Continuous Orthogonal Mode Decomposition: Haptic Signal Prediction in Tactile Internet

Mohammad Ali Vahedifar; Mojtaba Nazari; Qi Zhang

eess.SPApr 10, 2026

Continuous Orthogonal Mode Decomposition: Haptic Signal Prediction in Tactile Internet

Authors: Mohammad Ali Vahedifar, Mojtaba Nazari, Qi Zhang

Organizations: DIGIT and Department of Electrical and Computer Engineering, Aarhus University, Denmark

Abstract

The Tactile Internet demands sub-millisecond latency and ultra-high reliability, as even slight latency or packet loss can destabilize haptic control. To address this, we propose the Mode-Domain Architecture (MDA), a bilateral predictive neural network architecture designed to restore missing signals on both the human and robot sides. Unlike conventional models that implicitly extract features from raw data, MDA employs a novel Continuous-Orthogonal Mode Decomposition framework. By integrating an orthogonality constraint, we overcome the pervasive issue of ``mode overlapping" found in state-of-the-art decomposition methods. Experimental results demonstrate that this structured feature extraction achieves high prediction accuracies of 98.6% (human) and 97.3% (robot). Furthermore, the model achieves ultra-low inference latency of 0.065 ms, significantly outperforming existing benchmarks and meeting the stringent real-time requirements of haptic teleoperation.

Figures & tables

Fig. 1: Mode-Domain Architecture. C-OMD decomposes each haptic signal into

K

orthogonal modes processed by per-mode Temporal Convolutional Network (TCN) encoders and Cross-Mode Self-Attention within each side. Cross-Side Cross-Attention (main path) lets the human latent attend to robot keys/values and vice versa; a parallel Linear Coupling branch (dotted skip) provides a stable residual

W_{c}\tilde{z}

added before LayerNorm, ensuring gradient flow even when attention weights are noisy. Fused latents

\hat{z}^{h},\hat{z}^{r}

are decoded and summed to reconstruct the predicted signals.

Fig. 2: (a) Per-mode TCN encoder: dilations

d{=}1,2,4

with residual skip. (b) Per-mode TCN decoder: inverted dilations

d{=}4,2,1

with linear projection

\mathbb{R}^{d}\!\to\!\mathbb{R}^{H}

. (c) Cross-Side Cross-Attention with residual coupling detail:

z_{\text{attn}}

and

z_{\text{lc}}{=}W_{c}\tilde{z}

are summed and layer-normalized. (d) Cross-Mode Self-Attention over

K

mode latents.

Fig. 3: (a,b,c) Prediction accuracy (left axis, solid lines) and inference time (right log-axis, dashed lines) vs. prediction horizon

H\in\{1,5,10,25,50,100\}

samples for VMD (

\square

), SVMD (

\triangle

), and C-OMD (

\bigstar

) across three architectures. The green line marks the TI latency constraint

\Delta t=H\,\text{ms}

f_{s}{=}1\,

kHz.

Fig. 4: (a) Prediction accuracy over sliding windows across three architectures at horizon

H{=}5

. (b) Prediction accuracy (left axis, solid) and inference time (right log-axis, dashed) vs. number of modes

K\in\{2,\ldots,8\}

for C-OMD with the MDA architecture, evaluated at

H\in\{1,5,10,25,50,100\}

. (c) SNR robustness on the Force signal: accuracy (%, left axis) and relative degradation (%, right axis, faint) as channel SNR degrades from

30\,\text{dB}

0\,\text{dB}

Inf. (ms) — Human

Inf. (ms) — Robot

Accuracy (%) — Human

Accuracy (%) — Robot

Arch.

Decomp.

GFLOPs

H{=}1

H{=}10

H{=}100

H{=}1

H{=}10

H{=}100

Mamba

VMD

0.28

0.49

0.48

0.51

0.50

89.8{\scriptstyle\pm 0.8}

81.4{\scriptstyle\pm 1.1}

61.2{\scriptstyle\pm 1.9}

88.1{\scriptstyle\pm 0.9}

79.7{\scriptstyle\pm 1.2}

59.0{\scriptstyle\pm 2.1}

SVMD †

1.85

1.95

1.96

1.93

2.02

2.04

2.01

92.3{\scriptstyle\pm 0.7}

84.6{\scriptstyle\pm 1.0}

65.8{\scriptstyle\pm 1.7}

90.7{\scriptstyle\pm 0.8}

83.0{\scriptstyle\pm 1.1}

63.5{\scriptstyle\pm 1.9}

C-OMD

0.13

0.06

0.07

0.06

96.2{\scriptstyle\pm 0.5}

90.1{\scriptstyle\pm 0.8}

76.4{\scriptstyle\pm 1.4}

94.7{\scriptstyle\pm 0.6}

88.5{\scriptstyle\pm 0.9}

74.1{\scriptstyle\pm 1.5}

Trans. +Fourier

VMD

0.32

0.51

0.50

0.53

0.54

0.52

91.2{\scriptstyle\pm 0.7}

83.5{\scriptstyle\pm 1.0}

63.5{\scriptstyle\pm 1.8}

89.6{\scriptstyle\pm 0.8}

81.8{\scriptstyle\pm 1.1}

61.2{\scriptstyle\pm 2.0}

SVMD †

1.98

2.04

2.05

2.02

2.12

2.14

2.10

93.8{\scriptstyle\pm 0.6}

86.4{\scriptstyle\pm 0.9}

68.1{\scriptstyle\pm 1.6}

92.2{\scriptstyle\pm 0.7}

84.8{\scriptstyle\pm 1.0}

65.9{\scriptstyle\pm 1.8}

TABLE I: Total GFLOPs : decomposition + model floating-point operations per forward pass (

K{=}3

H{=}100

). Inf. (ms) : inference time at

H{=}1

per signal type and side. Acc. (%) : mean

\pm

std over 5-fold at

H\in\{1,10,100\}

. Green = best; underline = second-best.

Tactile Sensing

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In visually ambiguous manipulation such as detecting button click tactile feedback is often the sole source of ground truth. However, fusing tactile data poses a significant challenge due to a spatiotemporal mismatch: tactile perception requires high-frequency processing with long-horizon memory (System 1), whereas visual policies operate at low control frequencies (System 2). Existing architectures struggle to bridge this gap: Transformers are computationally prohibitive for high-frequency loops (>100Hz), while LSTMs suffer from forgetting over extended interaction histories. In this paper, we introduce TacMamba, a hierarchical architecture that aligns high-bandwidth tactile reflexes with low-frequency visual planning. Our approach comprises three core contributions: (1) a custom high-frequency tactile interface designed for flexible integration; (2) a Mamba-based Tactile History Compressor that encodes continuous force history into a compact state with O(1) inference latency (0.45 ms), enabling plug-and-play fusion with VLA models without joint pre-training and (3) a Tactile-Guided Dual-Stage Training strategy that leverages temporal discrimination for self-supervised representation learning and phase-uniform sampling to mitigate data sparsity. Experiments on discrete counting and implicit state switching demonstrate that TacMamba achieves 100% success rates, significantly outperforming the visual-only pi_0.5 baseline, while strictly satisfying hard real-time constraints.

Abstract

Tactile Sensing

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