EMG2Force Model Architecture

• EMG2Force architecture is a deep learning framework that maps sEMG and IMU signals to precise force estimations for various applications.
• It integrates parallel encoders and transformer-based fusion to capture both time-domain and spectral features from multimodal sensor data.
• Empirical evaluations show marked improvements in accuracy, underscoring its impact on robotics, rehabilitation, and biomechanical analysis.

The EMG2Force model architecture denotes a class of deep learning systems mapping surface electromyography (sEMG) signals—optionally augmented with inertial measurement unit (IMU) data—to the estimation of biological or interaction forces, such as per-finger or joint-level force trajectories. These models are foundational for translating biosignal recordings into actionable force traces, enabling force-sensitive robot manipulation, neuromusculoskeletal analysis, exoskeleton force control, and related areas. The predominant paradigm integrates time-domain and frequency-domain signal representations with multimodal sensor streams, using deep neural architectures distinguished by parallel encoding, modality fusion strategies, and calibration protocols (He et al., 24 Jun 2026, Zhang et al., 2022, Hajian et al., 2022).

1. Input Modalities, Preprocessing, and Feature Construction

EMG2Force systems are characterized by the concurrent capture of sEMG (multi-channel, typically 8–28 differential channels), IMU kinematic signals (commonly 9–10 axes), and time-aligned ground truth force data. sEMG signals are commonly recorded from anatomically guided electrode sites (for hand/forearm models), at sampling rates from 250 Hz to 2 kHz, while IMU streams (3-axis accelerometer, gyroscope, magnetometer, and/or quaternion estimation) are obtained at matching or resampled rates.

Preprocessing pipelines include:

• Segmentation and normalization: Multi-second windows (e.g., 5 s at 250 Hz, yielding 1250-sample tensors) or short windows (e.g., 50 ms at 2048 Hz, yielding 102-sample tensors) are extracted. Channel-wise z-score normalization is applied (zero mean, unit variance per channel over training set), or min–max/MVC normalization for musculoskeletal models (He et al., 24 Jun 2026, Zhang et al., 2022, Hajian et al., 2022).
• Spectral representations: Time-frequency analysis via short-time Fourier transform or periodogram is performed on concatenated raw or band-passed signals, producing spectrograms (e.g., 18×F×$T'$ with F~64–128 bins, $T'$ temporal frames) or channel-wise PSD matrices (e.g., 51×28) (He et al., 24 Jun 2026, Hajian et al., 2022).
• Motion/kinematic augmentation: IMU data are low-pass filtered (e.g., Savitzky–Golay), optionally synchronized and concatenated with sEMG before feature extraction (Hajian et al., 2022).
• Force ground-truth for supervision: Sourced from fingertip sensors (per-finger, 5D) or dynamometers/force transducers (joint/muscle-level force), aligned with sEMG-IMU frames (He et al., 24 Jun 2026).

2. Parallel Encoder Architectures

EMG2Force models employ parallel feature encoding to maximize temporal and spectral signal coverage:

• Time-domain encoder: Typically a stack of 1D convolutional blocks (kernel size 3–5, stride ≤2), interspersed with normalization (layer norm or batch norm), nonlinear activation (GELU, ReLU), and dropout. Temporal reduction (by ×4–8) and channel expansion (to, e.g., $H_t=256$) yield tokenized representations $T_{\mathrm{feat}}\in\mathbb{R}^{H_t\times N'}$ aligned with downsampled time (He et al., 24 Jun 2026).
• Spectral/frequency encoder: The preprocessed spectrogram or periodogram is processed by a vision backbone (e.g., frozen DINOv3 Vision Transformer (He et al., 24 Jun 2026)) or 2D convolutional neural network base learners (2–3 conv blocks, 16–128 filters, batch norm as per validation scheme). Extracted embeddings are projected to a fixed dimension ($H_s=256$ or more), producing $F_{\mathrm{feat}}\in\mathbb{R}^{H_s\times N'}$ (Hajian et al., 2022).
• IMU/motion encoder: Parallel 2D CNN base learners (input: $(T\times D\times 1)$, e.g., 102×9×1 for 50 ms windows) extract kinematic features, with deeper branches for dynamic conditions or inter-subject generalization (Hajian et al., 2022).

Each encoder branch processes its respective modality independently up to the fusion stage, preserving the raw and spectral cues unique to each information type.

3. Fusion, Temporal Modeling, and Output Regression

Fusion is commonly implemented at the feature or token level:

• Token concatenation: Outputs from time-domain and spectral (and, where included, IMU) encoders are concatenated along the feature dimension to yield a combined multimodal token stream $M\in\mathbb{R}^{(H_t+H_s+\cdots)\times N'}$ (He et al., 24 Jun 2026, Hajian et al., 2022).
• Transformer-based integration: A multi-layer transformer decoder (self-attention, residual, and feed-forward layers; MLP hidden size $4\times$ input dim) models long-range dependencies and temporal context within the fused representation, producing embeddings $Z\in\mathbb{R}^{H_z\times N'}$ (e.g., $T'$0) (He et al., 24 Jun 2026).
• Dense regression heads: Final force estimates are produced by mapping each temporal embedding (or global pooled encoding) via a linear or multi-layer perceptron regression head, outputting dimensionality matching the force application (e.g., 5 for per-finger, N+1 for $T'$1 in musculoskeletal joints, or scalar for end-point force) (He et al., 24 Jun 2026, Zhang et al., 2022, Hajian et al., 2022).

No cross-modal attention or gating is used prior to the fusion stage in the primary models; fusion is deferred to transformers or feature concatenation.

4. Loss Functions, Training, and Calibration

• Loss formulation: The principal supervisory objective is mean-squared error (MSE) between predicted and reference force traces:

$T'$2

where $T'$3 is the number of output force channels/tips, $T'$4 the time steps per window (He et al., 24 Jun 2026, Hajian et al., 2022). In biomechanics-informed settings, additional soft physics constraints penalize violations of joint torque equations, yielding composite losses such as $T'$5 as in (Zhang et al., 2022):

$T'$6

• Training protocols: Models are pre-trained on large, multimodal, manually labeled force datasets (e.g., 10 hours, batch size 128, AdamW or Adam optimizer with weight decay, linear warmup and cosine LR annealing) (He et al., 24 Jun 2026, Hajian et al., 2022). Data augmentation may include windowed crops and channel-wise Gaussian noise.
• User-specific calibration: Given inter-individual variability in EMG–force mappings, a brief fine-tuning phase is employed. For example, 15-minute calibration sessions per individual (approx. 2000 windows) and adaptation of the final transformer layers and output head (learning rate $T'$7, early stopping at 5 epochs) are sufficient for high-fidelity subject transfer (He et al., 24 Jun 2026).
• Cross-validation and regularization: Dropout and L2 weight penalties address overfitting, particularly for inter-subject generalization (Hajian et al., 2022).

5. Empirical Performance and Ablation Insights

Ablation studies across multiple EMG2Force architectures demonstrate the necessity of multimodal and multiview integration:

• Spectral features: Exclusion of the spectral branch increases force MAE by ~24% (e.g., from 0.92 N to 1.14 N), confirming the complementarity of frequency-domain cues for motor-unit firing pattern representation (He et al., 24 Jun 2026, Hajian et al., 2022).
• IMU/kinematics: Removal of IMU streams degrades accuracy (e.g., MAE from 0.92 N to 1.02 N), underscoring the role of wrist and limb motion cues in resolving muscle activation ambiguities (He et al., 24 Jun 2026, Hajian et al., 2022). Average relative improvements from IMU augmentation reach >10% in intra-subject, higher for dynamic contractions and inter-subject scenarios.
• Electrode arrangement: Uniform electrode layouts, as opposed to muscle-guided positioning, increase error by ~18%, highlighting the importance of spatial specificity in EMG source separation (He et al., 24 Jun 2026).
• Cross-domain robustness: Deeper or more regularized variants (increased filter count, more extensive dropout, no batch norm for inter-subject conditions) yield improved generalization to new subjects and dynamic contraction types (Hajian et al., 2022).

Mean $T'$8 values exceeding 0.8 are routinely achieved for intra-subject force regression under diverse contraction regimes, with modest decreases under more challenging inter-subject or dynamic scenarios (Hajian et al., 2022).

6. Comparative Architectures and Domain-Specific Extensions

Representative implementations elucidate core architectural trends:

Reference	Modality Inputs	Parallel Encoders	Fusion Stage/Type	Output Dimension	Physics Constraint
(He et al., 24 Jun 2026)	8-ch sEMG + 10-IMU	1D Conv (time), ViT (spectral)	Token concat $T'$9 Transformer	5 (per finger)	No
(Hajian et al., 2022)	28-ch sEMG + 9-IMU	3 × 2D CNNs (time, freq, IMU)	Feature concat $H_t=256$0 Dense	Scalar/Vector force	No
(Zhang et al., 2022)	Multi-ch sEMG	1D Conv (no pooling)	FC (regression)	N+1 (forces + angle)	Yes (physics-informed $H_t=256$1)

Physics-informed variants regularize purely data-driven force predictions by integrating soft constraints from biomechanical models, improving plausibility and generalization, especially in low-data regimes (Zhang et al., 2022).

7. Applications and Methodological Impact

EMG2Force architectures are central to domains requiring accurate, temporally resolved force estimation from noninvasive biosignals:

• Robot skill acquisition: ForceBand’s EMG2Force is employed to annotate human demonstrations with per-finger force traces using only wearable sEMG+IMU, achieving 87% success on force-critical manipulation tasks (pick, squeeze, place) and >50% MAE improvement versus vision-only baselines (He et al., 24 Jun 2026).
• Clinical and rehabilitation devices: End-point force regression from EMG–IMU is crucial for exoskeleton/autonomous orthoses, closed-loop neuroprosthetic feedback, and physiologic monitoring (Hajian et al., 2022).
• Biomechanical analysis: Physics-informed EMG2Force models have enabled simultaneous estimation of muscle force and joint kinematics, producing regularized predictions consistent with physical laws (Zhang et al., 2022).

The fusion-centric, subject-calibrated approach delineates a pathway to robust, noninvasive, and accurate force estimation in real-world and research contexts.