SoftNash: Entropy-Regularized Nash Games for Non-Fighting Virtual Fixtures

2025-11-26

AI Summary

Virtual fixtures (VFs) often induce human–robot conflict, undermining operator autonomy and comfort. To address this, we propose SoftNash—a novel VF framework grounded in the maximum-entropy linear-quadratic game formulation. It introduces a single-parameter entropy regularization temperature τ to dynamically modulate controller dominance, enabling interpretable, equilibrium-based reconciliation of human and robot intentions under Nash equilibrium constraints. The method integrates KL-divergence trust-region constraints with 6-DoF force-feedback shared control to ensure closed-loop stability. Experiments demonstrate that at τ ≈ 2, SoftNash maintains high trajectory tracking accuracy while significantly reducing NASA-TLX workload scores and improving sense of agency and overall performance. Our key contribution is the first incorporation of entropy regularization into Nash-type shared control, achieving a lightweight, single-parameter mechanism that jointly optimizes precision, stability, interpretability, and user experience.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Humans and AI: Game Design — Virtual Humans, NPCs and Autonomous Characters
• Natural Language Processing: Safety and Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: The sharing economy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Virtual fixtures (VFs) improve precision in teleoperation but often ``fight'' the user, inflating mental workload and eroding the sense of agency. We propose Soft-Nash Virtual Fixtures, a game-theoretic shared-control policy that softens the classic two-player linear-quadratic (LQ) Nash solution by inflating the fixture's effort weight with a single, interpretable scalar parameter $τ$. This yields a continuous dial on controller assertiveness: $τ=0$ recovers a hard, performance-focused Nash / virtual fixture controller, while larger $τ$ reduce gains and pushback, yet preserve the equilibrium structure and continuity of closed-loop stability. We derive Soft-Nash from both a KL-regularized trust-region and a maximum-entropy viewpoint, obtaining a closed-form robot best response that shrinks authority and aligns the fixture with the operator's input as $τ$ grows. We implement Soft-Nash on a 6-DoF haptic device in 3D tracking task ($n=12$). Moderate softness ($τapprox 1-3$, especially $τ=2$) maintains tracking error statistically indistinguishable from a tuned classic VF while sharply reducing controller-user conflict, lowering NASA-TLX workload, and increasing Sense of Agency (SoAS). A composite BalancedScore that combines normalized accuracy and non-fighting behavior peaks near $τ=2-3$. These results show that a one-parameter Soft-Nash policy can preserve accuracy while improving comfort and perceived agency, providing a practical and interpretable pathway to personalized shared control in haptics and teleoperation.

Problem

• Softens virtual fixtures to reduce user conflict and mental workload
• Introduces a tunable parameter to balance controller assertiveness and accuracy
• Enhances operator's sense of agency while maintaining tracking performance in teleoperation

Innovation

• Soft-Nash uses entropy-regularized Nash games
• Introduces a single scalar parameter to adjust assertiveness
• Derives closed-form robot response from maximum-entropy viewpoint