NeuralActuator: Neural Actuation Modeling for Robot Dynamics and External Force Perception

Dou, Zhiyang; Onyemelukwe, John U.; Zhang, Hangxing; Zhang, Heng; Guo, Minghao; Tian, Yunsheng; Lipiec, Michal Piotr; Jacob, Joshua; Liu, Chao; Chen, Peter Yichen; Ivanov, Yuri; Matusik, Wojciech

NeuralActuator: Neural Actuation Modeling for Robot Dynamics and External Force Perception

A neural actuator model for low-cost servo-driven robot platforms, linking actuator telemetry to differentiable dynamics, sensorless force perception, and force-aware sim-to-real control.

Robotics: Science and Systems (RSS) 2026

Finalist for the Outstanding Student Paper and Outstanding Paper Awards.

Zhiyang Dou¹ John U. Onyemelukwe^1* Hangxing Zhang^1* Heng Zhang¹ Minghao Guo¹ Yunsheng Tian¹ Michal Piotr Lipiec¹ Joshua Jacob¹ Chao Liu¹ Peter Yichen Chen¹ Yuri Ivanov^2,† Wojciech Matusik¹

¹ MIT ² Amazon Robotics

^* Research Assistant at MIT CDFG, equal contribution.
^† The work of this author does not relate to their position at Amazon.

Abstract

Differentiable simulators have advanced policy learning and model-based control across diverse robotic tasks. To date, actuator dynamics remain underexplored and are a major source of sim-to-real error, especially on low-cost platforms where the linear current-torque model breaks down under commanded-target tracking due to friction, hysteresis, backlash, and thermal effects. Beyond forward dynamics, accurate actuator models also support force perception, which is crucial for jointly modeling force and position control in manipulation tasks. We present NeuralActuator, a neural actuator model that jointly predicts torques, external contact forces, force detection gates, and motor conditions. We introduce a twin-arm teleoperation system that collects motor states alongside ground-truth forces from interactions and known external forces, contributing a dataset named Neural Actuation Dataset (NAD). NeuralActuator is trained through differentiable simulation using only pose trajectories as supervision, eliminating the need for torque sensors. A Transformer-based architecture captures temporal dependencies while enabling efficient real-time inference. We validate NeuralActuator across three platforms spanning low-cost and industrial arms, and show that it enables accurate dynamics modeling, sensorless force estimation, motor condition estimation, and improved behavior-cloning control when used as a pretrained module.

Overview

Low-cost robot actuation as a path to dynamics, force perception, and real-robot control.

Force-gauge validation for NeuralActuator — **Force-gauge validation.** Real contact trials, simulated rollouts, and predicted force curves across contact onset, steady force, and release.

Downstream manipulation tasks with payloads — **Downstream manipulation tasks.** Payload configurations used for lift-and-hold and pick-and-place robot control experiments.

NeuralActuator targets the actuator-modeling gap that is especially visible on low-cost robot arms: affordable servos expose rich telemetry, but the conventional linear current-to-torque model breaks down under commanded-target tracking due to friction, hysteresis, backlash, and thermal effects. The model learns how commanded targets, measured states, current, temperature, and recent history translate into torque, then reuses the same temporal representation to estimate external contact forces and motor condition.

Low-cost actuator dynamics

Learns joint-level torque for servo-driven arms instead of relying on a fixed current-to-torque conversion, capturing friction, hysteresis, saturation, thermal effects, and degraded motor behavior.

Sensorless force perception

Estimates contact force and force gates from actuator-side signals, enabling contact onset, payload change, and release detection without deployment-time force sensors.

Method

Problem formulation, NAD, and Transformer actuator model.

Problem Formulation

NeuralActuator models each servo-driven joint as a history-dependent mapping from commanded pose, current, measured state, thermal state, and recent telemetry to real torque. The same input stream is also used to estimate end-effector contact force and motor condition, enabling dynamics modeling, sensorless force perception, and actuator health monitoring from actuator-side signals.

Neural Actuation Dataset (NAD)

NAD is collected with a twin-arm teleoperation setup that records commanded pose, measured pose, current, voltage, temperature, and force supervision from force sensors, force gauges, and known payloads.

NeuralActuator data collection setup — **NAD data collection.** Leader-follower teleoperation records synchronized robot states, actuator telemetry, and external force labels.

Force data verification — **Data verification.** Time-synchronized video and trajectory logs with visualized external force.

Dataset composition. NAD includes free-motion, force-labeled, and motor-conditioned trajectories for actuator dynamics, force prediction, and condition monitoring.

Component	Description	Duration
Free motion	No external force	~34.15 min
Force labeled	Known weights or force sensing	~46.24 min
Motor condition	Degraded actuation	~14.13 min
Total	-	~94.52 min

NeuralActuator

NeuralActuator formulates actuation as a history-dependent mapping from commanded targets, proprioception, and actuator telemetry to torque, external force, contact gate, and motor condition. The torque head is trained through differentiable simulation from pose trajectories, while the force, gate, and condition heads use direct supervision when labels are available.

01 Torque-Label-Free Differentiable Actuator Learning

Learns joint torque from real pose trajectories by backpropagating through differentiable simulation, avoiding torque labels and reliable current-to-torque calibration on low-cost platforms.

\begin{matrix} θ^{⋆} = \underset{θ}{arg min} \sum_{t} L_{pose} (q_{t + 1}^{sim}, q_{t + 1}^{real}) \\ q_{t + 1}^{sim} = π_{q} [DiffSim (s_{t}, τ_{θ} (H_{t}))] \end{matrix}

02 History-Dependent Nonlinear Actuator Modeling

Uses a Transformer over commands, proprioception, and actuator telemetry to model nonlinear and time-varying torque behavior associated with friction, backlash, saturation, hysteresis, and thermal drift.

03 Unified Actuation and Proprioceptive Force Perception

Jointly predicts actuator torque (τ), the 3-axis end-effector external force (f_ext), contact gate (g), and motor condition (c), supporting sensorless force perception, motor-health monitoring, and force-aware downstream control.

\begin{matrix} M (q) \ddot{q} + C (q, \dot{q}) \dot{q} + g_{grav} (q) = τ + {J_{v} (q)}^{⊤} f_{ext} \\ τ_{ext} = {J_{v} (q)}^{⊤} f_{ext} \end{matrix}

Experiments

Rollout accuracy, force estimation, baselines, motor condition, and runtime.

Rollout and Force Estimation

Force sensor measurements and results — **External force estimation.** Estimated end-effector forces across directional pushes and payload manipulation tasks.

Accuracy summary. Units are shown in the table header: joint errors in degrees, gripper errors in millimeters, and force errors in Newtons.

Benchmark	Horizon (steps)	J1 (deg)	J2 (deg)	J3 (deg)	J4 (deg)	Grip (mm)	Force (N)
No-load rollout	600 steps	3.1	2.8	3.2	3.1	0.2	-
Force-sensor test	500 steps	1.78	3.31	2.01	1.58	0.65	0.23
Weight-based test	600 steps	2.97	4.06	3.51	3.77	0.50	0.11

Force-estimation baselines. All entries are force MAE in Newtons (N). NeuralActuator predicts external force from simulated rollout states, while classical baselines consume ground-truth states at each step.

Method	Go Up 200g (N)	Go Up 300g (N)	Go Up 400g (N)	Pick 200g (N)	Pick 300g (N)	Pick 400g (N)	Pick 500g (N)	Avg. (N)
ID-Linear	1.37	1.81	2.30	0.72	0.95	1.22	1.47	1.41
ID-Friction	1.06	1.59	2.15	0.62	0.82	1.10	1.31	1.23
GMO	0.58	0.66	1.23	0.33	0.47	0.63	0.75	0.66
NeuralActuator	0.12	0.20	0.07	0.24	0.00	0.19	0.05	0.12

Motor Condition and Runtime

Motor condition prediction — **Motor condition estimation.** Abnormal resistance produces higher current under similar position trajectories.

Degraded motor data collection inset — **Motor degradation setup.** Rubber-band-constrained joint used to collect motor-conditioned trajectories.

Motor condition detection. A learned condition head separates normal operation from mechanically degraded trajectories.

Method	Accuracy	Precision	Recall	AUC-ROC
Threshold	58.6%	0.0%	0.0%	0.45
SVM	59.9%	52.6%	31.7%	0.62
Random Forest	67.1%	62.3%	52.4%	0.72
NeuralActuator	91.0%	84.5%	96.2%	0.95

Runtime performance. The model is lightweight enough for simulation and real-time control, with sub-millisecond GPU inference latency.

Metric	Value	Unit	Metric	Value	Unit
Parameters	1.42M	-	Mean time	0.25	ms
FLOPs (forward)	5.46M	-	P95 time	0.31	ms
Parameter memory	5.43	MB	Throughput (batch=1)	4,019	Hz
-	-	-	Throughput (batch=32)	10,992	Hz

Sim-to-Real Robot Control

Frozen actuator model for payload-aware behavior cloning.

High-level robot tasks — **High-level pick-and-place.** Time-lapse snapshots under heavier and shape-varied payloads.

Pick and place robot experiment — **Pick-and-place with payloads.** Real executions and simulated rollouts with estimated external forces.

Lift and hold robot experiment — **Lift-and-hold with payloads.** Real and simulated rollouts with visualized forces from 200g to 500g.

Behavior cloning success rates. Results are averaged over 40 real-robot trials and compare position-only control against a force-aware policy using the frozen NeuralActuator module.

Task	Without NeuralActuator	With NeuralActuator
Pick-and-place	80%	92.5%
Go up-and-stay	85%	95%

Supporting Results

Cross-platform validation, force generalization, visual supervision, and dataset details.

These results expand the main experiments along four directions: transfer across robot platforms, robustness to unseen payloads, differentiable visual supervision, and the data collection details needed to reproduce NAD.

Cross-Platform Dynamics and Learned Torque

NeuralActuator is built around low-cost servo-driven platforms, where actuator nonlinearity is a dominant sim-to-real bottleneck. The same formulation is also evaluated on an industrial manipulator to test generality, and the learned torque traces expose the current-to-torque variation that motivates replacing a fixed linear actuator model.

Robot platforms used for NeuralActuator — **Cross-platform validation.** Low-cost and industrial robot arms across multiple actuator families.

Current torque relationship — **Learned torque values.** The effective current-to-torque mapping varies across joints, phases, saturation, and noise.

Force Generalization

Force prediction is evaluated beyond the exact training objects with two unseen payload geometries and surface conditions. During the still-holding phase, the pretrained model predicts 2.80 N for a 261 g object with 2.56 N ground truth, and 2.40 N for a 226 g object with 2.21 N ground truth.

Novel contact geometry weights — **Novel contact geometries.** Predicted vs. ground-truth forces for unseen objects: 2.80 N vs. 2.56 N (261 g) and 2.40 N vs. 2.21 N (226 g).

Visual Supervision

Because the actuator model sits inside a differentiable simulator, it can be combined with differentiable rendering. The visual-supervision example refines camera and robot state by aligning rendered robot silhouettes with image masks.

Differentiable rendering appendix figure — **Visual supervision.** Differentiable rendering aligns robot silhouettes during hand-eye calibration.

Dataset and Robot Details

NAD is built from a leader-follower collection rig, controlled payloads, force-sensor interactions, and motor-condition interventions. These setup figures document how the three supervision sources are produced and how the robot gripper is modeled in simulation.

**Data collection hardware.** Twin-arm setup, force/torque sensor, force gauge, and payload set.

Free motion data collection — **Free-motion data.** Contact-free trajectories for nominal actuator dynamics.

Weight-labeled data collection — **Weight-labeled data.** Payload tasks for repeatable gravity-induced force labels.

Motor restricted data collection — **Motor-restricted data.** Pick-and-place trajectories under constrained actuator conditions.

Force sensor data collection — **Force-sensor data.** Directional interaction trials with an external force/torque fixture.

OpenManipulator-X motor — **Robotic arm actuator.** Dynamixel motor used in the OpenManipulator-X leader-follower system.

**Robot gripper schematic.** Top and side views used to derive the gripper aperture from motor rotation.

Gauge Pushing

A separate gauge-pushing test isolates contact transitions from the payload tasks above. The predicted force tracks the measured force through contact onset, sustained pushing, and release.

Architecture and Adaptation

The final checks compare temporal model choices, show rapid online calibration from a small batch of new trajectories, and verify that NeuralActuator can be inserted into another differentiable physics backend.

Architecture ablation. Transformer history modeling improves force prediction while remaining competitive on rollout accuracy.

Model	J1	J2	J3	J4	Grip	Force
MLP	4.55	5.81	3.48	2.16	0.91	0.47
GRU	1.83	2.08	1.68	1.70	0.65	0.49
LSTM	2.91	7.66	3.21	3.08	0.71	0.41
NeuralActuator	1.78	3.31	2.01	1.58	0.65	0.23

Online learning progress plot — **Online adaptation.** Rapid fine-tuning from a small batch of newly collected trajectories.

Warp simulation results — **Warp simulation.** NeuralActuator integrated with another differentiable physics backend.

Quantitative Results

Rollout accuracy, force prediction, adaptation, and cross-platform tests.

Dynamics and Force Prediction

Gradient behavior across rollout horizons.

H	Torque Grad.	\|\|grad L\|\|	Cos.
64	2.73e-2	8.77	0.96
128	2.59e-2	17.33	1.00
256	1.72e-2	22.35	0.99
320	1.45e-2	22.91	0.99
500	9.37e-3	20.29	0.98

Simulation accuracy on the test set. J1-J4: joint-angle MAE (deg). Grip: gripper-aperture MAE (mm).

Task	@100					@300					@600
	J1	J2	J3	J4	Grip	J1	J2	J3	J4	Grip	J1	J2	J3	J4	Grip
backward_forward	2.4	4.3	4.4	4.2	0	2.3	5.9	3.9	4.2	0	3.1	4.8	4.9	4.5	0
circular_ccw	1.7	5.2	2.2	2.6	0	1.5	3.1	2.0	3.4	0	2.5	2.3	2.1	2.8	0
circular_cw	3.6	3.2	1.4	2.2	0	3.1	1.9	1.2	2.6	0	2.6	1.7	2.0	2.8	0
go_up_stay_still	2.5	1.8	2.3	1.2	0	3.1	2.1	3.1	2.5	0	3.1	1.5	3.5	2.7	0
joint_sweep_1	2.3	2.5	1.8	1.4	0	1.9	1.0	2.6	1.8	0	2.9	1.9	2.0	1.6	0
joint_sweep_2	2.1	4.3	4.6	1.2	0	1.8	6.7	8.4	1.1	0	2.4	4.6	5.2	1.7	0
joint_sweep_3	3.7	4.5	3.1	1.9	0	3.4	2.6	2.8	2.8	0	3.1	2.6	2.5	3.4	0
joint_sweep_4	2.6	4.8	2.5	3.4	0	2.9	3.3	2.4	3.2	0	2.4	2.9	2.2	4.6	0
joint_sweep_5	1.7	3.0	1.7	3.1	0.4	2.6	3.9	2.3	2.7	0.5	5.5	3.3	5.1	3.0	0.7
pick_place_empty	2.6	2.5	2.2	3.5	1.1	1.9	3.6	2.7	3.2	1.1	3.1	2.7	2.0	3.9	1.0
Average	2.5	3.6	2.6	2.5	0.2	2.5	3.4	3.1	2.8	0.2	3.1	2.8	3.2	3.1	0.2

Simulation and force prediction accuracy on the force-sensor test set. F: force MAE (N).

Task	@100						@300						@500
	J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F
force_X+	0.9	2.3	0.9	1.6	1.0	0.36	1.1	1.8	2.4	1.3	1.0	0.46	0.9	1.9	2.7	1.7	1.0	0.50
force_X-	1.4	1.1	0.8	1.1	1.0	0.39	1.6	2.3	1.3	2.3	1.0	0.42	2.0	2.9	1.5	3.0	1.0	0.44
force_Y+	2.3	5.7	2.8	0.6	0.1	0.36	2.1	4.5	2.6	0.9	0.2	0.38	2.7	4.8	2.1	0.9	0.3	0.44
force_Y-	1.4	1.6	3.1	0.5	0.1	0.38	1.5	3.0	3.1	1.3	0.1	0.36	1.4	3.6	3.1	1.5	0.2	0.38
force_Z+	3.3	6.2	3.3	0.8	0.1	0.39	2.3	5.6	2.5	1.9	0.2	0.43	2.5	4.4	2.2	2.3	0.3	0.46
force_Z-	1.0	5.9	0.6	0.6	1.0	0.36	2.9	6.6	2.8	2.5	1.0	0.64	3.8	6.4	3.5	2.0	1.0	0.57
ref_X+	0.6	2.0	1.5	1.2	1.0	0.01	0.8	1.8	1.0	1.1	1.0	0.02	1.0	1.6	1.1	1.1	1.0	0.01
ref_X-	2.0	2.5	0.5	1.1	1.0	0.00	1.4	2.3	0.5	1.0	1.0	0.00	1.5	2.2	0.8	1.3	1.0	0.00
ref_Y+	2.0	1.0	2.0	0.6	0.1	0.00	2.1	3.3	2.1	1.1	0.2	0.00	1.9	3.7	1.7	1.1	0.4	0.00
ref_Y-	1.0	1.8	1.2	1.3	0.1	0.00	1.6	4.5	2.0	2.2	0.1	0.00	1.2	4.0	2.4	1.6	0.3	0.00
ref_Z+	1.2	1.7	2.1	0.5	0.1	0.00	1.6	3.8	2.2	1.2	0.2	0.00	1.5	2.9	2.0	1.3	0.3	0.00
ref_Z-	0.6	2.3	0.9	0.9	1.0	0.02	0.7	1.6	1.1	1.1	1.0	0.01	0.9	1.3	1.0	1.1	1.0	0.01
Avg	1.48	2.84	1.64	0.90	0.55	0.19	1.64	3.43	1.97	1.49	0.58	0.23	1.78	3.31	2.01	1.58	0.65	0.23

Simulation and force prediction accuracy on the weight-based test set.

Task	Weight	@100						@300						@600
		J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F
go up and stay	200g	1.3	5.0	2.6	2.4	0.1	0.12	3.4	3.9	4.2	2.3	0.1	0.10	3.1	3.3	4.3	2.9	0.1	0.16
go up and stay	300g	2.6	5.3	5.7	3.7	0.1	0.20	1.8	3.4	5.7	5.4	0.0	0.17	3.5	2.5	3.4	4.6	0.0	0.20
go up and stay	400g	2.2	4.1	1.4	5.0	0.1	0.07	2.9	2.1	2.1	6.1	0.1	0.12	2.0	1.4	3.0	7.1	0.2	0.11
pick and place	200g	0.7	3.1	4.3	3.4	1.1	0.24	2.7	3.9	4.0	4.0	1.1	0.08	2.9	5.1	2.9	3.0	1.0	0.11
pick and place	300g	0.5	4.5	3.7	0.9	0.3	0.00	1.2	5.1	4.8	1.5	0.2	0.00	2.7	7.8	4.9	3.2	0.3	0.09
pick and place	400g	0.8	2.1	2.8	2.9	1.1	0.19	2.8	1.4	3.4	3.6	1.1	0.06	2.4	2.0	3.8	3.3	1.0	0.03
pick and place	500g	2.7	1.8	1.7	3.3	1.1	0.05	4.8	2.8	1.7	2.3	1.1	0.02	4.2	6.3	2.3	2.3	0.9	0.04
Avg		1.54	3.70	3.17	3.09	0.56	0.12	2.80	3.23	3.70	3.60	0.53	0.08	2.97	4.06	3.51	3.77	0.50	0.11

Dataset and Adaptation

Task composition of the dataset.

Category	Task	Variant	#Frames	Duration (s)
Free motion	Circular trajectory	Clockwise	8615	147.06
Free motion	Circular trajectory	Counterclockwise	8428	143.90
Free motion	Joint sweep	Motor 1	22935	392.04
Free motion	Joint sweep	Motor 2	8688	148.47
Free motion	Joint sweep	Motor 3	11357	193.95
Free motion	Joint sweep	Motor 4	15012	256.57
Free motion	Joint sweep	Motor 5	7338	125.21
Free motion	Lean back and extend forward		12261	209.35
Free motion	Pick & place (empty)		15288	261.08
Free motion	Go up and stay still		10011	171.14
Force-labeled	Go up and stay still	200g	10606	181.26
Force-labeled	Go up and stay still	300g	11259	192.40
Force-labeled	Go up and stay still	400g	11291	192.89
Force-labeled	Pick and place	200g	13245	226.15
Force-labeled	Pick and place	300g	13129	224.31
Force-labeled	Pick and place	400g	15124	258.54
Force-labeled	Pick and place	500g	13957	238.49
Force-labeled	Force sensor	+X	5005	85.17
Force-labeled	Force sensor	+X w/o interaction	5005	85.21
Force-labeled	Force sensor	-X	5169	87.94
Force-labeled	Force sensor	-X w/o interaction	5169	88.00
Force-labeled	Force sensor	+Y	7444	126.74
Force-labeled	Force sensor	+Y w/o interaction	7444	126.78
Force-labeled	Force sensor	-Y	6921	117.88
Force-labeled	Force sensor	-Y w/o interaction	6921	117.91
Force-labeled	Force sensor	+Z	6906	117.59
Force-labeled	Force sensor	+Z w/o interaction	6906	117.63
Force-labeled	Force sensor	-Z	5565	94.69
Force-labeled	Force sensor	-Z w/o interaction	5565	94.73
Motor condition	Pick & place w/ weight	Motor restricted	10113	168.26
Motor condition	Pick & place w/ weight	Motor in good condition	13245	226.15
Motor condition	Pick & place w/o weight	Motor restricted	11252	192.41
Motor condition	Pick & place w/o weight	Motor in good condition	15288	261.08

Visual-supervision and architecture settings.

Group	Metric / Model	Value 1	Value 2	Value 3	Value 4	Value 5
Silhouette IoU	Initialization	Mean 0.2589	Std 0.0441
Silhouette IoU	Robot refinement	Mean 0.2974	Std 0.0754
Silhouette IoU	Joint refinement	Mean 0.8515	Std 0.0065
Runtime	Joint refinement	1845 iterations	180.23 s
Architecture	MLP	Hidden 416	Latent 208	1.14M params	LR 3e-5	Clip 0.3
Architecture	GRU	Hidden 325	Latent 162	1.43M params	LR 1e-4	Clip 1.0
Architecture	LSTM	Hidden 275	Latent 137	1.44M params	LR 1e-4	Clip 1.0
Architecture	NeuralActuator	Hidden 192	Latent 96	1.44M params	LR 1e-4	Clip 1.0

Online adaptation before (B) and after (A). J1-J4: joint-angle MAE (deg). Grip: gripper-aperture MAE (mm). F: force MAE (N).

Task	@100												@300												@500
	J1 B	J1 A	J2 B	J2 A	J3 B	J3 A	J4 B	J4 A	Grip B	Grip A	F B	F A	J1 B	J1 A	J2 B	J2 A	J3 B	J3 A	J4 B	J4 A	Grip B	Grip A	F B	F A	J1 B	J1 A	J2 B	J2 A	J3 B	J3 A	J4 B	J4 A	Grip B	Grip A	F B	F A
force_X+	0.9	0.3	2.1	0.7	1.0	0.8	0.8	0.8	1.0	1.0	0.36	0.37	2.1	1.2	2.3	1.0	0.7	1.5	0.9	0.8	1.0	1.0	0.46	0.41	2.7	1.6	4.0	1.3	0.6	1.9	0.9	0.8	1.0	1.0	0.52	0.41
force_X-	0.2	0.5	1.1	1.7	0.9	1.2	0.7	1.3	1.0	1.0	0.39	0.39	1.7	0.7	1.6	1.6	1.4	0.7	0.8	1.2	1.0	1.0	0.41	0.40	2.5	0.9	1.9	1.6	2.0	0.8	0.9	1.2	1.0	1.0	0.42	0.41
force_Y+	2.1	1.8	5.4	3.4	0.8	1.1	1.2	1.3	0.0	0.1	0.37	0.37	2.3	1.5	4.5	3.2	1.1	1.1	1.6	1.0	0.1	0.1	0.39	0.37	3.0	1.2	3.7	2.3	2.5	1.2	3.1	1.7	0.3	0.3	0.45	0.39
force_Y-	1.1	1.2	0.6	1.3	1.1	1.8	1.8	1.8	0.1	0.1	0.38	0.38	1.6	1.0	3.1	2.6	1.2	1.4	2.1	2.0	0.1	0.1	0.36	0.36	1.7	1.0	2.3	2.0	2.5	1.1	2.1	1.6	0.2	0.2	0.38	0.37
force_Z+	2.9	4.0	5.2	3.6	1.3	3.1	0.6	0.5	0.1	0.1	0.39	0.39	2.7	2.1	4.0	2.7	1.4	1.5	0.7	0.9	0.2	0.1	0.44	0.42	5.0	1.8	3.2	2.0	1.7	1.5	1.4	1.5	0.3	0.2	0.46	0.45
force_Z-	0.7	0.9	6.2	3.5	2.0	0.6	1.0	0.7	1.0	1.0	0.36	0.36	2.0	0.7	7.1	2.3	1.8	0.8	3.3	1.2	1.0	1.0	0.61	0.38	2.6	1.0	7.2	1.6	2.0	0.8	3.0	1.1	1.0	1.0	0.54	0.40
ref_X+	1.4	0.4	1.6	0.4	1.0	1.0	0.8	0.8	1.0	1.0	0.01	0.08	1.5	0.5	1.3	0.6	0.8	0.8	1.0	1.2	1.0	1.0	0.02	0.08	1.3	0.5	1.1	0.6	0.6	1.0	1.4	1.9	1.0	1.0	0.01	0.05
ref_X-	0.4	0.7	3.2	0.6	2.4	0.5	0.7	1.0	1.0	1.0	0.00	0.00	0.7	0.6	2.4	1.2	1.9	0.5	0.9	0.9	1.0	1.0	0.00	0.04	0.8	0.6	2.2	1.0	2.2	0.7	1.1	0.8	1.0	1.0	0.00	0.05
ref_Y+	1.4	1.8	1.0	2.8	1.4	1.4	1.3	1.9	0.1	0.1	0.00	0.00	2.2	1.7	3.3	3.3	1.0	1.2	1.8	1.4	0.2	0.2	0.00	0.01	2.2	1.2	4.4	2.4	1.0	1.1	1.3	1.3	0.4	0.3	0.00	0.01
ref_Y-	2.0	1.2	2.2	1.9	0.8	0.4	2.7	1.3	0.0	0.1	0.00	0.01	2.5	1.5	4.8	2.7	0.7	0.8	3.2	1.8	0.1	0.1	0.00	0.01	2.0	1.2	4.9	2.1	0.7	1.3	2.7	2.0	0.3	0.2	0.00	0.01
ref_Z+	0.6	0.9	1.3	0.8	0.4	1.3	1.4	1.3	0.1	0.1	0.00	0.00	1.3	1.2	3.4	1.6	0.4	1.0	1.2	1.0	0.2	0.2	0.00	0.00	1.0	1.1	3.4	1.5	0.5	1.2	0.9	1.3	0.3	0.3	0.00	0.00
ref_Z-	1.8	0.5	1.9	0.8	1.1	0.9	0.5	0.7	1.0	1.0	0.03	0.14	1.7	0.6	0.9	0.7	1.1	0.8	0.8	0.8	1.0	1.0	0.02	0.11	1.6	0.5	0.8	0.7	1.0	0.7	0.8	1.1	1.0	1.0	0.01	0.08
Avg	1.28	1.19	2.65	1.81	1.19	1.17	1.13	1.12	0.55	0.55	0.19	0.21	1.86	1.09	3.22	1.96	1.11	1.02	1.53	1.18	0.59	0.58	0.23	0.22	2.20	1.04	3.25	1.58	1.44	1.10	1.64	1.35	0.66	0.65	0.23	0.22

Cross-Platform Evaluation

SO-101 arm evaluation. Joint errors are in degrees and force errors are in Newtons.

Platform	Task	Lift & Hold / @500						Pick & Place / @500
		J1	J2	J3	J4	J5	F	J1	J2	J3	J4	J5	F
SO-101	300g	2.27	8.20	6.40	5.40	2.37	0.64	3.73	5.63	4.17	6.17	2.47	0.73
SO-101	400g	2.83	9.30	9.63	4.00	5.73	0.57	3.53	6.83	2.43	5.23	5.13	0.63
SO-101	500g	2.27	7.63	9.77	7.13	2.67	0.47	3.80	5.60	1.53	6.73	3.33	0.54

7-DoF industrial arm per-joint, force, and torque MAE.

Task	@100									@500
	J1	J2	J3	J4	J5	J6	J7	F	Torque	J1	J2	J3	J4	J5	J6	J7	F	Torque
200g	0.6	1.1	3.7	1.7	0.7	0.4	1.5	0.42	0.50	0.8	1.2	3.7	1.9	1.4	2.3	1.2	0.31	0.50
300g	0.4	1.2	2.8	2.0	0.8	0.5	1.1	0.35	0.68	0.6	1.0	2.7	1.7	1.1	1.7	0.9	0.28	0.59
400g	1.0	1.2	1.9	1.8	0.7	0.5	0.8	0.36	0.79	1.0	0.8	1.3	1.4	0.9	1.5	0.6	0.27	0.69
500g	1.4	1.1	0.9	1.7	0.8	0.6	0.4	0.27	0.87	1.7	0.7	0.7	1.4	0.8	1.3	0.5	0.26	0.79
600g	2.0	1.3	1.0	1.6	0.7	0.9	0.4	0.30	0.98	2.4	0.7	1.4	1.4	0.7	1.1	0.5	0.28	0.90
Avg	1.1	1.2	2.0	1.8	0.7	0.6	0.8	0.34	0.76	1.3	0.9	2.0	1.6	1.0	1.6	0.8	0.28	0.69

Gauge pushing test set.

Task	@100						@300						@600
	J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F	J1	J2	J3	J4	Grip	F
high_push_front	0.91	1.68	1.18	0.62	0.00	0.07	1.62	1.29	0.53	0.32	0.00	0.08	1.48	1.16	1.44	1.09	0.00	0.09
high_push_top	0.73	1.01	0.78	1.61	0.01	0.10	1.38	1.35	1.97	1.92	0.01	0.11	1.62	1.57	2.72	2.01	0.01	0.12
mid_push_front	0.66	0.52	0.96	0.61	0.30	0.06	0.85	0.51	0.60	0.99	0.31	0.07	0.95	0.56	0.48	0.98	0.31	0.08
mid_push_top	0.49	0.54	0.87	0.74	0.30	0.09	0.64	0.43	0.73	1.07	0.31	0.10	0.89	0.52	0.75	0.78	0.31	0.11
low_push_front	0.61	0.75	1.83	0.23	0.32	0.08	0.87	0.56	1.65	0.33	0.32	0.09	1.29	0.88	1.12	0.98	0.33	0.10
low_push_top	1.00	0.36	1.05	0.29	0.31	0.08	1.17	0.84	2.11	0.74	0.32	0.09	1.35	0.76	2.27	1.04	0.32	0.10
Avg	0.73	0.81	1.11	0.68	0.21	0.08	1.09	0.83	1.27	0.90	0.21	0.09	1.26	0.91	1.46	1.15	0.21	0.10

Future Directions

Scaling actuator learning across data, robot morphologies, and force-aware control.

01 Synthetic-to-Real Actuator Pretraining

Leverages large-scale synthetic actuator data for pretraining, followed by real-world fine-tuning, to reduce costly hardware data collection.

02 Cross-Morphology Actuation Learning

Extends NeuralActuator across robot morphologies and actuator families for more generalizable actuation modeling.

03 Scalable Whole-Body Force Perception

Moves beyond single-arm end-effector force estimation toward multi-joint and whole-body force-aware robot control.