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General Performance Guarantee for Human Torque Estimation-Based Task-Agnostic Assistive Exoskeleton Control

Duy Hoang, Bastien Berret, Olivier Bruneau, Laurent Fribourg

arXiv:2609.39558v1cs.ROcs.LGcs.SYeess.SY

TL;DR

Task-agnostic exoskeleton control depends on human-torque estimates, but estimation errors can produce assistance mismatched with user intention. The paper uses a dead-zone torque modulation strategy with a theoretical lower bound on matched-assistance probability. Experiments report reduced muscle activation and preserved movement smoothness across tasks.

  • Problem

    Torque-estimation errors in task-agnostic exoskeleton control can produce reversed or excessive assistance, while task-specific controllers rely on predefined task information.

    Source: §I · p. 1

  • Method

    A dead-zone middle-level controller modulates estimated human torque, with its threshold derived from a generalization-error bound to guarantee a lower bound on matched-assistance probability.

    Source: §I · p. 2, C. Guarantee on Matched Assistance… · p. 3

  • Results

    Across subjects and tasks, DZA reduced muscle activation by 8.9% relative to TR mode and 6.0% relative to DA, while achieving smoother trajectories than DA.

    Source: B. Results on EMG Assistance · p. 8, C. Discussion · p. 8

  • Takeaways & Limitations

    The experiments on the ABLE exoskeleton across multiple testing tasks verified the approach’s general effectiveness, with movement smoothness and reduced human physical effort.

    Source: §V · p. 9

Abstract

from arXiv · show

Accurate human torque estimation is crucial for enabling task-agnostic control in robotic exoskeleton systems. However, estimation errors may cause mismatches between the robot assistance and the human intention, degrading controllability and task performance. In this paper, we address this issue by formally defining matched assistance as scenarios in which the robot positively contributes to human movement. Based on this definition, we develop a theoretical framework to design the robot's desired interaction torque that guarantees a lower bound on the matched assistance probability. Importantly, the proposed guarantee holds over the entire torque distribution, including unseen data beyond the training tasks. This provides our method with strong reliability and generalization, both of which are critical for effective exoskeleton control. The proposed strategy is implemented on the ABLE upper-limb exoskeleton and evaluated in a multi-task setup. Experimental results validate the theoretical guarantees and demonstrate that the proposed strategy achieves effective general performance across several tasks, guaranteeing movement smoothness while reducing human physical effort.

I. INTRODUCTION

Task-specific exoskeleton controllers rely on predefined task information, motivating task-agnostic control for broader movements. This paper addresses torque-estimation mismatches with a dead-zone middle controller and uses matched assistance probability to characterize general performance.

I. INTRODUCTION

  • Task-specific controllers depend on predefined trajectories, targets, or load information, motivating task-agnostic control for movements beyond prescribed scenarios.Task-agnostic control aims to provide effective, intuitive assistance without prior knowledge of the task.Source: §I · p. 1

B. Matched Assistance Probability

  • Torque-estimation errors can cause reversed or excessive assistance, degrading comfort and control efficiency; matched assistance means helping in the correct direction without exceeding required assistance.The paper frames a high matched-assistance rate as a potential route to compliant, smooth human–robot interaction.Source: §I · p. 1
  • The dead-zone sets desired torque to zero at low estimated torque and permits assistance at high torque; its threshold is derived from a generalization-error bound to guarantee a lower bound on matched-assistance probability.This contrasts with direct assistance, which uses the estimator output unchanged, and scaled assistance, which reduces torque magnitude but cannot remove reversed mismatches.Source: §I · p. 2, B. Matched Assistance Probability · p. 3

I. INTRODUCTION

  • The proposed dead-zone strategy reduced muscle activation by an average of 8.9% versus transparent mode while preserving movement smoothness across a wide range of tasks.The introduction reports evaluation on four test tasks and describes the 8.9% reduction relative to transparent mode.Source: §I · p. 2

A. Exoskeleton Control Strategy

  • The three-level controller uses EMG to estimate human torque, modulates it in a middle layer, then tracks the desired interaction torque with a low-level controller.The paper identifies the middle-level modulation design as its main contribution.Source: A. Exoskeleton Control Strategy · p. 2

C. Guarantee on Matched Assistance Probability

The section develops an analytical dead-zone threshold from an upper bound on expected torque-estimation error, then outlines how to obtain that bound by retraining a linear output layer over fixed features.

C. Guarantee on Matched Assistance Probability

  • The threshold is selected analytically from an upper bound on expected absolute torque-estimation error over all possible EMG-torque pairs.This avoids task-specific robot experiments for threshold tuning and supports guarantees beyond evaluated scenarios.Source: C. Guarantee on Matched Assistance… · p. 3

1) Guarantee on torque estimation generalization error:

  • The bound framework applies to estimation models with a linear output layer and separates feature extraction from bounded-error model retraining.The feature extractor is first trained conventionally, then frozen while the linear output layer is retrained to minimize generalization error on an independently drawn training subset.Source: 1) Guarantee on torque estimation… · pp. 3–4
  • At each gradient-descent step, an upper bound on generalization error is computed, and training stops when the bound begins increasing to retain the tight bound LB*.Proposition 1 states that, with probability at least 1 − δ over the sample, the generalization error satisfies the stated bound.Source: 1) Guarantee on torque estimation… · p. 4

2) Analytical approach for designing the dead-zone:

The analytical design connects the dead-zone threshold to a lower bound on matched-assistance probability. Under a zero-mean normal estimation-error assumption and a generalization-error bound, the theorem supplies a guarantee and a practical threshold choice.

2) Analytical approach for designing the dead-zone:

  • Across both negative and nonnegative human torques, matched assistance is bounded below by the probability that estimation error stays within Tdz.The proposition covers both torque-sign cases across the entire torque distribution.Source: 2) Analytical approach for designing… · p. 4
  • Under zero-mean normal estimation error and LD ≤ LB*, Theorem 1 guarantees a lower bound on matched-assistance probability for the chosen dead-zone threshold.The theorem links the bound on expected absolute estimation error to the probability guarantee.Source: 2) Analytical approach for designing… · p. 4
  • The theorem gives a probability lower bound for any threshold without explicitly knowing σ, providing a practical guideline for threshold selection.The authors suggest Tdz = 2LB* to balance movement smoothness against maintaining assistance availability.Source: 2) Analytical approach for designing… · pp. 4–5
  • The analysis assumes zero-mean normal estimation error, while a less restrictive theorem without the zero-mean assumption is presented in Appendix B.The zero-mean assumption is described as consistent with empirical observations in Fig. 5.Source: 2) Analytical approach for designing… · p. 5

III. EXPERIMENTAL METHOD

Two experiments are described to test the matched-assistance probability guarantee and evaluate practical task-agnostic exoskeleton control.

III. EXPERIMENTAL METHOD

  • The evaluation comprises one experiment on the probability guarantee and another on practical exoskeleton control in a task-agnostic setup.Source: §III · p. 5
  • One experiment examines whether the dead-zone increases matched-assistance probability and validates the theoretically selected threshold.Source: §III · p. 5
  • The other experiment evaluates the control strategy in practical exoskeleton control under a task-agnostic setup.Source: §III · p. 5

A. Experiment on General Performance Guarantee

The guarantee experiment examines the dead-zone's effect on matched assistance and the theoretically chosen threshold, using random trajectory tracking with participants wearing an upper-limb exoskeleton.

A. Experiment on General Performance Guarantee

1) Participant and task:

  • The experiment uses the 17-subject multi-joint dataset, with each participant completing 10 random-trajectory-tracking trials while wearing an upper-limb exoskeleton.Source: 1) Participant and task · p. 5
  • Movements occur in the parasagittal plane and involve shoulder and elbow flexion and extension, with the exoskeleton connected at the wrist through a forearm-mounted orthosis.Source: 1) Participant and task · p. 5

2) Torque estimation models:

The section describes five EMG-to-torque model architectures, procedures for checking the generalization and matched-assistance guarantees, and the positive contribution index used alongside matched-assistance probability. It also outlines a multi-task experiment intended to assess control-strategy generalizability and effectiveness.

2) Torque estimation models:

  • Five EMG-to-torque architectures are considered: MVLR, NLMap, 4HNN, LSTM, and CNN-LSTM, each using a distinct mapping or feature-extraction design, –.The CNN-LSTM extracts spatio-temporal information from filtered EMG signals.Source: 2) Torque estimation models · p. 5

3) Evaluation of generalization guarantee:

  • The evaluation estimates generalization error as test-set mean absolute error, checks it against LB∗, and evaluates matched-assistance probability using Tdz = 2LB∗ against the 0.89 lower bound.The test set contains seven trials, compared with three training trials, to support estimation of quantities that cannot be directly accessed,.Source: 3) Evaluation of generalization… · p. 5

4) Matched assistance probability versus assistance:

  • The positive contribution index (PCI) is positive for matched assistance and negative for mismatched assistance; matched-assistance probability remains the primary criterion.PCI is a secondary comparison metric when matched-assistance probabilities are comparable.Source: 4) Matched assistance probability… · p. 5

B. Experiment on EMG Assistance:

  • The multi-task experiment evaluates the proposed strategy using a controller trained on one standard trajectory-tracking task and tested on four additional tasks.The experiment is intended to assess generalizability and effectiveness across those tasks.Source: B. Experiment on EMG Assistance · p. 5

1) Participant and task:

Five healthy subjects trained the high-level torque estimator during a random-trajectory task, then performed four testing tasks under three control conditions. The study records EMG, motion, and interaction data and uses a 4HNN-based controller with a bound-derived dead-zone.

1) Participant and task:

  • Five healthy subjects completed two sessions: random trajectory tracking supplied training data, followed by four testing tasks under DZA, direct assistance, and transparent control.Random trajectory tracking was used as the training task, and the testing tasks and control conditions were ordered randomly.Source: 1) Participant and task · p. 6

2) Data collection and processing:

  • EMG from eight muscles, motion capture, and end-effector interaction forces were processed to calculate human joint-torque labels.EMG was filtered, rectified, enveloped, and normalized by each muscle’s maximum voluntary contraction before torque-label calculation.Source: 2) Data collection and processing · p. 6

3) Assistive controller design:

  • A two-output 4HNN estimated shoulder and elbow torques, and the middle-level controller applied Tdz = 2LB∗ for each subject.The 4HNN was chosen over deeper models because it trained in under five minutes, versus more than 45 minutes for the deep models.Source: 3) Assistive controller design · p. 6

4) Evaluation of assistance performance:

The experiments test generalization-error and matched-assistance guarantees, then assess contribution, movement smoothness, and muscle activation. Dead-zone modulation kept matched-assistance probabilities above the theoretical bound while increasing matched assistance across the evaluated models.

4) Evaluation of assistance performance:

  • Movement smoothness was measured by integrated squared jerk, while physical effort was evaluated by average muscle activation normalized using task-specific MVC.Lower integrated squared jerk indicates smoother trajectories.Source: 4) Evaluation of assistance performance · p. 6

2) Guarantee on matched assistance probability:

1) Guarantee on generalization error:

3) Smoothness versus assistance:

  • With dead-zone modulation, all models showed positive contribution, increasing from MVLR and NLMap to 4HNN, LSTM, and CNN-LSTM.The authors relate higher estimation accuracy to a lower threshold for guaranteeing matched assistance and thus higher positive contribution.Source: Figure 6 · p. 7, 3) Smoothness versus assistance · pp. 7–8

B. Results on EMG Assistance

Across testing tasks, DZA preserved smoothness while reducing muscle activation; its dead-zone threshold links assistance to torque-estimation generalization, with practical experiments limited to the 4HNN model.

B. Results on EMG Assistance

  • DZA matched TR’s average smoothness, was smoother than DA, and reduced muscle activation by 8.9% versus TR and 6.0% versus DA.DZA also achieved lower muscle activation than DA for all five subjects; both assistive conditions were below TR for four of five.Source: B. Results on EMG Assistance · p. 8

C. Discussion

  • DZA prioritizes human controllability: it behaves like TR at low torque and assists at high torque, achieving smoother trajectories than DA and lower activation than TR and DA.The control objective is to preserve natural task execution rather than maximize assistance.Source: C. Discussion · p. 8
  • A smaller generalization-error bound permits a smaller dead-zone threshold and more robot contribution; 4HNN contributions averaged 2.5 N·m at the shoulder and 1.5 N·m at the elbow.Those contributions were associated with 8.9% lower muscle activation than TR; LSTM and CNN-LSTM showed higher average contributions, but were not tested in practical robot experiments.Source: C. Discussion · pp. 8–9
  • In an offline comparison on the same 17-subject dataset, DZA exceeded SCA in matched-assistance probability and average PCI for both shoulder and elbow torque.A physical human–robot comparison remains future work.Source: C. Discussion · p. 9, Figure 8 · p. 9

V. CONCLUSION

  • The conclusion reports that ABLE experiments across multiple testing tasks verified general effectiveness, with guaranteed movement smoothness and reduced human effort.The framework derives its threshold from general-performance evaluation based only on the training task, without additional robot testing tasks.Source: §V · p. 9

APPENDIX A: PROOF OF PROPOSITION 1

The proof invokes a hypothesis class and its Rademacher complexity, then applies a proposition to obtain the bound used to complete the proof.

APPENDIX A: PROOF OF PROPOSITION 1

  • At GD step k*, the proof defines hypothesis class F_k* containing f_h(·).The excerpt does not further specify the class’s contents.Source: Appendix A · p. 9
  • The proof uses Theorem 5.5 of to bound the Rademacher complexity R_S(F_k*) of that hypothesis class.Source: Appendix A · p. 9
  • Proposition 1 of for p = 1 gives a bound with probability at least 1 − δ over a sample S of size n; substitution into (20) yields (6) and completes the proof.Source: Appendix A · p. 9

APPENDIX B: EXTENDED VERSION OF THEOREM 1

The extended theorem bounds matched-assistance probability under normal estimation error and a bounded expected absolute error; its proof establishes an auxiliary-function inequality using monotonicity.

APPENDIX B: EXTENDED VERSION OF THEOREM 1

  • If estimation error is normal and L_D ≤ L_B*, the theorem states that T_dz ≥ L_B* guarantees a lower bound on matched-assistance probability.Source: Appendix B · p. 9
  • For T_dz ≥ β, the proof aims to show G(u, v) ≥ G(β, γ) throughout u ∈ [0, β] and v ∈ (0, γ].It introduces the auxiliary function before establishing this inequality.Source: Appendix B · p. 9
  • The proof examines derivatives of G with respect to u and v for fixed values of the other variable, then uses those derivative results to derive the inequality.Source: Appendix B · p. 9
  • For the auxiliary function g, g′(s) = 2Φ(s) − 1 ≥ 0 for s ≥ 0, so g(s) ≥ g(0); the proof then combines this with (29).The derivation uses ϕ′(s) = −sϕ(s) and Φ′(s) = ϕ(s).Source: Appendix B · p. 10
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