Frequency-aware decomposition learning for sensorless wrench estimation in vibration-rich robotic contact

Hyeonbeen Lee; Min-Jae Jung; Tae-Kyeong Yeu; Jong-Boo Han; Daegil Park; Simon Stepputtis; Jin-Gyun Kim

cs.ROApr 14, 2026

Frequency-aware decomposition learning for sensorless wrench estimation in vibration-rich robotic contact

Authors: Hyeonbeen Lee, Min-Jae Jung, Tae-Kyeong Yeu, Jong-Boo Han, Daegil Park, Simon Stepputtis, Jin-Gyun Kim

Organizations: Department of Mechanical Engineering, Kyung Hee University, South Korea

Abstract

Force and torque (F/T) sensors enable contact-aware control by providing reactive feedback, but they are often fragile and expensive. To overcome these limitations, sensorless methods estimate F/T or wrench solely from robot proprioception, and have shown success in slow interaction tasks such as grasping. However, their low-pass characteristics limit the estimation of high-frequency signals, which are critical in rapid-contact tasks such as grinding. Communication delays can also make their estimates outdated during deployment, but few methods address this directly. To bridge these gaps, we propose a Frequency-aware Decomposition Network (FDN) to estimate vibration-rich wrench in a sensorless, multi-step-ahead manner. Considering higher-frequency stochasticity, FDN spectrally decomposes the wrench horizon into a low-frequency trend and a high-frequency residual, and estimates each by pointwise regression and a learned conditional distribution, respectively. The frequency-aware layers impose band decomposition priors on the outputs and adaptively enhance frequency amplitudes of the inputs. FDN requires neither an identified robot model nor an F/T sensor during estimation. On real-world grinding data from our 6-DoF hydraulic manipulator, FDN reduces high-frequency amplitude error by up to 47% over the baselines under assumed time delays and maintains competitive low-frequency pointwise accuracy, while the baselines fail to balance these two. We also find multi-step-ahead estimation feasible, with FDN estimating a 1,000 ms horizon within 11 ms on a single CPU thread. Ablation studies further support our design choices. In an exploratory study, transferring wrench dynamics learned from an open-source everyday manipulation dataset reduces low-frequency error by 8%, while high-frequency dynamics appear domain-specific.

Figures & tables

Figure 1: Illustration of our grinding task and the Frequency-aware Decomposition Network (FDN). J1 to J6 represent the joint numbers, and ‘EE’ denotes the end-effector. Cylinder drive types are either revolute (‘R’) or prismatic (‘P’), indicated above the joint numbers. Fixed and controlled components are colored in grey and yellow, respectively. The robot grinds the block by moving in $\mathbf{-x}$ and $\mathbf{-z}$ directions. FDN produces decomposed wrench estimates over a prediction horizon from a proprioception history, trained using ground truth from a wrist F/T sensor.

Figure 2: Illustration of the proposed Frequency-aware Decomposition Network (FDN).

Figure 3: Frequency-aware layers. FFT and IFFT denote the Fast Fourier Transform and its inverse. (a) A learnable frequency enhancement filter ( $\mathrm{FEF}$ ) layer. (b) Denoising high-pass filter ( $\mathrm{FPF}_{\mathrm{high}}$ ) and low-pass filter ( $\mathrm{FPF}_{\mathrm{low}}$ ).

Figure 4: Visualization of the ‘Stiff-2’ episode in the collected hydraulic dataset. (a) Trajectories of $\Delta q_{4}$ , $\dot{q}_{4}$ , $\ddot{q}_{4}$ and $\Delta p_{4}$ . (b) Denoised and decomposed trajectories of $F_{\mathbf{x}}$ and $M_{\mathbf{y}}$ with cutoffs $f_{c}=1$ Hz and $f_{c}^{\mathrm{dn}}=15$ Hz.

Episode	Dataset	Duration	In-contact	$N_{\boldsymbol{q},\Delta\boldsymbol{p}}$	$N_{\boldsymbol{W}}$	$\max\|\boldsymbol{F}\|$	$\max\|\boldsymbol{M}\|$	$d_{\mathbf{x}}$	$d_{\mathbf{z}}$	$\mathbb{E}[v_{\mathbf{x}}]$
Unit	-	[s]	[s]	-	-	[N]	[Nm]	[mm]	[mm]	[mm/s]
Soft-1	Test	289.18	214.11	28,861	28,924	$\|F_{\mathbf{x}}\|=122$	$\|M_{\mathbf{x}}\|=35$	158.31	11.75	-0.74
Soft-2	Test	149.34	114.15	14,909	14,937	$\|F_{\mathbf{x}}\|=96$	$\|M_{\mathbf{y}}\|=27$	154.70	12.58	-1.36
Soft-3	Training	230.33	141.70	22,933	23,035	$\|F_{\mathbf{x}}\|=155$	$\|M_{\mathbf{y}}\|=47$	213.84	13.79	-1.51
Soft-4	Training	152.04	108.32	15,121	15,205	$\|F_{\mathbf{z}}\|=116$	$\|M_{\mathbf{x}}\|=42$	160.00	12.57	-1.48
Soft-5	Training	176.63	130.39	17,618	17,663	$\|F_{\mathbf{x}}\|=134$	$\|M_{\mathbf{y}}\|=41$	206.74	13.23	-1.59

Table 1: Overview of the collected hydraulic grinding dataset. For

\max|\boldsymbol{F}|

and

\max|\boldsymbol{M}|

, the channel with the maximum magnitude is indicated.

Figure 5: Power spectrum of raw training wrench windows. Each channel is normalized to zero mean and unit variance before the Fourier transform. Power spectrum before denoising (a) and after denoising (b). Yellow vertical lines indicate the decomposition cutoff $f_{c}=1$ Hz and the denoising cutoff $f_{c}^{\mathrm{dn}}=15$ Hz applied during training.

Multi-step-ahead		$\mathrm{wRMSE}$ , High-frequency Windowed RMS Error
	Time Delay	100 ms		1,000 ms
	Force/Torque Unit	[N]	[Nm]	[N]	[Nm]
	MINN	24.359 $\pm$ 0.035	4.909 $\pm$ 0.003	24.431 $\pm$ 0.032	4.925 $\pm$ 0.003
	RBF	24.130 $\pm$ 0.110	4.753 $\pm$ 0.018	24.164 $\pm$ 0.109	4.759 $\pm$ 0.017
	GPR	24.974 $\pm$ 0.004	4.958 $\pm$ 0.001	25.013 $\pm$ 0.004	4.970 $\pm$ 0.001
	LSTM	18.592 $\pm$ 0.237	3.867 $\pm$ 0.046	19.110 $\pm$ 0.211	3.938 $\pm$ 0.043

Table 2: High-frequency windowed RMS errors of models.

Multi-step-ahead		$\mathrm{pRMSE}$ , Low-frequency Pointwise RMSE
	Time Delay	100 ms		1,000 ms
	Force/Torque Unit	[N]	[Nm]	[N]	[Nm]
	MINN	12.230 $\pm$ 0.494	3.612 $\pm$ 0.095	12.274 $\pm$ 0.489	3.623 $\pm$ 0.093
	RBF	10.455 $\pm$ 0.256	3.076 $\pm$ 0.109	10.432 $\pm$ 0.265	3.067 $\pm$ 0.109
	GPR	9.362 $\pm$ 0.016	2.285 $\pm$ 0.019	9.362 $\pm$ 0.018	2.281 $\pm$ 0.019
	LSTM	13.040 $\pm$ 1.102	3.289 $\pm$ 0.192	13.189 $\pm$ 1.029	3.300 $\pm$ 0.189

Table 3: Low-frequency pointwise RMSE of models.

Multi-step-ahead		$\mathrm{CRPS}$
	Time Delay	100 ms		1,000 ms
	Force/Torque Unit	[N]	[Nm]	[N]	[Nm]
	MINN	13.006 $\pm$ 0.100	3.900 $\pm$ 0.038	13.029 $\pm$ 0.101	3.905 $\pm$ 0.038
	RBF	12.561 $\pm$ 0.134	3.855 $\pm$ 0.063	12.574 $\pm$ 0.142	3.856 $\pm$ 0.064
	GPR	12.095 $\pm$ 0.005	3.520 $\pm$ 0.007	12.124 $\pm$ 0.005	3.528 $\pm$ 0.007
	LSTM	14.622 $\pm$ 0.518	4.332 $\pm$ 0.029	14.847 $\pm$ 0.581	4.368 $\pm$ 0.058

Table 4: Continuous ranked probability scores of models.

Figure 6: Test episode reconstructions with $t_{\mathrm{delay}}=100$ ms. We visualize the $F_{\mathbf{x}}$ and $M_{\mathbf{y}}$ , which are representative channels in our experimental setting described in Section 5.1 . The upper two rows correspond to the ‘Soft-1’ episode, and the lower rows correspond to the ‘Stiff-1’ episode. Colored areas illustrate the prediction interval defined by $\mu\pm 3\sigma$ .

Figure 7: Band-specific errors evaluated at every horizon step from $t+1$ to $t+100$ , computed on a normalized scale and aggregated over channels and test episodes. (a) and (b) report $\mathrm{pRMSE}$ and $\mathrm{wRMSE}$ , respectively. The upper axis gives the corresponding time delay at the 100 Hz sampling rate, where $t+10$ and $t+100$ are the delays reported in Tables 2 and 3 .

	HF $\mathrm{wRMSE}$	LF $\mathrm{pRMSE}$	$\mathrm{CRPS}$
w/o FEF	0.518 $\pm$ 0.002 (+3.4%)	0.569 $\pm$ 0.006 (+6.8%)	0.534 $\pm$ 0.003 (+3.1%)
w/o FEF-W	0.518 $\pm$ 0.003 (+3.4%)	0.572 $\pm$ 0.009 (+7.3%)	0.534 $\pm$ 0.005 (+3.1%)
w/o FEF-MoE	0.515 $\pm$ 0.002 (+2.8%)	0.565 $\pm$ 0.000 (+6.0%)	0.531 $\pm$ 0.001 (+2.5%)
w/o FPF	0.500 $\pm$ 0.001 (-0.2%)	0.537 $\pm$ 0.012 (+0.8%)	0.520 $\pm$ 0.005 (+0.4%)
w/o ModSpec	0.553 $\pm$ 0.002 (+10.4%)	0.606 $\pm$ 0.001 ( +13.7% )	0.559 $\pm$ 0.001 ( +7.9% )
w/o TrdHead	0.615 $\pm$ 0.049 ( +22.8% )	0.631 $\pm$ 0.063 ( +18.4% )	0.513 $\pm$ 0.013 (-1.0%)

Table 5: Architectural ablation results. Metrics are aggregated on the normalized scale.

Ablated Inputs	HF $\mathrm{wRMSE}$	LF $\mathrm{pRMSE}$	$\mathrm{CRPS}$
$\boldsymbol{\dot{q}}$	0.500 $\pm$ 0.004 (+0.2%)	0.583 $\pm$ 0.014 (+9.6%)	0.542 $\pm$ 0.007 (+4.6%)
$\boldsymbol{\ddot{q}}$	0.499 $\pm$ 0.002 (+0.0%)	0.574 $\pm$ 0.026 (+7.9%)	0.538 $\pm$ 0.013 (+3.9%)
$\boldsymbol{\dot{q}},\boldsymbol{\ddot{q}}$	0.531 $\pm$ 0.002 (+6.4%)	0.587 $\pm$ 0.041 (+10.3%)	0.539 $\pm$ 0.024 (+4.1%)
$\boldsymbol{u}(=\Delta\boldsymbol{p})$	0.572 $\pm$ 0.003 (+14.6%)	0.604 $\pm$ 0.003 (+13.5%)	0.554 $\pm$ 0.002 (+6.9%)
$\boldsymbol{\dot{q}},\boldsymbol{\ddot{q}},\boldsymbol{u}$	0.701 $\pm$ 0.050 (+40.5%)	0.666 $\pm$ 0.014 (+25.2%)	0.583 $\pm$ 0.007 (+12.5%)
$\varnothing$	0.499 $\pm$ 0.003	0.532 $\pm$ 0.007	0.518 $\pm$ 0.002

Table 6: Effect of input variables on estimation performance. Metrics are aggregated on the normalized scale.

Figure 8: Channel-wise marginal distributions of the normalized training residuals. Each panel overlays histograms of the three force residual channels (Left) and three torque residual channels (Right). Solid lines indicate fitted Gaussian probability density functions.

Figure 9: Correlation analysis of the normalized training residuals. (a) Channel-wise temporal autocorrelation functions of the six wrench residual channels over the $T=100$ prediction horizon. (b) Pearson cross-channel correlation matrix averaged over the horizons.

	HF $\mathrm{wRMSE}$	LF $\mathrm{pRMSE}$	Correlation DoF
$I_{T}\otimes R_{C}$ (Channel)	0.533 $\pm$ 0.004 (+6.8%)	0.555 $\pm$ 0.020 (+4.3%)	15
$R_{T}\otimes I_{C}$ (Time)	0.602 $\pm$ 0.003 (+20.6%)	0.551 $\pm$ 0.018 (+3.6%)	4,950
$R_{T}\otimes R_{C}$ (Time-Channel)	0.638 $\pm$ 0.005 (+27.9%)	0.554 $\pm$ 0.018 (+4.1%)	4,965
$I$ (Independent)	0.499 $\pm$ 0.003	0.532 $\pm$ 0.007	0

Table 7: Effect of residual correlation structure on band-specific estimation performance. Metrics are aggregated on the normalized scale.

	Wall Time [ms]	Relative	Optimized Parameters
MINN	0.038 $\pm$ 0.003	0.004	3,974
RBF	0.062 $\pm$ 0.004	0.006	868
GPR	16.663 $\pm$ 0.737	1.582	3,302,563
LSTM	6.229 $\pm$ 0.423	0.591	80,902
CNN	5.936 $\pm$ 0.226	0.564	81,766
LSTM-ED	13.186 $\pm$ 0.520	1.252	151,814

Table 8: CPU inference time and model sizes.

Datasets	Pretraining (RH20T)	Downstream
HF $\boldsymbol{W}$ Energy	9.839%	85.188%
LF $\boldsymbol{W}$ Energy	90.161%	14.812%
Task	Everyday Manipulation	Block Grinding
Actuation	Electric	Hydraulic
Actuation Signal	Motor Torque	Differential Pressure
Drive Type	Revolute	Prismatic and Revolute

Table 10: Properties of pretraining and downstream datasets, including band energy ratios of the wrench. ‘LF’ and ‘HF’ indicate bands in

f\leq 1

Hz and

f>1

Hz, respectively.

Figure 10: Channel-averaged power spectrum of $\boldsymbol{W}$ in the pretraining (RH20T) and downstream (Hydraulic) datasets, computed from the training splits only. Each channel is normalized to zero mean and unit variance before the Fourier transform, and the spectra are shown without denoising to display the full frequency content. Both axes are logarithmic. Vertical lines mark the cutoffs $f_{c}=1$ Hz and $f_{c}^{\mathrm{dn}}=15$ Hz applied during training.

Explore similar work

SixthSense: Task-Agnostic Proprioception-Only Whole-Body Wrench Estimation for Humanoids
May 2, 2026Xingzhou Chen, Xiayan Xu, Yan Ning +8Proprioception Contact Wrench Estimation
The Hong Kong University of Science and Technology, Hong Kong SAR, China · Zhejiang University, Hangzhou, China · Tencent Robotics X, Shenzhen, China
Scalable Open-Source Visuotactile Sensor for 6-Axis Contact Wrench Estimation in Tensegrity Robots
Jul 17, 2026Wenzhe Tong, Jonathan Mi, Xili Yi +2Tactile Contact Wrench Estimation
Robotics Department, University of Michigan, Ann Arbor, MI, 48109, USA
Context-Aware Force Estimation for Deformable Tool Manipulation in Robotic Environmental Swabbing via Few-Shot Continual Adaptation
Jul 8, 2026Siavash Mahmoudi, Chaitainya Kuppar Reddy, Yang Tian +1Ground Reaction Forces Deformable Linear Objects
Department of Biological and Agricultural Engineering, University of Arkansas, Fayetteville, AR 72701, USA · Department of Food Science, University of Arkansas, Fayetteville, AR 72701, USA

May 2, 2026, cs.ROJ/K move · Enter open · S save

SixthSense: Task-Agnostic Proprioception-Only Whole-Body Wrench Estimation for Humanoids

Xingzhou Chen, Xiayan Xu, Yan Ning, Jiyu Yu+7

The Hong Kong University of Science and Technology, Hong Kong SAR, China · Zhejiang University, Hangzhou, China · Tencent Robotics X, Shenzhen, China

Proprioception Contact Wrench Estimation Humanoid Teleoperation

Open paper AskPDF arXiv

Humanoid robots are entering our physical world at scale, yet as oversized toys--good at singing and dancing, but short on force-interaction capabilities for practical tasks. Bridging this gap necessitates prioritizing reliable contact perception as a fundamental requirement. Estimating external wrenches in humanoids is complicated by floating-base dynamics and indeterminate contact locations. Existing analytical frameworks require idealistic assumptions and hard-to-obtain measurements, which are often unavailable in practice. To bridge this gap, we propose SixthSense, a task-agnostic approach that infers whole-body contact timing, location, and wrenches from proprioception and IMU data alone. To capture the multi-modal dynamics between unstructured contact inputs and the uncertain motion outputs, we employ conditional flow matching to tokenize proprioceptive histories and estimate a spatiotemporally sparse contact-event flow. SixthSense serves as a plug-and-play perception module for applications including collision detection, physical human-robot interaction, and force-feedback teleoperation. Experiments across standing, walking, and whole-body motion-tracking policies showcased unprecedented performance in diverse behaviors.

Abstract

Explore similar work

SixthSense: Task-Agnostic Proprioception-Only Whole-Body Wrench Estimation for Humanoids

Scalable Open-Source Visuotactile Sensor for 6-Axis Contact Wrench Estimation in Tensegrity Robots

Context-Aware Force Estimation for Deformable Tool Manipulation in Robotic Environmental Swabbing via Few-Shot Continual Adaptation