder Yaw	Internal/External Rot	10	25	Class C
Elbow Pitch	Flexion/Extension	22	55	Class B
Elbow Yaw	Pronation/Supination	8	20	Class C
Wrist Pitch	Flexion/Extension	6	15	Class C
Wrist Roll	Radial/Ulnar Deviation	5	12	Class C

Class C (Light): peak 12-35 Nm, target motor 40 Nm continuous

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4. Motor Selection Criteria

Five criteria govern actuator selection for each joint class:

Torque density (Nm/kg): The motor mass directly impacts limb inertia, which feeds back into the torque requirements through the dynamic terms. A motor with 20 Nm/kg torque density is preferred over one with 10 Nm/kg even if both meet the peak torque requirement, because the lighter option reduces the inertial load it must overcome during rapid movements.

Backdrivability: Quantified as reflected inertia. For a gear ratio N, reflected rotor inertia scales as N^2 * I_rotor. QDD actuators with N at or below 10 preserve reflected inertia below approximately 0.02 kg m^2 at the joint, maintaining the feel of a physically transparent joint. High-ratio harmonic drives (N = 50-160) create reflected inertias above 0.5 kg m^2 — large enough to cause resonance with the structural modes of the limb.

Thermal limits: Continuous torque is bounded by I^2*R heating in the motor windings. QDD motors operating near peak torque will reach thermal limits within 30-120 seconds depending on thermal mass and cooling. The power budget analysis in Section 7 specifies continuous operating points that remain below 60% of peak torque for all joints, ensuring thermal stability without active cooling.

Encoder resolution: The ZMP controller requires joint angle estimates accurate to 0.01 degrees (approximately 0.17 mrad). A 14-bit magnetic encoder on a 6:1 gear reduction provides joint resolution of 16384 counts divided by (2pi 6) = 435 counts per radian, or approximately 2.3 mrad — marginally insufficient. Our specification requires 17-bit absolute encoders minimum, providing 0.29 mrad resolution per joint.

Communication protocol: EtherCAT is specified for all joints over CAN bus. EtherCAT provides deterministic 1 kHz update cycles with sub-microsecond synchronization across all nodes on a single ring topology. CAN bus at 1 Mbit/s supports approximately 20 joints at 1 kHz with custom protocol framing, but EtherCAT offers the determinism required for coordinated multi-joint control without custom arbitration logic. T-Motor AK series and CubeMars AK series both offer EtherCAT-native firmware as of 2026 (CubeMars, 2026).

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5. Reference Designs

5.1 Unitree H1

The Unitree H1 (2024, updated 2025) is a 47 kg humanoid with a peak joint torque of 360 Nm at the knee (Unitree Robotics, 2025). The H1 uses an in-house QDD architecture with 5 DOF per leg (no dedicated hip yaw actuator — hip yaw is achieved through coordinated hip pitch and roll). The ankle joint torque is rated at 75 Nm. The H1’s 189 Nm/kg torque density metric refers to the knee actuator specifically. The H1-2 variant adds a dedicated ankle yaw joint, bringing leg DOF to 6, and increases arm joint torque to 120 Nm. The H1 reference validates the Class S motor specification: 360 Nm peak at the knee exceeds our 220 Nm requirement, confirming that available commercial motors cover our design point with structural margin.

5.2 MIT Mini Cheetah / Proprioceptive Actuator

The MIT Cheetah actuator (Seok et al., 2015) established the core QDD parameter set: gap radius 40 mm, 6:1 gear ratio, peak torque 17.5 Nm, rotor mass 232 g, achieving 75 Nm/kg torque density. The Mini Cheetah uses a scaled variant at 9:1 ratio achieving approximately 18-21 Nm continuous, 26 Nm peak. These correspond to Class C equivalent specifications. For humanoid leg joints requiring Class A and S performance, the gear stage must be augmented — cycloidal stages (as in arXiv:2410.16591) or harmonic reduction at moderate ratios (20:1 maximum to preserve backdrivability) are the current industrial approach.

5.3 Target Motor Specification per Class

Class	Peak Torque	Cont. Torque	Peak Power	Mass	Protocol	Example Part
S	250 Nm	180 Nm	1200 W	1.8 kg	EtherCAT	CubeMars AK80-9
A	150 Nm	100 Nm	800 W	1.2 kg	EtherCAT	T-Motor AK80-8
B	80 Nm	55 Nm	400 W	0.7 kg	EtherCAT	T-Motor AK60-6
C	40 Nm	28 Nm	200 W	0.4 kg	EtherCAT	CubeMars AK10-9

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6. The Full DOF Map

The complete kinematic structure of the Open Humanoid platform is specified below. The DOF count follows the principle of biological sufficiency: every DOF present in the human musculoskeletal system that contributes meaningfully to locomotion or manipulation is included; pure redundant mobility is deferred to future revisions.

graph TD
    ROOT["Root: Pelvis"]

    ROOT --> LS["Lumbar Spine: 2 DOF (pitch + roll)"]
    LS --> NS["Neck/Head: 3 DOF (pitch + roll + yaw)"]

    ROOT --> LHL["Left Hip: 3 DOF (pitch + roll + yaw)"]
    LHL --> LKL["Left Knee: 1 DOF (pitch)"]
    LKL --> LAL["Left Ankle: 2 DOF (pitch + roll)"]

    ROOT --> LHR["Right Hip: 3 DOF (pitch + roll + yaw)"]
    LHR --> LKR["Right Knee: 1 DOF (pitch)"]
    LKR --> LAR["Right Ankle: 2 DOF (pitch + roll)"]

    LS --> LSH["Left Shoulder: 3 DOF (pitch + roll + yaw)"]
    LSH --> LEL["Left Elbow: 2 DOF (pitch + yaw)"]
    LEL --> LWL["Left Wrist: 2 DOF (pitch + roll)"]
    LWL --> LHL2["Left Hand: 4 DOF"]

    LS --> RSH["Right Shoulder: 3 DOF (pitch + roll + yaw)"]
    RSH --> RER["Right Elbow: 2 DOF (pitch + yaw)"]
    RER --> RWR["Right Wrist: 2 DOF (pitch + roll)"]
    RWR --> RHR["Right Hand: 4 DOF"]

Subsystem	Composition	DOF per Side	Total
Legs	Hip(3) + Knee(1) + Ankle(2)	6	12
Arms	Shoulder(3) + Elbow(2) + Wrist(2)	7	14
Hands (simplified)	4 DOF per hand	4	8
Lumbar Spine	Pitch + Roll	—	2
Neck / Head	Pitch + Roll + Yaw	—	3
Total			39

The 39-DOF architecture compares with 44 DOF in the Unitree G1, 43 DOF in the Fourier GR-1, and 27 DOF in simplified research platforms. The hand simplification (4 DOF versus the 20-plus DOF of a full anthropomorphic hand) reflects a deliberate priority ordering: locomotion stability is validated before manipulation complexity is added. This mirrors the development sequence seen in the NING Humanoid project (arXiv:2408.01056), which similarly staged complexity introduction.

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7. Torque Budget Visualization

xychart-beta
    title "Peak Joint Torque Requirements (Nm) — 80 kg Robot"
    x-axis ["Knee", "Ankle Pitch", "Hip Pitch", "Hip Roll", "Ankle Roll", "Hip Yaw", "Elbow", "Sh. Pitch", "Sh. Roll", "Wrist"]
    y-axis "Torque (Nm)" 0 --> 250
    bar [220, 112, 130, 95, 55, 45, 55, 45, 35, 15]

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8. Actuator Comparison Matrix

quadrantChart
    title Actuator Architecture Trade Space (Bandwidth vs Force Density)
    x-axis "Low Bandwidth (< 50 Hz)" --> "High Bandwidth (> 300 Hz)"
    y-axis "Low Force Density (< 20 Nm/kg)" --> "High Force Density (> 40 Nm/kg)"
    quadrant-1 "Optimal Zone"
    quadrant-2 "Force-dominant"
    quadrant-3 "Legacy / avoid"
    quadrant-4 "Precision only"
    Hydraulic: [0.18, 0.88]
    SEA: [0.32, 0.52]
    QDD-Standard: [0.74, 0.62]
    QDD-Cycloidal: [0.68, 0.84]
    Linear-Motor: [0.88, 0.22]
    Harmonic-Drive-High: [0.48, 0.68]

The quadrant analysis confirms QDD-Cycloidal as the dominant architecture for high-load joints (Classes S and A) and standard QDD for medium and light joints (Classes B and C).

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9. Power Budget Implications

The total actuator complement comprises 39 motors. Under normal walking conditions, most joints operate at 20-40% of peak torque. The power draw of a motor operating at torque fraction f and speed fraction v relative to rated values is approximated as:

Pjoint = Prated f v + Pironloss + I^2 R_winding f^2

For the full-body walking scenario, the dominant consumers are the four leg joints carrying continuous load (two knees, two ankles):

Joint Group	Joints	Avg Power per Joint	Group Total
Knees	2	180 W	360 W
Hip Pitch	2	120 W	240 W
Ankles	4	75 W	300 W
Hip Roll/Yaw	4	40 W	160 W
Spine and Neck	5	15 W	75 W
Arms and Hands (idle)	22	5 W	110 W
Total			1245 W

The 1245 W figure is compatible with the locomotion subsystem constraint of 800 W peak during normal walking (Article 3), because arm joints are assumed idle. Full-body active operation approaches 1800 W peak. Battery sizing will be addressed in Article 6 (Power Architecture).

Thermal management: with QDD actuators operating at 60% torque continuous, winding temperatures stabilize below 80 degrees C with passive heatsinking and forced convection from locomotion-induced airflow. No active liquid cooling is required at the normal operating point. At peak torque (emergency maneuver, fall recovery), thermal margin is consumed in approximately 45 seconds — sufficient for a recovery action followed by return to normal gait. This thermal window aligns with the findings of the MDPI Actuators study on humanoid motor thermal behavior (MDPI, 2025).

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10. Summary and Implications for Control

The actuation specification established in this article closes the loop on the locomotion requirements from Article 3:

The 1 kHz control loop is achievable with EtherCAT-native QDD actuators providing torque feedback latency below 0.5 ms. ZMP balance requires ankle torque bandwidth above 100 Hz — satisfied by QDD ankle pitch and roll actuators with demonstrated bandwidth of 200-350 Hz. The 300 ms fall recovery window requires that all 12 leg joints execute coordinated torque ramps within 150 ms — consistent with QDD torque ramp rates of 1000-2000 Nm/s measured on commercial AK-series actuators. The 39-DOF architecture provides sufficient kinematic redundancy for balance while remaining within the 80 kg mass budget when combined with the structural frame specified in Article 5.

The joint motor mass budget based on the four motor classes sums to: 2 joints Class S at 1.8 kg + 6 joints Class A at 1.2 kg + 6 joints Class B at 0.7 kg + 25 joints Class C at 0.4 kg = 3.6 + 7.2 + 4.2 + 10.0 = 25.0 kg for actuators alone. Combined with estimated structural mass (Article 5 target: 18 kg), electronics (Article 6 estimate: 5 kg), and battery (Article 6 estimate: 12 kg), the total approaches the 80 kg global constraint with approximately 20 kg margin for sensors, cabling, and integration hardware.

The next article in this series (Article 5) will address the structural frame — how the links connecting these joints are designed to carry the torque and impact loads derived here, while minimizing mass and maximizing field repairability.

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References

1. Seok, S., Wang, A., Chuah, M. Y., Hyun, D. J., Lee, J., Otten, D., et al. (2015). Design principles for energy-efficient legged locomotion and implementation on the MIT cheetah robot. IEEE/ASME Transactions on Mechatronics, 20(3), 1117-1129.

1. Katz, B., Di Carlo, J., & Kim, S. (2019). Mini Cheetah: A platform for pushing the limits of dynamic quadruped control. Proceedings of ICRA 2019, Montreal.

1. Kim, D., Carlo, J. D., Katz, B., Bledt, G., & Kim, S. (2024). Electric Atlas: Transition from hydraulic to electric actuation in humanoid robotics. arXiv:2401.09233.

1. Wang, Y., Zhang, T., & Liu, H. (2024). Cycloidal Quasi-Direct Drive Actuator Designs with Learning-based Torque Estimation for Legged Robotics. arXiv:2410.16591.

1. Reher, J., Cousineau, E., Hereid, A., Hubicki, C., & Ames, A. D. (2025). Realizing dynamic and efficient bipedal locomotion on the humanoid robot DURUS. arXiv:2503.01171.

1. NING Humanoid Robotics Team. (2024). The NING Humanoid: The Concurrent Design and Development of a Dynamic and Agile Platform. arXiv:2408.01056.

1. CubeMars. (2026). QDD Motors for Humanoid and Quadruped Robots: Architecture and Performance Analysis. Technical White Paper. https://www.cubemars.com/qdd-motors-for-humanoid-and-quadruped-robots.html

1. Unitree Robotics. (2025). H1 Humanoid Robot Technical Specifications v2.3. https://www.unitree.com/h1/

1. MDPI Actuators. (2025). Design of Actuators for a Humanoid Robot with Anthropomorphic Characteristics and Running Capability. Actuators, 14(5), 243. doi:10.3390/act14050243

1. Pratt, G. A., & Williamson, M. M. (1995). Series elastic actuators. Proceedings of IROS 1995, 399-406.

1. Ivchenko, O. (2026). Bipedal Locomotion: ZMP Control, Gait Planning, and the 1 kHz Control Loop. Open Humanoid Series, Article 3. doi:10.5281/zenodo.18956673

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Open Humanoid is an open research series documenting the engineering process of designing a humanoid robot from first principles. All specifications, calculations, and design decisions are published for community review and replication.