[Robot Hardware 04] - Actuators (3): QDD Actuators
Robot hardware from a Physical AI perspective - QDD actuators
In the previous post, we saw that a high reduction ratio amplifies the torque of a small motor while reflecting the motor rotor’s inertia to the output shaft in proportion to the square of the reduction ratio. We also saw that reducer friction, backlash, and finite torsional stiffness affect force transmission and control bandwidth at the output shaft.
A QDD (Quasi-Direct Drive) actuator is a design philosophy that tries to reduce these problems by lowering the reduction ratio itself. It does not remove the reducer completely like a true direct-drive system. Instead, it combines a high-torque-density motor with a relatively low reduction ratio to approach the physical characteristics of direct drive.
The main design goals of QDD are:
- Low mechanical impedance: Make the inertia and friction of the motor and reducer appear small at the output shaft.
- High backdrivability: Allow a force applied externally to the output shaft to produce motion on the motor side without large resistance.
- High torque transparency: Let motor-generated torque reach the output shaft without being strongly distorted by reducer friction and nonlinearities.
- High interaction bandwidth: Respond quickly to external contact and rapidly changing torque commands.
These properties are useful in systems that frequently contact the environment, such as quadrupeds, humanoids, exoskeletons, and force-controlled robot arms.
Structure and Design Philosophy
There is no universal reduction-ratio threshold that defines QDD. In general, a high-torque-density motor is combined with a relatively low ratio—from a single digit to a few tens or less—but the appropriate range depends on motor torque density, rotor inertia, required output torque, and target bandwidth.
With a low reduction ratio, the gear provides little torque amplification, so the motor itself must generate substantial torque. QDD motors often have the following characteristics:
- large air-gap radius
- high torque constant
- high current density
- many poles
- high torque-to-mass ratio
- an efficient heat path to the housing
Outer-rotor BLDC/PMSM motors are common because they make a large air-gap radius easier to achieve, but an outer-rotor structure is not required for QDD. A low-ratio planetary gearbox is a representative reducer, but the key is not a particular gear type. The goal is to achieve low reflected inertia, low backdrive torque, and sufficient stiffness together.
Some QDD modules place the reducer and bearings inside the motor to reduce axial length. Adding an encoder, motor driver, and temperature sensor makes it possible to build an integrated joint module that is easy to replace and expand.
Force–Motion Transparency
The central characteristic of QDD is how little distortion is introduced as force and motion pass in both directions between the motor and the environment.
The mechanical impedance of a rotary joint can be written as
\[Z(s)=\frac{\tau(s)}{\omega(s)}=J_{eq}s+B_{eq}+\frac{K_{eq}}{s}\]Here, $J_{eq}$ is the equivalent inertia visible at the output shaft, $B_{eq}$ is viscous friction and damping, and $K_{eq}$ is transmission torsional stiffness. Real reducers also have stiction, Coulomb friction, backlash, and hysteresis that are not included in this linear model.
QDD reduces the following two effects by using a low reduction ratio:
\[J_{\mathrm{reflected}}=N^2J_m\] \[\tau_{\mathrm{friction,out}}\approx N\tau_{\mathrm{friction,in}}\]The first relationship shows that a lower reduction ratio makes the motor rotor’s reflected inertia smaller at the output shaft. The second is a simplified intuition that input-side friction can also have a larger effect on output torque as the reduction ratio grows. Actual friction transmission depends on reducer architecture and load conditions.
Low reflected inertia makes it easier for the joint to respond passively to rapidly changing external force. Low friction lets small external forces produce joint motion instead of being hidden by stiction, and can improve the accuracy of estimating output torque from motor current.
Low mechanical impedance does not guarantee perfect transparency at every frequency. Actual performance also depends on the motor’s electrical time constant, driver voltage, current-control bandwidth, encoder resolution, structural stiffness, load inertia, and controller.
Two Ways to Evaluate QDD
There is no single officially defined quantitative criterion for QDD. To understand its performance, this post separates two perspectives: dynamic transparency and quasi-static torque transparency.
Dynamic Transparency
Dynamic transparency describes the actuator’s response to rapidly changing external force and motion. The main design variable is reflected inertia at the output shaft.
\[J_{\mathrm{reflected}}=N^2J_m\]Low reflected inertia reduces the effective mass seen at the contact point, lowers initial impact force, and makes passive joint motion during collision easier. It also makes larger angular acceleration possible at the same torque, which helps achieve fast motion and high mechanical bandwidth.
Low inertia by itself does not dissipate impact energy. Structural damping, electrical regeneration, active torque control, or an elastic element is still needed to remove or store impact energy.
Quasi-Static Torque Transparency
Quasi-static torque transparency describes how linear and repeatable the relationship is between motor-generated torque and output-shaft torque at low speed.
It is affected by:
- stiction and Coulomb friction
- reducer efficiency
- backlash and lost motion
- torque ripple and cogging torque
- bearing and seal friction
- assembly preload
High quasi-static torque transparency makes it easier to control small output torques precisely and estimate joint torque from motor current. A low reduction ratio alone does not automatically produce high transparency; reducer and bearing design and assembly quality also matter.
Proprioceptive Actuation
A concept closely associated with QDD is proprioceptive actuation.
This does not simply mean directly measuring external force from motor current alone. It is an actuator and control philosophy that uses joint position, velocity, and current to control joint torque and indirectly regulate contact force with the environment.
For a permanent-magnet motor driven by FOC, motor torque in a normal operating region can be approximated as
\[\tau_m\approx K_t i_q\]Including reduction ratio and transmission efficiency, actuator output torque is approximately
\[\tau_{\mathrm{act}} \approx \eta N K_t i_q\]This is not the same as the torque applied by the environment. Actuator torque also includes the torque used to accelerate links, compensate for gravity, and overcome internal friction.
External torque can be estimated conceptually as
\[\tau_{\mathrm{ext}} \approx \tau_{\mathrm{act}} -M(q)\ddot q -C(q,\dot q)\dot q -G(q) -\tau_f(q,\dot q)\]By reducing reflected inertia and friction, QDD reduces the internal torque that is difficult to model in this relationship. Even without a separate output-torque sensor, this makes it easier to perform relatively accurate torque control and contact estimation using motor current and joint state.[2]
During fast acceleration, under a large gravitational load, or during impact, however, external force cannot be determined directly from current alone. Accurate estimation requires robot dynamics, friction, and the variation of motor torque constant with temperature to be considered as well.
Benefits and Remaining Problems in Learning-Based Control
QDD does not change the learning algorithm itself, but it can make the actual actuator behavior simpler and more repeatable.
Low friction and small backlash reduce nonlinearities between command and actual joint response. High backdrivability softens the overly rigid response that can occur when the robot contacts the environment. These properties can reduce the difference between an ideal actuator model in simulation and the real hardware.
QDD does not eliminate the Sim-to-Real Gap, however. Real systems still differ through:
- motor current and voltage limits
- temperature dependence of torque constant and friction
- communication and computation delay
- sensor noise
- structural flexibility and contact-model error
- battery-voltage variation
- driver protection and saturation behavior
When transferring a learning-based policy to a real robot, actuator system identification, delay modeling, domain randomization, and real-hardware validation are still required even with QDD.
Thermal and Electrical Limits
One of the most important QDD trade-offs is heat.
If output torque is $\tau_{out}$, the torque that the motor must generate is approximately
\[\tau_m \approx \frac{\tau_{out}}{\eta N}\]As reduction ratio $N$ decreases, the motor must directly generate more torque to produce the same output torque. The required current increases as
\[i_q \approx \frac{\tau_{out}}{\eta N K_t}\]Copper loss in the windings is proportional to the square of current:
\[P_{\mathrm{copper}}\approx I_{\mathrm{RMS}}^2R\]A low reduction ratio can therefore reduce reflected inertia and friction while requiring higher motor current and copper loss.
This is especially important when the joint remains still while supporting gravity or an external load. Mechanical output is then nearly zero, but current continues to flow through the windings. Most of the consumed power becomes heat, making static holding a difficult operating condition for a QDD actuator.
Dynamic work alternates between positive and negative work, and regenerative braking can recover some mechanical energy. Regeneration cannot recover the $I^2R$ loss already generated in the windings, however, and fast motion can itself require high RMS current. QDD is therefore not automatically thermally favorable for every dynamic task.
Actual design should consider all of the following together:
- continuous and peak torque
- RMS and peak phase current
- winding resistance and torque constant
- winding and housing thermal resistance
- motor thermal time constant
- continuous current limit of the driver
- battery and DC-bus voltage
- cooling method and actuator mounting condition
- torque–speed duty cycle of the task
QDD is not completed by choosing a low reduction ratio alone. It is an actuator co-design problem in which motor, reducer, driver, power supply, and cooling system are designed together to balance required torque and speed, reflected inertia, and thermal limits.
Next post: [Robot Hardware 05] - Actuators (4): Torque Ripple
References
[1] B. Katz, J. Di Carlo, and S. Kim, “A Low Cost Modular Actuator for Dynamic Robots,” 2018. https://dspace.mit.edu/handle/1721.1/118671
[2] P. M. Wensing, A. Wang, S. Seok, D. Otten, J. Lang, and S. Kim, “Proprioceptive Actuator Design in the MIT Cheetah: Impact Mitigation and High-Bandwidth Physical Interaction for Dynamic Legged Robots,” IEEE Transactions on Robotics, vol. 33, no. 3, pp. 509–522, 2017. https://doi.org/10.1109/TRO.2016.2640183