Data-Driven External Force Sensing

Updated 12 June 2026

Data-driven external force sensing is a technique that estimates contact forces using machine learning models trained on empirical sensor data, bypassing traditional sensor limitations.
It integrates modalities like resistive, vision-based, optical, and EMG sensors to capture detailed force profiles for applications in robotics, prostheses, and soft actuators.
Hybrid approaches combining neural regression with physics-based models enhance accuracy and transferability in complex, contact-rich scenarios.

Data-driven external force sensing refers to the estimation and reconstruction of contact forces applied to a physical system using computational models trained on empirical data, rather than relying strictly on classical physics-based sensors or analytical models. This paradigm enables force perception in manipulators, prostheses, and soft robots that lack traditional force/torque (F/T) sensors, or where embedding such sensors is impractical, costly, or physically infeasible. Approaches range from learning-based interpretation of embedded, distributed, or proprioceptive sensors to multi-modal fusion of exteroceptive (e.g., vision, EMG) data streams, supplemented by statistical or neural network models tailored to the system dynamics and physical constraints.

1. Physical and Signal Modalities for External Force Sensing

Data-driven force sensing leverages diverse physical measurement modalities:

Distributed Resistive, Capacitive, or Strain Sensing: Multi-tap resistive arrays embedded within soft robot bodies exploit local piezoresistive response, offering high spatial resolution for contact-induced deformations. Screen-printed serpentine traces with multiple electrical taps enable localized resistance measurements for each segment, which are converted into local strain fields using gauge models (ΔRᵢ/Rᵢ⁰ = k·εᵢ) (Tian et al., 2023).
Vision-based Tactile Sensing: Internal or external cameras capture high-resolution marker displacements within deformable elastomers (e.g., GelSight, TacTip) or observe actuator deformations. Deep neural networks decode contact force distributions from marker images or RGB deformation patterns (Chen et al., 2 Mar 2025, Collins et al., 2022).
Optical Transducers: Non-invasive optical assemblies (LED–slit–photodiode modules) measure instrument shaft deflection via slit displacement in minimally invasive surgery, supporting six-axis force/moment reconstruction (Hadi-Hosseinabadi et al., 2021).
Robot Intrinsic Sensing: Force estimation by mapping joint positions, velocities, currents, and accelerations directly to end-effector wrench, trained against F/T ground truth (no additional hardware required) (Shan et al., 2023, Oh et al., 10 Jun 2026).
Electromyography (EMG): Neural operator approaches (e.g., Koopman theory) infer grip force from processed surface EMG signals, showing high estimation fidelity on human grasp tasks (Bazina et al., 2024).

These modalities can be combined, e.g., by fusing proximal force measurements with distal robot state for actuation compensation (Yang et al., 29 May 2026).

2. Data-driven Model Architectures and Calibration Procedures

Data-driven external force reconstruction is distinguished by the use of machine-learned mappings from raw sensor outputs to force estimates:

Neural Regression Models: Multi-layer perceptrons (MLPs), recurrent neural networks (LSTM/GRU), convolutional networks, and domain-specific hybrid networks are trained with synchronized sensor–force datasets (Tian et al., 2023, Shan et al., 2023, Jang et al., 2024).
- Network input: vectorized raw sensor signals (e.g., resistances, images, motor signals), sometimes after pre-processing (filtering, normalization).
- Output: continuous force or wrench estimates, possibly with auxiliary classification for contact state.
- Training: Mean-squared error loss, Adam/SGD optimization, domain randomization or augmentation to ensure robustness.
Hybrid Physics-driven Approaches: Neural correction networks augment inverse finite element methods (FEM). FEM computes a physics-consistent estimate given sensor-derived boundary conditions, with neural nets learning residual force errors arising from unmodeled phenomena (hysteresis, nonlinearities) (Tian et al., 2023).
Marker-to-marker Translation Networks and Spatio-temporal Predictors: When transferring force models across heterogeneous tactile systems, vision-based or taxel sensor signals are converted to marker-based binary images. Cross-sensor translations are realized by VAE–diffusion architectures, followed by ConvGRU/residual neural regression on time sequences (Chen et al., 2 Mar 2025).
Koopman Operator and DMD-based Mappings: For processed EMG streams, time-delayed vector embeddings serve as observation lifts, and static Koopman operators (Tikhonov-regularized regression) provide force estimates. Dynamic Koopman prediction is realized with Hankel-structured DMD and refined Ritz approaches for short-term forecasting (Bazina et al., 2024).

Calibration protocols require comprehensive, well-labeled data—typically joint sensor–force ground truth pairs collected under diverse loading, contact, and environmental conditions. Data-driven model retraining is rapid, and only a brief, instrument-agnostic, one-time calibration may be required (Hadi-Hosseinabadi et al., 2021, Oh et al., 10 Jun 2026).

3. Inverse Problem, Physics Integration, and Theoretical Guarantees

External force estimation in data-driven pipelines involves solving an inverse problem, often augmented by physical modeling to impose structural priors:

Inverse FEM with Strain Gauge Data: Multi-tap strain is mapped to Dirichlet boundary conditions. The inverse FEM is regularized (minimize_{f_ext_s} ∥K_ss u_sensor − f_act_s − f_ext_s∥² + λ∥f_ext_s∥²), yielding closed-form Tikhonov solutions for f_ext. Accuracy is contingent upon mesh/model fidelity and known contact locations (Tian et al., 2023).
Robot Dynamics Residuals: Neural networks learn the mapping from state histories and signals (q, ẋ, motor currents) to expected free-motion joint torques; real-time residuals between measured and predicted torques are interpreted as external contact torques (NEXT), enabling scalable, robot-specific force sensing without explicit modeling (Oh et al., 10 Jun 2026).
Distributed Tactile Sensing: Deep encoder–decoder architectures regress spatially distributed force maps directly from image-domain tactile signals, facilitating model-based checks (e.g., local frictional slip) without explicit analytical conversion (Griffa et al., 2021).
Hysteresis and Nonlinear Dynamic Estimation: Koopman operator and DMD frameworks accommodate memory and dynamic phenomena, outperforming direct regression in tasks with substantial hysteresis or non-stationarity (Bazina et al., 2024).

Structural embedding of physical constraints into neural architectures (physics-informed nets, hybrid regularization) is suggested to improve extrapolation and robustness at the limits of training coverage.

4. Quantitative Performance, Error Analysis, and Transferability

Benchmarking is conducted across a range of manipulation and contact tasks:

Approach/Modality	Typical RMSE Error	Generalization Characteristics
Multi-tap resistive + inverse FEM	3% shape, 11% force (0–5 N) (Tian et al., 2023)	Robust to sensor noise/mild misalignment; requires known contact loci
Vision-based tactile + DNN	<1 N normal/shear F_z/shear, R²>0.8 (Chen et al., 2 Mar 2025)	Cross-sensor transfer via marker-translation reduces MAE by 80–90% over naive mapping
Proximal optical + shallow neural net	0.3–0.4 N lateral force, 2–12 Nmm moment (Hadi-Hosseinabadi et al., 2021)	Agnostic to tool, rapid retraining; axial force limited by unmodeled friction
Robot-internal net (MLP, LSTM)	Sub-1 N joint (NEXT) (Oh et al., 10 Jun 2026), 1–2 N flange (Shan et al., 2023)	Generalizes across tasks if training spans relevant IK manifold and contact scenarios
Soft-finger sensor + GRU	<0.1 N RMSE, R²>0.9 in x/z (Jang et al., 2024)	Maintains performance across shapes/surface frictions with no object-specific retraining
Koopman-EMG estimator	~5.5% wMAPE force estimation (Bazina et al., 2024)	Robust to electrode placement; fast retraining; transfer possible with spectral mask search

These methodologies often achieve human-level just-noticeable-difference (JND) limits in manipulation and grasping scenarios, and force estimation accuracy sufficient for integration into closed-loop policy learning, surgical manipulation, and robust teleoperation.

5. Applications in Robotics, Manipulation, and Human–Machine Interaction

Data-driven force estimation frameworks are deployed in:

Soft robot proprioception and shape/force awareness: Embedded ink-based resistive arrays plus inverse FEM enable 3% shape and 11% force error, facilitating material property, object, or contact inference under full internal actuation (Tian et al., 2023).
Tactile manipulators and slip detection: Vision-based tactile arrays trained in simulation generalize to rich grasp scenarios and supply real-time force maps, supporting Coulomb and incipient slip detection for adaptive control (Griffa et al., 2021).
Transferable multi-modal tactile sensing: GenForce enables marker-to-marker translation so that force models trained on one tactile sensor can be rapidly deployed on disparate taxel/vision hardware with minimal paired data collection (Chen et al., 2 Mar 2025).
Robot teleoperation and force-aware learning: Neural torque estimation (NEXT) plus force-informed re-weighting (FIRST) in behavior cloning yield >17% improvement in contact-rich policy execution compared to model-based or vision-only baselines, with scaling to low-cost arms lacking dedicated F/T sensors (Oh et al., 10 Jun 2026).
Minimally invasive surgery and haptic feedback: Shaft-integrated force sensors plus learned transformer-based dynamics compensation outperform prior LSTM or model-based methods in cable-actuated end effectors, resolving 3D end-effector forces under large internal tensions (Yang et al., 29 May 2026).
Human–machine rehabilitation and assistive devices: Koopman-driven force prediction from a single EMG channel demonstrates ~5.5% error in instantaneous force estimation, robust to sensor placement and computationally suitable for real-time wearable control (Bazina et al., 2024).

6. Limitations, Open Challenges, and Future Directions

Key practical and theoretical limitations include:

Contact localization: Most high-precision model-based solutions require a priori knowledge of the force application locus. Distributed contact or arbitrary, multi-point force inference remains open (Tian et al., 2023).
Training data coverage: Performance and robustness are correlated with the statistic diversity and relevance of training data. Non-representative or poorly labeled data degrades reliability, especially for unmodeled configurations or force regimes (Shan et al., 2023).
Physical interpretability and failure modes: Model-based force correction mitigates some neural model non-transparency, but edge cases—large deformations, saturation, multi-contact—can produce unphysical predictions (Chen et al., 2 Mar 2025).
Hardware limitations: Sensor range, hysteresis, and cross-talk can constrain accuracy and observability of certain force components (e.g., axial forces in cannulated instruments) (Yang et al., 29 May 2026, Hadi-Hosseinabadi et al., 2021).
Generalizability: Direct force transfer across sensors, actuators, or morphological variants without substantial paired training is nontrivial but is being addressed via translation and domain adaptation frameworks (Chen et al., 2 Mar 2025).
Real-time constraints and computational complexity: Most pipelines operate well within 100 Hz real-time control but model size and input dimensionality (e.g., long input histories for LSTM/transformers) can impact deployment on resource-constrained platforms (Bazina et al., 2024).

7. Outlook and Research Impact

Data-driven external force sensing has dramatically broadened the applicability of force perception in robotics and human–machine systems by decoupling force estimation from specialized hardware. The development of hybrid architectures integrating physical constraints, transfer learning across sensors via representation translation, and the scaling of policy learning with force feedback to commodity robots highlight a maturing and robust research direction. Anticipated advances include further domain-adaptive methods for cross-platform generalization, self-calibration during task execution, and deeper coupling with policy and skill learning frameworks for autonomous, contact-rich manipulation without conventional F/T instrumentation (Tian et al., 2023, Chen et al., 2 Mar 2025, Oh et al., 10 Jun 2026).