Forward Jump
A dynamic jump along the forward axis targeting roughly 1.0 m horizontal displacement and 0.2 m apex height.
IEEE RA-L publication
Task-Aware Actuator Parameter Allocation for Multibody Robots
This project page presents a task-aware co-design framework that allocates actuator parameters joint-by-joint for humanoids. The method combines continuous CMA-ES search, data-driven actuator regressions, constrained full-order trajectory optimization, and RL-based sim-to-sim validation across several tasks and pelvis topologies.
Experimental Tasks
The showcased scenarios are chosen to stress the actuator allocation in different ways: short high-power bursts, prolonged loaded motion, and whole-body manipulation with asymmetric support. Together they force the design loop to balance leg, torso, and arm requirements.
Stair Ascent with Load
Semi-squat stair climbing over five steps while carrying a 10 kg payload, emphasizing sustained leg torque and balance.
Workout Motion
A manipulation-style motion with 5 kg weights in each hand, deliberately shifting support and creating asymmetric full-body loading.
Methodology
The core algorithm couples actuator synthesis and full-body motion optimization. For every candidate vector of motor masses and gear ratios, regression models reconstruct peak torque, motor constant, rotor inertia, geometry, and stage-dependent efficiency; the robot model is updated; an inner constrained trajectory optimization is solved; and the resulting motion is scored by a scalar fitness.
Regression-Driven Actuator Model
Regression fits built from manufacturer data for 119 motors and 58 gearboxes provide practical estimates of peak torque, rotor inertia, motor constant, geometry, and stage-dependent transmission efficiency.
Inner Motion Optimization
The inner problem solves full-order constrained trajectories with torque-velocity, kinematic, and contact constraints, then evaluates motor losses, positive mechanical work, and gearbox friction in a unified energy model.
Outer Search Loop
CMA-ES explores the continuous design space with a population of 100 over 100 iterations. Each individual encodes motor mass and gear ratio for the robot joints, with the optimizer updating the search distribution over time.
The fitness combines trajectory quality with actuation efficiency:
F = Jtraj + ωemEem + ωfEf,
where Eem includes electrical losses and
positive mechanical energy, and Ef
captures transmission friction losses.
Regression Models
A practical contribution of the paper is the bridge between continuous design variables and realistic actuator properties. The models below are fitted from manufacturer datasheets and allow the optimizer to stay in a continuous search space without collapsing the design problem to a small discrete parts catalog.
Regression models for key actuator parameters based on manufacturer datasheets (TMotor, MyActuator, Encos, KUBO, AT Drive, PAN-Motor, and MAXON). The obtained results can be used either to define requirements for the development of a custom actuator, or to identify suitable electric motors and gearboxes via the k-nearest neighbors method on dataset.
Inner Motion Optimization Results
This section visualizes the trajectories returned by the inner constrained motion optimization. Choose one topology and all three tasks below will update.
Topology for all tasks
Outer Loop Ablation on Loss Terms
The paper also isolates how the objective changes the resulting actuator allocation on the PRY configuration.
Case I: Friction Only
Objective weighting: ωem = 0, ωf = 1.
- Electrical Energy
- 43113.98 J
- Cost of Transport
- 13.5455
- Total Mass
- 57.47 kg
Case II: Electrical Focus
Objective weighting: ωem = 1, ωf = 0.
- Electrical Energy
- 20234.94 J
- Cost of Transport
- 7.4353
- Total Mass
- 48.93 kg
Case III: Combined
Objective weighting: ωem = 1, ωf = 1.
- Electrical Energy
- 26728.75 J
- Cost of Transport
- 8.3624
- Total Mass
- 51.34 kg
Weighting electrical losses drives the design toward lower electrical
energy and higher optimal gear ratios, which increases reflected
inertia and reduces backdrivability. Weighting gearbox friction alone
pushes the design toward lower gear ratios and better
backdrivability, but with noticeably higher electrical energy
consumption.
Detailed actuator parameters by robot joint across all ablation cases.
| Joint | Parameter | Case 1 | Case 2 | Case 3 |
|---|---|---|---|---|
| torso_yaw | mass[g] | 433 | 603 | 561 |
| gear_ratio | 36.1 | 68.0 | 43.5 | |
| diameter[mm] | 82.7 | 86.0 | 88.9 | |
| length[mm] | 69.5 | 97.6 | 76.4 | |
| peak_torque[Nm] | 93.9 | 205.5 | 149.0 | |
| no_load_vel[rad/sec] | 13.4 | 6.9 | 10.5 |
| Joint | Parameter | Case 1 | Case 2 | Case 3 |
|---|---|---|---|---|
| hip_pitch | mass[g] | 2483 | 1279 | 1401 |
| gear_ratio | 7.0 | 25.0 | 15.4 | |
| diameter[mm] | 139.7 | 111.6 | 114.4 | |
| length[mm] | 104.1 | 104.1 | 107.7 | |
| peak_torque[Nm] | 160.2 | 213.4 | 146.0 | |
| no_load_vel[rad/sec] | 45.2 | 15.2 | 24.1 | |
| hip_roll | mass[g] | 1625 | 1300 | 1388 |
| gear_ratio | 20.0 | 25.0 | 24.9 | |
| diameter[mm] | 119.1 | 112.1 | 114.1 | |
| length[mm] | 114.0 | 104.7 | 107.3 | |
| peak_torque[Nm] | 225.1 | 217.3 | 233.5 | |
| no_load_vel[rad/sec] | 18.0 | 15.1 | 15.0 | |
| hip_yaw | mass[g] | 1640 | 739 | 743 |
| gear_ratio | 14.2 | 25.0 | 24.6 | |
| diameter[mm] | 119.4 | 95.9 | 96.1 | |
| length[mm] | 114.4 | 84.7 | 84.8 | |
| peak_torque[Nm] | 161.7 | 115.4 | 114.2 | |
| no_load_vel[rad/sec] | 25.3 | 17.1 | 17.4 | |
| knee_pitch | mass[g] | 1944 | 1654 | 1559 |
| gear_ratio | 25.0 | 24.9 | 24.8 | |
| diameter[mm] | 125.1 | 119.7 | 117.8 | |
| length[mm] | 122.1 | 114.8 | 112.2 | |
| peak_torque[Nm] | 347.7 | 286.1 | 266.0 | |
| no_load_vel[rad/sec] | 13.8 | 14.4 | 14.6 | |
| ankle_pitch | mass[g] | 809 | 734 | 1256 |
| gear_ratio | 25.0 | 25.0 | 24.8 | |
| diameter[mm] | 98.4 | 95.8 | 111.0 | |
| length[mm] | 87.6 | 84.4 | 103.4 | |
| peak_torque[Nm] | 127.5 | 114.5 | 207.4 | |
| no_load_vel[rad/sec] | 16.8 | 17.1 | 15.3 | |
| ankle_roll | mass[g] | 809 | 734 | 1256 |
| gear_ratio | 25.0 | 25.0 | 24.8 | |
| diameter[mm] | 98.4 | 95.8 | 111.0 | |
| length[mm] | 87.6 | 84.4 | 103.4 | |
| peak_torque[Nm] | 127.5 | 114.5 | 207.4 | |
| no_load_vel[rad/sec] | 16.8 | 17.1 | 15.3 |
| Joint | Parameter | Case 1 | Case 2 | Case 3 |
|---|---|---|---|---|
| shoulder_pitch | mass[g] | 863 | 530 | 751 |
| gear_ratio | 30.9 | 69.3 | 37.9 | |
| diameter[mm] | 100.1 | 82.9 | 96.4 | |
| length[mm] | 89.7 | 93.2 | 85.2 | |
| peak_torque[Nm] | 169.1 | 182.1 | 178.1 | |
| no_load_vel[rad/sec] | 13.4 | 6.9 | 11.3 | |
| shoulder_roll | mass[g] | 880 | 407 | 341 |
| gear_ratio | 36.2 | 69.4 | 42.6 | |
| diameter[mm] | 100.7 | 76.8 | 77.4 | |
| length[mm] | 90.4 | 85.0 | 63.7 | |
| peak_torque[Nm] | 202.7 | 137.9 | 86.9 | |
| no_load_vel[rad/sec] | 11.4 | 7.4 | 11.9 | |
| shoulder_yaw | mass[g] | 955 | 407 | 331 |
| gear_ratio | 26.3 | 70.0 | 34.9 | |
| diameter[mm] | 103.0 | 76.8 | 76.7 | |
| length[mm] | 93.2 | 85.0 | 63.0 | |
| peak_torque[Nm] | 161.3 | 139.0 | 69.0 | |
| no_load_vel[rad/sec] | 15.4 | 7.3 | 14.7 | |
| elbow_pitch | mass[g] | 401 | 407 | 388 |
| gear_ratio | 48.0 | 69.0 | 44.5 | |
| diameter[mm] | 80.9 | 76.8 | 80.2 | |
| length[mm] | 67.5 | 85.0 | 66.7 | |
| peak_torque[Nm] | 115.4 | 137.0 | 103.4 | |
| no_load_vel[rad/sec] | 10.2 | 7.4 | 11.1 | |
| elbow_yaw | mass[g] | 463 | 327 | 327 |
| gear_ratio | 43.2 | 37.6 | 25.1 | |
| diameter[mm] | 84.3 | 76.4 | 76.5 | |
| length[mm] | 71.2 | 62.7 | 62.8 | |
| peak_torque[Nm] | 120.7 | 73.4 | 49.1 | |
| no_load_vel[rad/sec] | 11.0 | 13.7 | 20.5 |
Citation
If you use this work, please cite the paper as follows.
@article{task-aware_actuator2026,
title = {Task-{Aware} {Actuator} {Parameter} {Allocation} for {Multibody} {Robots}},
doi = {10.1109/LRA.2026.3674006},
journal = {IEEE Robotics and Automation Letters},
author = {Nasonov, Kirill and Kakanov, Mikhail and Skvortsova, Valeria and Zaliaev, Eduard and Borisov, Ivan},
year = {2026},
pages = {1--6},
}