---
title: Neural External Torque Estimation (NEXT)
url: https://www.emergentmind.com/topics/neural-external-torque-estimation-next
type: topic
---

# Neural External Torque Estimation (NEXT)

Neural External Torque Estimation (NEXT) is a class of sensorless, data-driven methodologies for estimating external joint torques or wrenches in robotic and human biomechanical systems using only internal or minimally intrusive signals and without dedicated force/torque sensors. NEXT approaches leverage neural network architectures to learn direct or physics-informed mappings from proprioceptive, electromyographic, or exteroceptive signals to joint torques, thereby enabling force feedback, adaptive control, collision detection, and advanced human-robot interaction in settings where conventional force sensing is impractical or cost-prohibitive.

## 1. Fundamental Problem Formulation and Theoretical Foundation

The estimation of external joint torque is grounded in the joint-space or floating-base rigid-body dynamics:

$$ \tau_m = M(q) \ddot{q} + C(q, \dot{q}) \dot{q} + g(q) + \tau_{ext} $$

where $q$ are joint positions, $\tau_m$ are the measured or commanded motor torques (or their proxies, e.g., currents), and $\tau_{ext}$ are the torques induced by external contacts, objects, or interaction forces. In practice, direct numerical inversion to estimate $\tau_{ext}$ is highly sensitive to modeling errors and unmodeled effects such as joint friction, nonrigid contacts, or sensor bias.

NEXT circumvents explicit model inversion by training a neural network regressor (or hybrid model) to map historic or multimodal input sequences $x$ directly to an external torque estimate, often in the form:

$$ \hat{\tau}_{ext} = \tau_m - f_\theta(x) $$

where $f_\theta$ encodes the "free-space" dynamics via supervised regression, and the residual with respect to the observed system input ($\tau_m$) yields the (sensorless) estimate of external torque [2606.12406].

The paradigm generalizes to floating-base systems, soft manipulators, and even exoskeletons, with appropriate adaptation to input modalities and output targets [2402.11221][2301.13413][2408.16599].

## 2. Neural Architectures and Input Modalities

NEXT methods deploy a variety of architectures, tuned to task and platform:

- **Temporal Models:** LSTMs and GRUs are used to ingest time-series proprioceptive signals (joint positions, velocities, deltas from setpoints), achieving high prediction fidelity with short memory horizons (window sizes $H \sim [20,100]$ time steps). Stateless (sliding-window) operation is preferred for robustness to drift [2606.12406][2402.11221][2309.04138].
- **Physics-Informed RNNs:** Physics-Informed Gated Recurrent Networks (PiGRN) tightly couple GRUs to physics constraints and output not only torque, but kinematic state and external mass, with a loss comprising both data fidelity and inverse dynamics residuals [2408.16599].
- **Multilayer Perceptrons (MLPs):** For systems with strong priors and feature-engineered inputs (e.g., PCA-reduced EMG or windowed statistics), shallow MLPs can rival temporal models in torque estimation accuracy, especially in small-sample regimes [2601.16712].
- **Temporal Convolutional Networks (TCNs):** Dilated/causal TCNs process short windows of IMU, EMG, or encoder data to extract instantaneous torque or classify gait phase, enabling real-time adaptive exoskeleton control [2508.00691][2601.16712].
- **Hybrid Residual Architectures:** NEXT variants incorporate hierarchical or parallel residual MLPs, with explicit long-term memory of static/dynamic transitions ("Motion Discriminator"), critical for accurate friction-hysteresis cancellation [2309.16219].

Inputs span joint encoder positions, velocities, commands, motor currents, IMUs (kinematic/kinetic state), sEMG (muscle activation), visual data, and hybrid stacks including task context.

## 3. Data Collection, Training Procedures, and Loss Functions

Robust training of NEXT models requires strategic dataset design and loss construction:

- **Dataset Diversity:** Datasets are collected across free-space, contact-rich, and specialized manipulation scenarios (sliding, assembly, hand-guiding), covering the full operational envelope and, when relevant, divided by inverse-kinematic classes for transferability [2301.13413].
- **Labeling:** Ground-truth torque is derived from either direct F/T sensors (used only during training), inverse dynamics (from kinematics and known masses), or momentum observer baselines corrected for model uncertainty [2402.11221][2408.16599].
- **Physics-Informed Losses:** In addition to standard supervised losses (MSE, weighted Huber), physics-informed networks impose model-based constraints—penalizing violations of the rigid-body inverse dynamics with physics residual loss terms, which are weighted alongside data loss [2408.16599].
- **Augmentation and Regularization:** Temporal mixing (sliding windows, segmentation), domain-conditional normalization, random torque exploration, and Dropout or weight decay are used to enhance robustness and generalization [2601.16712][2402.11221].
- **Hyperparameters:** Learning rates are typically $1\times 10^{-3}$–$1\times 10^{-4}$ for Adam/AdamW optimizers; batch sizes from 32 to 1024 are reported, with early stopping on validation loss.

Quantitative performance is reported via RMSE, MAE, $R^2$, and relative error metrics on held-out or cross-environment splits. For example, LSTM-based NEXT on a Franka manipulator achieves per-joint $L_1$ error of $0.547\pm 0.348$ Nm in contact vs. $1.47$ Nm for disturbance observer and $4.40$ Nm for classical inverse dynamics [2606.12406].

## 4. Real-Time Performance and Implementation Constraints

NEXT frameworks are designed for compute-efficient inference, enabling closed-loop control:

- **Latency and Throughput:** MLPs with $1024$ units/layer yield $2.4$ ms/frame inference at 100 Hz on a CPU [2301.13413]. GRU/LSTM models deliver $<2$ ms latency at similar rates. Multi-threaded HRDL yields $<1$ ms evaluation at 570 Hz [2309.16219]. PiGRN and TCN exoskeleton models are deployed at 100 Hz–1 kHz, with total pipeline including preprocessing and filtering remaining within tens of milliseconds [2508.00691][2408.16599].
- **Online Integration:** Real-time estimates feed directly into admittance controllers, policy learning modules (e.g., force-informed re-sampling training), or teleoperation feedback loops, supplanting physical force sensors [2606.12406][2508.00691][2309.16219].
- **Sensor Requirements:** Most variants require only encoders and, in some cases, base IMUs or sEMG; exteroceptive approaches (e.g., VFTS) extend sensing via camera modalities [2210.00051].

## 5. Empirical Performance and Applications

Applications validate NEXT capabilities across a spectrum of tasks:

| Application Domain        | Typical Inputs                     | Reported Accuracy (RMSE)       | Reference      |
|--------------------------|------------------------------------|-------------------------------|---------------|
| Robotic manipulation     | Encoders, currents                 | 1–3 N, 0.1–0.2 Nm             | [2301.13413]  |
| Teleoperation, BC        | Proprioceptive seq., LSTM          | 0.54 Nm (Franka, contact)     | [2606.12406]  |
| Humanoid collision detection | Encoders, IMU                   | 1–2 Nm (legs, sim), 2.6 Nm (real LL) | [2402.11221]  |
| Exoskeleton torque (EMG) | sEMG, joint kinematics             | 7.2 % (elbow NM), 11.4 % (shoulder NM), $r=0.92-0.98$ | [2408.16599]  |
| Stroke gait exoskeleton  | 3x IMU, encoder, TCN               | 0.16 Nm/kg, $R^2=0.74$         | [2508.00691]  |
| Soft gripper F/T sensing | RGB image (fisheye), ResNet-18     | 0.8–1.7 N, 0.05–0.18 Nm        | [2210.00051]  |

Downstream benefits include: sensorless compliant interaction, adaptive exoskeleton assistance, robust collision detection, fine manipulation (100-micron clearance assemblies), force-informed policy learning, and high-frequency feedback in complex unstructured environments.

## 6. Robustness, Generalization, and Limitations

NEXT architectures demonstrate several robustness features:

- **Physics hybridization** (MOB+GRU, PiGRN) attenuates drift and out-of-distribution errors relative to pure data-driven or pure model-based approaches, enabling sensitive, robust collision response [2402.11221][2408.16599].
- **Training with domain-specific augmentation** (e.g., random torque exploration, motion discriminator for hysteresis) enhances extrapolation to unseen contacts, friction regimes, and hardware variations [2309.16219][2402.11221].
- **Transfer learning** (pretraining on healthy populations, fine-tuning on post-stroke or variant hardware) improves generalization in highly variable or poorly sampled regimes [2508.00691].

Nonetheless, current limitations include dependence on data coverage (rare contacts, high-speed phenomena), ground-truth torque acquisition (reliance on external F/T during training or inverse-dynamics biases), and challenges with multi-contact localization or payload change adaptation. Explicit uncertainty quantification remains underdeveloped in most architectural instantiations.

## 7. Outlook and Future Directions

Key frontiers for NEXT research and deployment include:

- **Fully unsupervised or self-supervised online learning** to obviate the need for labeled ground-truth torque [2408.16599][2210.00051].
- **Integration of richer physics priors:** inclusion of actuation limits, muscle-tendon complex, multi-modal state inference, or compliant contact dynamics.
- **Modularity and scalability:** extension to whole-body floating-base and multi-limb systems via modularized network pools [2402.11221].
- **Robust domain adaptation and online meta-learning** for sustained accuracy amidst subject variation, hardware drift, or context shift.
- **Deployment to embedded/wearable platforms:** streamlined TCNs and lightweight MLPs/GRUs now enable on-device inference at sub-millisecond latency in embedded microprocessors [2508.00691].

A plausible implication is that NEXT architectures will underpin the next generation of sensorless, force-aware robot control and rehabilitation paradigms, filling the gap between model-based observers and cumbersome hardware-based sensing. The field continues to evolve toward robust, real-world deployment with minimal hardware overhead and maximal task generality.

Source: https://www.emergentmind.com/topics/neural-external-torque-estimation-next