Accurate actuation models are critical for bridging the gap between simulation and real robot behavior, yet obtaining high-fidelity actuator dynamics typically requires dedicated test stands and torque sensing. We present a trajectory-based actuator identification method that uses differentiable simulation to fit system-level actuator models from encoder motion alone. Identification is posed as a trajectory-matching problem: given commanded joint positions and measured joint angles and velocities, we optimize actuator and simulator parameters by backpropagating through the simulator, without torque sensors, current/voltage measurements, or access to embedded motor-control internals. The framework supports multiple model classes, ranging from compact structured parameterizations to neural actuator mappings, within a unified optimization pipeline. On held-out real-robot trajectories for a high-gear-ratio actuator with an embedded PD controller, the proposed torque-sensor-free identification achieves much tighter trajectory alignment than a supervised stand-trained baseline dominated by steady-state data, reducing mean absolute position error from 14.20 mrad to as low as 7.54 mrad (1.88 times). Finally, we demonstrate downstream impact for the same actuator class in a real-robot locomotion study: training policies with the refined actuator model increases travel distance by 46% and reduces rotational deviation by 75% relative to the baseline.
Figures & tables
Approach
Instrumentation
Data Regime
Optimization
Interpretability
Model complexity
Ideal PD/torque abstraction
None
Simulation assumption
—
High
Low
Domain randomization
None
Sim randomized
—
—
—
Test-stand characterization
Torque sensor + test stand
Test stand (primarily quasi-static)
Supervised
Low-High
Low-High
Offline traj-ID
None
Real rollouts
Self-supervised; gradient-free
High
Low
Learned actuator modules / residual action
None
Real rollouts
Self-supervised; gradient-based
Low
High
Differentiable traj-ID (ours)
None
Real rollouts
Self-supervised; gradient-based
Low–High
Low–High
TABLE I: Comparison of actuator modeling and compensation approaches. Model complexity is a qualitative proxy for the number of trainable parameters and runtime evaluation cost.
Fig. 1: Illustration of the trajectory-matching optimization: The real system follows a trajectory {si} under control inputs {ai} . Simulated states {si′} are generated using a parameterized simulator. At each timestep, the state prediction error ei:=si′−si is computed, and the total trajectory error is minimized during optimization.
Model
Supervision / data
Model type
Stand-based supervised baseline
Bench-Sup
Supervised.
MLP
Trajectory-based gradient-free baseline
Param-ES
Self-supervised; gradient-free.
PD gains, armature (evolution strategy)
Trajectory-based residual-action (ASAP) baseline
Residual-RL
Self-supervised.
MLP
TABLE II: Comparison of actuator models and training protocol.
Fig. 2: Measured vs simulated motor response under identical control inputs. Motor velocity measured on hardware (black dashed) versus simulated trajectories for each model (colored lines).
Fig. 3: Position MAE comparison across actuator models. Box-and-whisker plot of the mean absolute position error (Eq. 3 ) on the held-out trajectory. Boxes indicate the interquartile range; the central line indicates the median; whiskers show the spread of the observed values.
Fig. 4: Parameter, loss, and gradient norm convergence of TrajID-Param over 25 independent runs. Each run lasts 3000 epochs. Shaded regions indicate mean ± std.
Fig. 5: Validation MAE versus objective weight α ( wq=α , wq˙=1−α ) for TrajID-Param , TrajID-NN , and Torque-Oracle .
Fig. 6: Validation MAE versus prediction horizon for TrajID-Param , TrajID-NN , and Torque-Oracle .
Fig. 7: Robot Performance Comparison: Refined vs. Baseline RL Policies. The traveled distance is denoted as d , and the rotation deviation from the original direction is represented as ϕ . The top image shows robot performance using the baseline model, exhibiting excessive rotation and reduced travel distance. The bottom image shows the robot’s performance using the refined model, demonstrating improvements in both travel distance and rotational alignment.
Metric
Default Model
TrajID Model
(mean ± std)
(mean ± std)
RL Policy Comparison
Rotation deviation (deg) ↓
109±14.3
27±6.4
Travel distance (m) ↑
1.12±0.13
1.64±0.08
TABLE III: Comparison of our method vs. baseline
Figure 15Figure 16Figure 17Figure 18
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Fig. 8: Motor test-stand setup: Experimental apparatus used to characterize the actuator under controlled loading. The rig couples a test motor and a load (brake) motor through an inline torque transducer, enabling synchronized torque/velocity measurements.
Fig. 9: Measured vs. model-predicted torque. Steady-state motor torque τ (N m) versus motor velocity (rad/s) for two PWM duty-cycle commands ( u=0.2 and u=0.8 ). Gray markers show downsampled test-stand measurements; the orange curve shows the learned ( Bench-Sup ) model evaluated on a dense velocity grid.
Fig. 10: Table-top setup with actuator and rigid rod load used to collect identification trajectories.
Term
Formula
Scale
Tracking linear velocity
exp(−σ2(v−vcmd)2) for vx,vy
1.5
Tracking angular velocity (yaw)
exp(−4(ωz−ωzcmd)2)
1.5
Base upright (roll/pitch)
exp(−30∥[roll,pitch]∥2)
0.9
Base height
exp(−500(z/ztarget−1)2)
0.8
Base acceleration penalty
exp(−∑j∣ajroot∣)
0.1
Action smoothness
∥at−at−1∥2+∥at+at−2−2at−1∥2
-0.02
Appendix
TABLE IV: Reward terms used in the RL experiments.
Differentiable simulators have advanced policy learning and model-based control, yet actuator dynamics remain an important source of sim-to-real error. This is particularly acute on low-cost platforms, where the linear current-to-torque relation τ=KtI becomes unreliable during commanded-target tracking because of friction, hysteresis, backlash, and thermal effects. We present NeuralActuator, a neural actuator model that jointly predicts (i) a simulator-equivalent generalized-effort surrogate for trajectory propagation on low-cost servo platforms, (ii) external force with a contact-probability gate for sensorless force perception, and (iii) a motor-condition score for the supervised joint. We also introduce the Neural Actuation Dataset (NAD), collected with a twin-arm teleoperation system that records robot states and actuator telemetry together with external-force labels. The torque-surrogate head is trained through differentiable simulation from pose trajectories without direct generalized-effort labels, while the force, gate, and motor-condition heads receive direct supervision. A Transformer captures temporal dependencies while supporting real-time inference. We evaluate NeuralActuator on a 5-DoF OpenManipulator-X, a 6-DoF SO-101, and a 7-DoF Franka Emika Panda, spanning three actuator families and platforms costing approximately USD 500 to over USD 30,000. The low-cost platforms support dynamics and force evaluation, while the offline Franka experiment provides an additional payload-force-estimation benchmark. Experiments further demonstrate its application for motor condition estimation on OpenManipulator-X and improved behavior-cloning performance when NeuralActuator is used as a pretrained module.
Zhiyang Dou, John U. Onyemelukwe, Hangxing Zhang +9
Sampling-based system identification estimates physically meaningful parameters by tuning a simulator to reproduce the target system dynamics, providing an interpretable approach to improving sim-to-real transfer. Yet when the collected trajectories do not distinguish the effects of different parameters, multiple parameter combinations can reproduce those trajectories, leading to unreliable parameter estimates. To address this challenge, we introduce an Informationally Decoupled Trajectory Design framework (IDTD), which formulates the objective for the exploration policy built on the Schur complement score derived from the Fisher information matrix. To faithfully reflect parameter separability in the exploration objective, IDTD normalizes the score against the per-parameter information, selects the most favorable trajectory segment for each parameter, and aggregates the resulting scores logarithmically. The optimized trajectory is therefore composed of complementary intervals, each exposing a distinct subset of parameters whose contribution to the motion over that interval can be attributed unambiguously. Across diverse simulation environments, ranging from a linear-dynamics system to the Go2 quadruped, G1 humanoid, and Crazyflie quadrotor, IDTD reduces the parameter identification error by 39.6% on average relative to the strongest prior active-exploration baseline and attains improved downstream policy transfer. Furthermore, we validate the proposed trajectory design on a real K1 humanoid, demonstrating that the resulting identified parameters accurately capture the real-system dynamics.
Tendon drives paired with soft muscle actuation enable faster and safer robots while potentially accelerating skill acquisition. Still, these systems are rarely used in practice due to inherent nonlinearities, friction, and hysteresis, which complicate modeling and control. So far, these challenges have hindered policy transfer from simulation to real systems. To bridge this gap, we propose a sim-to-real pipeline that learns a neural network model of this complex actuation and leverages established rigid body simulation for the arm dynamics and interactions with the environment. Our method, called Generalized Actuator Network (GenAN), enables actuation model identification across a wide range of robots by learning directly from joint position trajectories rather than requiring torque sensors. Using GenAN on PAMY2, a tendon-driven robot powered by pneumatic artificial muscles, we successfully deploy dynamic but precise goal-reaching, ball-in-a-cup, and table tennis policies, trained entirely in simulation. To the best of our knowledge, this result constitutes the first successful sim-to-real transfer for a four-degrees-of-freedom muscle-actuated robot arm.
Jan Schneider, Mridul Mahajan, Le Chen +4
Max Planck Institute for Intelligent Systems, Tübingen · Boston University · ELLIS Institute Tübingen +4