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Human-Variability-Respecting Optimal Control for Physical Human-Machine Interaction

Sean Kille, Paul Leibold, Philipp Karg, Balint Varga, Sören Hohmann

TL;DR

This work addresses the mismatch between deterministic human models and neuroscientific evidence of stochastic human movement by introducing HVROC, a framework that couples a stochastic linear-quadratic sensorimotor human model with an optimal automation controller. It derives mean- and variance-propagation equations for the joint human-machine system and formulates a bi-level optimization to parametrically shape both mean behavior and variability. The method yields improved task accuracy and controllable variability in simulations of two 2D point-to-point tasks, outperforming a standard LQR benchmark and preserving human-like variability where desired. HVROC thus offers a principled way to design shared-control systems that respect human variability while enhancing performance in physical human-automation interaction.

Abstract

Physical Human-Machine Interaction plays a pivotal role in facilitating collaboration across various domains. When designing appropriate model-based controllers to assist a human in the interaction, the accuracy of the human model is crucial for the resulting overall behavior of the coupled system. When looking at state-of-the-art control approaches, most methods rely on a deterministic model or no model at all of the human behavior. This poses a gap to the current neuroscientific standard regarding human movement modeling, which uses stochastic optimal control models that include signal-dependent noise processes and therefore describe the human behavior much more accurate than the deterministic counterparts. To close this gap by including these stochastic human models in the control design, we introduce a novel design methodology resulting in a Human-Variability-Respecting Optimal Control that explicitly incorporates the human noise processes and their influence on the mean and variability behavior of a physically coupled human-machine system. Our approach results in an improved overall system performance, i.e. higher accuracy and lower variability in target point reaching, while allowing to shape the joint variability, for example to preserve human natural variability patterns.

Human-Variability-Respecting Optimal Control for Physical Human-Machine Interaction

TL;DR

This work addresses the mismatch between deterministic human models and neuroscientific evidence of stochastic human movement by introducing HVROC, a framework that couples a stochastic linear-quadratic sensorimotor human model with an optimal automation controller. It derives mean- and variance-propagation equations for the joint human-machine system and formulates a bi-level optimization to parametrically shape both mean behavior and variability. The method yields improved task accuracy and controllable variability in simulations of two 2D point-to-point tasks, outperforming a standard LQR benchmark and preserving human-like variability where desired. HVROC thus offers a principled way to design shared-control systems that respect human variability while enhancing performance in physical human-automation interaction.

Abstract

Physical Human-Machine Interaction plays a pivotal role in facilitating collaboration across various domains. When designing appropriate model-based controllers to assist a human in the interaction, the accuracy of the human model is crucial for the resulting overall behavior of the coupled system. When looking at state-of-the-art control approaches, most methods rely on a deterministic model or no model at all of the human behavior. This poses a gap to the current neuroscientific standard regarding human movement modeling, which uses stochastic optimal control models that include signal-dependent noise processes and therefore describe the human behavior much more accurate than the deterministic counterparts. To close this gap by including these stochastic human models in the control design, we introduce a novel design methodology resulting in a Human-Variability-Respecting Optimal Control that explicitly incorporates the human noise processes and their influence on the mean and variability behavior of a physically coupled human-machine system. Our approach results in an improved overall system performance, i.e. higher accuracy and lower variability in target point reaching, while allowing to shape the joint variability, for example to preserve human natural variability patterns.
Paper Structure (14 sections, 2 theorems, 22 equations, 3 figures, 1 table)

This paper contains 14 sections, 2 theorems, 22 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Human-Variability-Respecting Optimal Control
  3. Human-Machine System Model
  4. Human Behavior
  5. Human Variability-Respecting Optimal Control
  6. Automation
  7. Control Objectives
  8. Mean and Variance of the Coupled Human-Machine System
  9. Optimization-based Automation Parametrization
  10. Numerical Example
  11. Simulation Parametrization
  12. Results
  13. Discussion
  14. Conclusion

Key Result

Lemma 1

Let the system dynamics be described by eq:system, eq:sysOutA and eq:sysOutH. Let the human control and filter matrices be given by eq:L_H and eq:K_H, let Assumption assumption1 hold and the automation's control and filter matrices be provided by eq:L_A and eq:K_A. Then the joint mean $\mathrm{E}\le with

Figures (3)

  • Figure 1: Human-Machine System Model
  • Figure 2: Procedure depicting the bi-level optimization structure.
  • Figure 3: Mean and variance of the position $p_x$. Human-alone behavior is depicted in red. The joint behavior of our proposed HVROC with the simulated human is shown in blue; solid and dotted lines represent a high and low desired variability in the task-irrelevant area, respectively. Black depicts the joint behavior of the LQR and human.

Theorems & Definitions (6)

  • Remark 1
  • Lemma 1
  • proof
  • Proposition 1
  • Remark 2
  • proof