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Attribution-Gated Joint Estimation of Intention and Capability for Assist-as-Needed Upper-Limb Robots

Pengcheng Li, Shuxiang Guo, Hanze Wang, Jun Leng, Bin Wang, Mingchao Ding

arXiv:2610.21534v1cs.RO

TL;DR

AAN must distinguish changed movement intention from reduced voluntary capability because both can produce similar responses. The paper jointly estimates both quantities and uses an attribution gate to route shared evidence; the gated controller reports lower tracking RMSE across nine load–height conditions.

  • Problem

    AAN must distinguish intended-motion changes from reduced voluntary capability because both can produce similar kinematic and interaction responses, while assistance must balance participation and task completion.

    Source: §1 · p. 2

  • Method

    The method jointly estimates trajectory deformation and task-dependent voluntary torque capability, then uses an attribution gate to allocate shared observations between their update channels.

    Source: §1 · p. 3, §3.2 · p. 8

  • Results

    The gated controller achieved a condition-level mean tracking RMSE of 0.017 rad across nine load–height conditions, approximately 60% lower than independent estimation and 87% lower than error-based AAN.

    Source: §7 · p. 27

  • Takeaways & Limitations

    The attribution-gated approach adapts the reference trajectory and adjusts assistance without requiring hard event classification.

    Source: §7 · p. 27

    Healthy participants and external loads or acute fatigue simulated capability changes, so the results validate algorithmic function rather than therapeutic efficacy in clinical populations.

    Source: §6.4 · p. 26

Abstract

from arXiv · show

Assist-as-needed (AAN) control must distinguish between changes in intended motion and changes in effective voluntary torque capability, even though both can produce similar kinematic and interaction responses. A dual-measurand multimodal MHE-MPC architecture is developed as the base framework, in which the intended trajectory and the task-dependent effective voluntary torque capability are estimated online as distinct quantities, and both estimates are used to adapt robotic assistance. Building on this architecture, the ambiguity between the two update channels is formulated as a continuous credit-assignment problem and resolved by an attribution gate. A trajectory-change indicator is obtained from persistent corrective interaction, whereas a capability-change indicator is derived from the residual between normalized muscle activation and dynamics-reconstructed voluntary torque. Nine healthy participants completed factorial target-height-load trials and a pre-post fatigue cup-transport task. Without target-height input, the gated method generated correctly ordered Low-Middle-High references under every load: target changes were preferentially assigned to trajectory adaptation, whereas added load shifted adaptation toward the capability channel. It achieved the lowest RMSE in all nine conditions (0.017 rad versus 0.041 rad for ungated dual estimation and 0.127 rad for fixed-reference error-based AAN). Post-fatigue capability estimates decreased and assistance increased at all heights, supporting functional feasibility.

1. Introduction

AAN must balance task completion and preserved voluntary contribution despite ambiguous motion and interaction signals. The paper motivates jointly estimating intention and capability, then assigning shared evidence between their update channels.

1. Introduction

  • AAN must distinguish intended-trajectory changes from reduced voluntary capability because either can produce similar tracking and interaction responses.Excessive assistance may suppress participation, while insufficient assistance may compromise task completion or increase interaction load.Source: §1 · p. 2
  • Prior work adapts references from intention estimates, but stiffness estimates describe interaction properties rather than task-dependent voluntary torque capability.The authors identify joint online estimation of intended trajectory and effective voluntary capability as an unmet need.Source: §1 · pp. 2–3
  • Error-based AAN and capability-centered methods estimate assistance demand, but their deviations can also reflect purposeful trajectory changes.Direct sEMG-based assistance uses physiological effort information, with signal variability and session-specific calibration as practical considerations.Source: §1 · p. 3
  • The paper develops ungated dual-measurand MHE–MPC estimation and adds an attribution gate to allocate shared observations between trajectory and capability updates.The evaluation separates dual-estimation comparisons with error-based AAN from gated–ungated credit-assignment comparisons.Source: §1 · p. 3

2. Measurement System and Estimated Quantities

The measurement system combines a wearable robot and sensing hardware with joint-space torque reconstruction. The estimated quantities are a smooth intended-path deformation and a task-dependent envelope on available voluntary torque.

2.1. Robot and Sensor Platform

  • Cable-driven modules deliver elbow and wrist assistance, while IMUs measure joint angles and embedded control communicates with a ROS 2 upper-level controller.The platform weighs below 5 kg, with approximately 0.7 kg wearable mass; the embedded torque loop runs at 500 Hz and upper-level MPC at 50 Hz.Source: §2.1 · pp. 3–4

2.2. Sensor Signals and Voluntary Torque Reconstruction

  • Joint-space robot and human dynamics distinguish motor torque, human–robot interaction torque, and net voluntary torque, with interaction torque split into task-aligned assistance and corrective components.The robot model also groups cable compliance, friction, slack, linearization, and sensing errors as a lumped disturbance.Source: §2.2 · p. 5

2.3. Motion Intention and Capability Variables

  • Intention is represented by smooth deformation of a nominal trajectory, while effective voluntary capability is a joint-wise torque envelope that saturates the available voluntary contribution.The deformation parameter encodes path amplitude and direction; capability may reflect fatigue, activation–torque consistency, and external demand.Source: §2.3 · pp. 5–6

3. Joint Estimation of Intention and Capability

The estimation problem is to infer trajectory deformation and effective voluntary capability from overlapping motion, interaction, and muscle-activity observations. The architecture assigns updates through an attribution state before MHE and MPC estimate capability, intended motion, and assistance.

3.1. Problem Definition

  • The latent state combines intended-trajectory deformation with task-dependent effective voluntary capability, but deviations from the nominal path can reflect either a changed goal or insufficient capacity.Nominal tracking error alone cannot determine whether to change the reference or assistance; misclassification can produce unnecessary support or withhold needed support.Source: §3.1 · pp. 6–7

3.2. System Overview

  • MHE estimates effective capability from a recent observation window, while MPC predicts motion and jointly optimizes trajectory deformation and assistance.The supervisory attribution state α is computed before the optimizations: 1−α gates capability updates and α gates trajectory updates, using persistent corrective interaction and activation–torque disagreement as indicators.Source: §3.2 · pp. 7–8, Figure 2 · p. 7

3.3. Separating Intention and Capability Effects

Trajectory updates use persistent corrective interaction, while capability is estimated separately from task activation and reconstructed voluntary torque. Attribution-weighted moving-horizon estimation uses calibration-derived quantities as priors and limits the influence of outliers.

3.3.1. Trajectory Update From Corrective Torque

  • Joint-side interaction torque and opposing corrective torque are reconstructed from robot and human-limb dynamics before the corrective signal is observed.The calibration-derived maximum voluntary torque normalizes the corrective interaction.Source: §3.3.1 · pp. 8–9
  • A bounded leaky observer turns normalized corrective interaction into a signal of persistent need to change the reference path.Its dead zone rejects subthreshold noise, while exponential forgetting bounds the observer state under persistent excitation.Source: §3.3.1 · p. 9

3.3.2. Capability Estimation

  • The participant-specific activation scale and initial effective-capability estimate come from calibration, while calibrated effective capability serves only as the online prior.The linear activation-to-torque scaling in the MHE residual is a local approximation validated during calibration.Source: §3.3.2 · p. 9
  • Each moving-window sample contributes to capability estimation in proportion to its attribution to a capability-related change.A Huber loss limits the influence of EMG and acceleration outliers, and the estimate is constrained to a plausible torque range and rate of change.Source: §3.3.2 · pp. 9–10

3.4. Joint Estimation and Assistive Control

A gate allocates evidence between trajectory and capability updates, and the resulting estimates shape a bounded reference and assistance command. Receding-horizon MPC balances tracking, assistance, adaptation smoothness, and attribution consistency before combining the selected torque with impedance feedback.

3.4.1. Attribution Weight Update

  • Persistent corrective interaction and the dynamics–EMG residual provide separate trajectory and capability indicators for the attribution update.The indicators are dimensionless; the update uses stored sample-time attribution weights, a neutral-evidence threshold, and a bounded rate of change.Source: §3.4.1 · pp. 10–11

3.4.2. Reference Update and Assistance Calculation

  • The nominal trajectory is calibrated to the middle target, while the controller infers intended deviations because target height is not supplied to it.The gate complementarily shapes the trajectory-deformation residual in the MPC.Source: §3.4.2 · p. 11, §3.4.1 · p. 11

3.4.3. MPC Cost Function and Constraints

  • The receding-horizon MPC balances tracking, assistance, smooth adaptation, and attribution consistency while enforcing joint, deformation, and torque bounds.Assistance onset depends on predicted task demand exceeding a fraction of estimated voluntary capability, and the optimizer selects the smallest feasible nonnegative deficit.Source: §3.4.3 · pp. 12–13

3.4.4. Torque–Impedance Assistance

  • Only the first optimal assistive-torque command is applied, combined with compliant impedance feedback based on reference-tracking error and velocity error.The remaining predicted sequence serves as a warm start for the next cycle.Source: §3.4.4 · p. 13, §3.4.3 · p. 13

3.5. Tracking Stability and Command Boundedness

Under the stated boundedness assumptions, the tracking state is uniformly ultimately bounded; with a fixed reference and zero effective disturbance, the same inequality gives asymptotic convergence.

3.5. Tracking Stability and Command Boundedness

  • The analysis assumes bounded dynamics, cable-transmission, and command-hold errors, with bounded capability, assistance, and reference signals.The compact workspace assumptions include uniformly positive definite, bounded inertia and a skew-symmetric ˙M − 2C.Source: §3.5 · pp. 13–14
  • The Lyapunov argument establishes uniform ultimate boundedness of the tracking state under the stated conditions.For a fixed reference and zero effective disturbance, the same inequality yields asymptotic convergence.Source: §3.5 · p. 14

4. Experiments

Two experiments evaluate whether the controller distinguishes intention from capability changes and whether it tracks fatigue-related capability changes in a functional task. Nine healthy participants completed controlled reaching trials and pre–post cup transport after individual calibration.

4. Experiments

  • Two experiments test separation of intention and capability perturbations, then assess feasibility in a functional cup-transport task before and after induced fatigue.Experiment 1 varies intention and effective capability separately; Experiment 2 tests tracking a fatigue-induced capability decline and corresponding assistance increase without explicit fatigue modeling.Source: §4 · p. 14, §4.3 · p. 17

4.1.1. Participants and Equipment

  • Nine healthy young participants completed both experiments using a wearable robot, with adaptive assistance applied at the elbow.Experiment 1 used repeated reaching across target-height and wrist-load conditions; Experiment 2 required coordinated elbow, wrist, and forearm motion.Source: §4.1.1 · p. 15

4.1.2. Individual Calibration

  • Calibration established participant-specific EMG baselines and activation scale, a nominal middle-target trajectory, and an initial effective voluntary-torque prior.Neither target-height information nor load data were used in calibration.Source: §4.1.2 · p. 16

4.2. Experiment 1: Controlled Variation of Intention and Capability

  • Experiment 1 varied target height and wrist load against a shared middle-target nominal trajectory, with target and load changes temporally decoupled.The controller had to infer intended deviations online; load changes occurred at block boundaries while the target remained unchanged.Source: §4.2 · pp. 16–17
  • Three within-subject controllers compared error-based AAN, ungated dual-estimation MPC, and attribution-gated dual-estimation MPC.Each controller–load block included nine randomized trials, with the capability estimate reset to its calibrated prior at block boundaries.Source: §4.2 · p. 17

4.3. Experiment 2: Functional Task Under Induced Fatigue

  • The fatigue task used nine trials at three cup heights before and after weight lifting, while elbow assistance was adapted and wrist and forearm assistance remained fixed-gain.The controller was unchanged across the pre–post protocol.Source: §4.3 · p. 17

4.4. Statistical Analysis

  • Results were averaged within participants and analyzed with repeated-measures ANOVA, followed by Holm-corrected paired comparisons after significant omnibus effects.Statistical significance was set at p < 0.05.Source: §4.4 · pp. 17–18

5. Experimental Results

In Experiment 1, attribution-gated MPC had the lowest tracking RMSE across load–height conditions, while the gate’s attribution varied systematically with load and target height. In Experiment 2, capability estimates decreased and assistance increased after fatigue during cup transport.

5.1. Experiment 1: Dual Estimation and Credit Assignment

  • 0.017 rad condition-level RMSE for attribution-gated MPC was lower than 0.041 rad for independent estimation and 0.127 rad for error-based AAN.The gated method had the lowest tracking RMSE in every load–height condition; Table 1 reports the Experiment 1 outcomes.Source: §5.1 · p. 18, Table 1 · p. 20
  • α averaged 0.489 in Free–Middle, fell to 0.377 and 0.402 under Light and Heavy loads, and rose to 0.573 Low and 0.617 High under Free load.These shifts indicate load-linked weighting toward capability and target-height-linked weighting toward trajectory adaptation.Source: §5.1 · p. 21
  • For the gated controller, biceps normalized EMG rose from 0.028 Free to 0.085 Light and 0.245 Heavy, while height-averaged RMSE stayed at 0.018, 0.015, and 0.016 rad.The passage reports condition-specific assistance modulation, with a significant controller–height interaction (p < 0.001).Source: §5.1 · p. 21

5.2. Experiment 2: Functional Task Under Fatigue

  • After fatigue, terminal capability decreased by 8.005–10.783 N m across placement heights, assistance increased by 0.249–0.300 N m, and tracking RMSE rose by 0.007–0.025 rad.Mean and median sEMG frequencies also decreased (70.94 to 69.20 Hz and 51.74 to 49.39 Hz); those shifts did not reach significance.Source: §5.2 · p. 21, Figure 6 · p. 22, Table 2 · p. 22

6. Discussion

The discussion reports that the controller updated trajectory and capability as distinct quantities, with attribution shifting according to target and load evidence. Controlled reaching and a fatigue cup-transport task support its function, while the healthy-participant and elbow-only scope limits clinical and multi-joint conclusions.

6. Discussion

  • Prior work addressed intention recognition, fatigue detection, or trajectory adaptation separately, leaving shared evidence without closed-loop attribution between intention and capability.The discussion frames joint estimation and explicit attribution as needed to prevent the same observations from driving both estimates.Source: §6 · p. 24

6.1. Simultaneous Estimation of Intention and Capability

  • Gated reference endpoints stayed correctly ordered Low–Middle–High under all loads without target-height input, while capability estimates declined during Heavy load.The same Middle-target nominal trajectory was used across targets; reference adaptation followed target changes while the capability channel responded to added demand.Source: §6.1 · p. 24

6.2. Dynamic Credit Assignment Through the Attribution State

  • α stayed near neutral at Free–Middle, decreased with added load, and increased for Low and High targets under Free load.Load increased the EMG–dynamics residual without directionally consistent corrective torque; persistent corrective interaction supported trajectory-change evidence.Source: §6.2 · p. 25
  • During the displayed Heavy-load trials, α fell with downward reference revisions, then rose in the High trial as the reference moved upward while capability and assistance also changed.The authors report that RMSE improvement over independent estimation was not significant after correction.Source: §6.2 · p. 25

6.3. Controlled Evidence and Functional Feasibility

  • The factorial reaching experiment independently manipulated target height and load, mapping controller-state responses to known perturbation types.The authors characterize this design as providing strong internal validity.Source: §6.3 · pp. 25–26
  • In the fatigue cup-transport task, capability estimates decreased and assistance increased at every target height, but neither change reached significance.The authors also report significant RMSE increase and sEMG spectral compression, and describe the coordinated adaptations as preserved in the functional task.Source: §6.3 · p. 26

6.4. Limitations and Future Work

  • The study’s healthy participants, external loads, and acute fatigue do not reproduce clinical neuromuscular impairment or long-term adaptation; the authors describe the findings as algorithmic validation, not therapeutic efficacy.They also note that no single biosignal fully characterizes central and peripheral fatigue.Source: §6.4 · p. 26
  • Capability estimation and assistance were limited to elbow flexion, even though cup transport involved wrist and forearm motion.The authors identify multi-joint estimation as future work because it adds dimensionality and interactions between joint-level attribution states.Source: §6.4 · p. 26

7. Conclusion

The paper addresses ambiguity between intended motion changes and reduced voluntary capability by estimating both online and routing shared evidence through an attribution gate. Across nine load–height conditions, the gated controller had lower tracking RMSE than both comparison controllers, with fatigue-task findings offering further proof-of-concept evidence.

7. Conclusion

  • The method jointly estimates intended trajectory and effective voluntary capability online, routing shared sensory evidence through an attribution gate.The gate is intended to prevent the two signal types from contaminating each other without requiring hard event classification.Source: §7 · p. 27
  • 0.017 rad condition-level mean tracking RMSE across nine load–height conditions was approximately 60% lower than the independent-estimation variant and 87% lower than error-based AAN.The functional cup-transport task showed decreased post-fatigue capability estimates and increased assistance at all target heights, although these changes were not statistically significant.Source: §7 · p. 27
  • The fatigue-task findings support the framework while motivating larger studies in clinical populations.The reported post-fatigue capability and assistance changes were directionally consistent but not statistically significant.Source: §7 · p. 27

Ethics approval and informed consent

The study received institutional review board approval, and all participants gave written informed consent.

Ethics approval and informed consent

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