Torque Bandwidth in Humanoid Joints: How Fast a Joint Can Follow a Torque Command
Torque bandwidth: how fast a humanoid joint can follow a torque command
A joint’s peak torque says how hard it can push. Its torque bandwidth says how quickly that push can change. Bandwidth decides whether a humanoid can soften a foot strike, keep a grip steady when an object slips, or act as a soft spring for a person who bumps into it. Published figures run from under 10 Hz to 150 Hz, and they are rarely measured the same way.
Sources: Wensing et al. 2017; Paine et al., Valkyrie actuator control; Gealy et al. 2019, citing Aaron & Stein.
What torque bandwidth measures
Torque bandwidth is a frequency. To measure it, engineers feed the joint a sine-wave torque command and slowly raise its frequency, a sweep or chirp, while recording what the joint actually delivers. At low frequencies the output matches the command. As the frequency rises, the output shrinks and falls behind. The bandwidth is the frequency where the output amplitude has dropped to about 71% of the command, which is −3 dB on a Bode plot.
Two things make a bandwidth figure meaningful: what is being followed, and what is being held still. Position bandwidth includes the inertia of the limb being swung and is usually lower; the Blue arm from Berkeley reports 7.5 Hz for position and 13.8 Hz for torque. Open-loop figures describe the hardware alone, closed-loop figures include the controller. And many tests clamp the output so that only the actuator, not a free-swinging limb, is measured.
Figure 1 · Animated · Torque command and joint response at the bandwidth frequency
Illustration: humanoid.guide, computed from a first-order closed loop (gain 1/√2, phase −45° at the bandwidth). CSS animation, seamless one-cycle loop; static when reduced motion is requested.
Why a humanoid needs it
Walking happens at about one step per second and fast finger motions at 4–6 Hz, so it is tempting to think a joint needs little more than that. It does not work that way. Bandwidth sets how quickly the joint can react to what it did not plan for: a foot landing early, a box slipping in the hand, a person leaning on an arm. A 2025 benchmark proposal for humanoid actuation puts it bluntly: a joint with 5 Hz torque bandwidth cannot safely render compliant behaviours, and wrist and hand actuators need at least 5–10 Hz in torque mode. Its worked examples use targets of about 8 Hz for the ankle in walking and 10 Hz for the wrist in manipulation.
Learned control makes the point sharper. A humanoid policy typically runs at around 50 Hz and sends position and stiffness targets to each joint, which closes its own PD and current loops much faster. If the joint cannot realise the torque those targets imply, the policy sees a slower, softer robot than the one it was trained on.
What sets the limit
Every stage between the command and the limb adds lag. The drive’s current loop comes first; in the MIT Cheetah it runs at 20 kHz and reaches 400 Hz current bandwidth, and its authors note the usual rule that a loop should run 5–10 times faster than the bandwidth it controls. Then come the motor and reducer. Raising the gear ratio N multiplies torque, but reflected motor inertia grows with N² and friction grows too, which is why higher ratios lower torque-mode bandwidth.
A spring in the output is the biggest single lever. Wensing and colleagues modelled the Cheetah leg with its rigid transmission at a natural frequency of 79.7 Hz. Adding a series spring of 70 N·m/rad dropped the lowest natural frequency to 13.5 Hz, close to the 9 Hz closed-loop torque bandwidth reported for the StarlETH quadruped’s series elastic actuators. Heat is the last limit: at large amplitudes the motor runs out of current or thermal margin before it runs out of frequency, so the accessible bandwidth shrinks with torque amplitude.
Figure 2 · What sits between a torque command and the limb
Illustration: humanoid.guide, after Wensing et al. 2017 and Paine et al. (Valkyrie actuator control).
Published figures
The table and chart below collect bandwidths that research groups have published for legged-robot, humanoid and exoskeleton actuators. They split along architecture. Stiff, low-ratio quasi-direct-drive joints report the highest figures, from the Cheetah’s 103.7 Hz to Stanford Doggo’s 150 Hz. Series elastic actuators sit lower unless feedback pushes them up. None of the major commercial humanoid makers publishes a joint bandwidth figure.
Table 1 · Published bandwidth figures and what each one measured
| Actuator or robot | Type | Bandwidth | What was measured |
|---|---|---|---|
| Stanford Doggo leg | QDD, 3:1 belt | 150 Hz | Torque tracking of walking-like torque trajectories |
| MIT Cheetah leg | QDD, 5.8:1 planetary | 103.7 Hz | Motor driver to foot force, open loop; current loop 400 Hz |
| Valkyrie elbow | Rotary SEA, harmonic drive | 70 Hz | Closed-loop torque, up from 13 Hz passive |
| Hip-exoskeleton actuator | QDD, 8:1 | 62.4 Hz | Closed-loop torque, 20 N·m chirp (57.8 Hz at 10 N·m) |
| UT-SEA | Linear SEA, ball screw | 18 Hz | Force bandwidth |
| Blue arm | QDD, 7.125:1 belt | 13.8 Hz | Torque, 10 N·m chirp 0.1–60 Hz, link grounded; conservative estimate |
| StarlETH | SEA | 9 Hz | Closed-loop torque control |
| SA-SEA | Low-cost linear SEA | 8.5 Hz | Force bandwidth, against a 10 Hz target |
Sources: Kau et al. 2019; Wensing et al. 2017; Paine et al. (Valkyrie actuator control); Yu et al. 2020; Isik et al. 2017; Gealy et al. 2019. StarlETH value as cited by Wensing et al.
Chart 1 · Published torque or force bandwidths, Hz
Sources: Kau et al. 2019 (Doggo); Wensing et al. 2017 (Cheetah, open-loop motor-to-foot force; StarlETH cited there); Paine et al. (Valkyrie); Yu et al. 2020 (hip exo, 20 N·m chirp); Isik et al. 2017 (UT-SEA, SA-SEA); Gealy et al. 2019 (Blue, conservative estimate). Bars drawn at 2.5 px per Hz. Test methods differ; see Table 1.
Two routes to a fast joint
The quasi-direct-drive route makes the hardware itself fast. With a ratio below about 10:1 and a stiff transmission, motor current turns into output torque almost at once, and the joint can estimate torque from current without a sensor. The cost is heat: a low ratio means more current for the same torque, as covered in our quasi-direct-drive explainer.
The series elastic route accepts a slow plant and fixes it with control. Valkyrie’s elbow has a passive bandwidth of 13 Hz and its knee 11 Hz. With PD feedback on the measured spring torque, the elbow reached 70 Hz, 5.3 times its passive figure. The price shows up in the power bill: when the knee’s tracking bandwidth was raised from 30 to 82 Hz, power at the passive bandwidth frequency rose 3.6-fold, from 27 W to 97 W. Bandwidth can also be given away for cost. When UT Austin re-engineered its 18 Hz UT-SEA for low-cost industrial use, the new SA-SEA reached 8.5 Hz against a 10 Hz target.
How to read a bandwidth claim
Because there is no common test, bandwidth figures are easy to flatter. The same hip-exoskeleton actuator measured 57.8 Hz with a 10 N·m chirp and 62.4 Hz with a 20 N·m chirp. The 2025 benchmark proposal suggests a common protocol: sweep from 0.5 to 60 Hz at about 10% of continuous-safe torque and report gain and phase at 1, 5, 10 and 30 Hz. Until something like that is standard, these questions sort out most claims.
Table 2 · Six questions to ask about a bandwidth figure
| Question | Why it matters | Published example |
|---|---|---|
| Torque, force or position? | Position bandwidth includes the limb’s inertia and is usually lower | Blue: 7.5 Hz position, 13.8 Hz torque |
| Open or closed loop? | Feedback can lift a slow plant well above its passive bandwidth | Valkyrie elbow: 13 Hz passive, 70 Hz closed loop |
| At what amplitude? | The figure moves with test amplitude, and current and heat limits bite at large torques | Hip exo: 57.8 Hz at 10 N·m, 62.4 Hz at 20 N·m |
| Output fixed or free? | A grounded output removes load inertia and flatters the number | Blue: one link grounded to two load cells |
| What is the sensor? | Motor current, spring deflection and foot force are different signals | Cheetah: driver to foot force, measured at the foot |
| What does it cost in power? | Higher gains mean more current at the same frequency | Valkyrie knee: 27 W to 97 W for 30 to 82 Hz |
Sources: Gealy et al. 2019; Paine et al. (Valkyrie actuator control); Yu et al. 2020; Wensing et al. 2017. Test protocol suggestion from Sunbeam 2025: sweep 0.5–60 Hz at about 10% of continuous-safe torque, report gain and phase at 1, 5, 10 and 30 Hz.
- Ask for the Bode plot, not one number. Phase lag at 5–10 Hz says more about stability in contact than the −3 dB point alone.
- Ask for the load case. A grounded output removes the limb’s inertia; a free limb is the harder and more honest test.
- Ask for amplitude and temperature. Large torques and hot windings narrow the usable bandwidth.
Go deeper: The Humanoid Actuation Report
249 pages on motors, reducers, screws, bearings, encoders and drives, the vendors behind every major platform, and the cost curves that decide adoption to 2036.
The Humanoid Actuation Report All joints & actuators articles All humanoid.guide reportsKeep reading · Joints & actuators
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FAQ
What is torque bandwidth?
The highest frequency at which a joint can follow a sinusoidal torque command before its output falls to about 71% of the command, the −3 dB point. It is measured with a sine sweep or chirp and read off a Bode plot.
How much torque bandwidth does a humanoid joint need?
There is no standard. A 2025 benchmark proposal suggests at least 5–10 Hz for wrist and hand actuators and example targets of about 8 Hz for the ankle in walking. Published legged-robot joints reach 60–150 Hz, well above human muscle; the human biceps is cited at about 2.3 Hz position bandwidth.
Do series elastic actuators have low bandwidth?
Their passive bandwidth is limited by the spring: Valkyrie’s elbow sits at 13 Hz and its knee at 11 Hz. Feedback control lifted the elbow to 70 Hz, but higher bandwidth costs power: raising the knee from 30 to 82 Hz increased power at the test frequency from 27 to 97 W.
Why do quasi-direct-drive joints have high bandwidth?
A low gear ratio keeps reflected motor inertia and friction small, and the transmission is stiff, so the motor current reaches the output quickly. The MIT Cheetah’s 5.8:1 leg measured 103.7 Hz from motor driver to foot force.
Why can two bandwidth figures for similar joints differ so much?
Because the tests differ: torque or position, open or closed loop, small or large amplitude, output held or free, and which sensor is read. Compare figures only when the test conditions are stated.
Sources
- P. M. Wensing, A. Wang, S. Seok, D. Otten, J. Lang, S. Kim, Proprioceptive Actuator Design in the MIT Cheetah, IEEE T-RO 2017 (5.8:1; 400 Hz current, 103.7 Hz driver-to-foot-force bandwidth; 79.7 Hz rigid vs 13.5 Hz with a 70 N·m/rad spring; StarlETH 9 Hz)
- N. Paine et al., Actuator Control for the NASA-JSC Valkyrie Humanoid Robot, Journal of Field Robotics (elbow 13 Hz passive, 70 Hz closed loop; knee 11 Hz passive; 30 to 82 Hz raised power 27 to 97 W)
- K. Isik, S. He, J. Ho, L. Sentis, Re-Engineering a High Performance Electrical Series Elastic Actuator for Low-Cost Industrial Applications, Actuators 2017 (UT-SEA 18 Hz, SA-SEA 8.5 Hz, 10 Hz target)
- D. V. Gealy et al., Quasi-Direct Drive for Low-Cost Compliant Robotic Manipulation, 2019 (7.125:1; 13.8 Hz torque, 7.5 Hz position; biceps 2.3 Hz)
- S. Yu et al., Quasi-Direct Drive Actuation for a Lightweight Hip Exoskeleton with High Backdrivability and High Bandwidth, 2020 (8:1; 57.8–62.4 Hz at 10–20 N·m)
- N. Kau et al., Stanford Doggo: An Open-Source, Quasi-Direct-Drive Quadruped, 2019 (3:1; 150 Hz for walking-like torque trajectories)
- M. Sunbeam, Human-Level Actuation for Humanoids, arXiv 2511.06796, 2025 (bandwidth targets; 0.5–60 Hz sweep protocol; gear ratio lowers torque-mode bandwidth)
- B. Silva and N. Kottege, Accessible Torque Bandwidth of a Series Elastic Actuator Considering the Thermodynamic Limitations, 2020
- N. Paine and L. Sentis, A New Prismatic Series Elastic Actuator with Compact Size and High Performance, UT Austin (UT-SEA design; 277 N/mm effective spring)