Modeling and analysis of pHRI with Differential Game Theory (2307.10739v1)

Abstract: Applications involving humans and robots working together are spreading nowadays. Alongside, modeling and control techniques that allow physical Human-Robot Interaction (pHRI) are widely investigated. To better understand its potential application in pHRI, this work investigates the Cooperative Differential Game Theory modeling of pHRI in a cooperative reaching task, specifically for reference tracking. The proposed controller based on Collaborative Game Theory is deeply analyzed and compared in simulations with two other techniques, Linear Quadratic Regulator (LQR) and Non-Cooperative Game-Theoretic Controller. The set of simulations shows how different tuning of control parameters affects the system response and control efforts of both the players for the three controllers, suggesting the use of Cooperative GT in the case the robot should assist the human, while Non-Cooperative GT represents a better choice in the case the robot should lead the action. Finally, preliminary tests with a trained human are performed to extract useful information on the real applicability and limitations of the proposed method.

• The paper introduces a controller based on Cooperative Game Theory to model and analyze strategic interactions in physical Human-Robot Interaction.
• Simulations demonstrate that the proposed Cooperative Game Theory approach offers superior performance for cooperative problem-solving compared to traditional methods like LQR or Non-Cooperative Game Theory.
• This research provides insights into dynamic role arbitration and lays a foundation for developing more adaptive and intelligent human-robot control systems in real-world applications.

Modeling and Analysis of pHRI with Differential Game Theory: A Technical Summary

The submission under consideration explores the modeling and control of physical Human-Robot Interaction (pHRI) through the lens of Differential Game Theory, specifically by leveraging Cooperative and Non-Cooperative Game-Theoretic (NCGT) frameworks. This research explores the strategic interactions that occur when humans and robots engage cooperatively or non-cooperatively towards shared or individual tasks.

Core Contributions

The paper proposes a controller based on Cooperative Game Theory (CGT) which it juxtaposes against Linear Quadratic Regulator (LQR) and NCGT-based controllers. Through detailed simulations, it examines how varying control parameters influence system responses and control efforts of both human and robotic agents.

1. Modeling Framework: The paper deploys Game Theory (GT) as a tool to model interactive behaviors in pHRI environments. Specifically, it uses a Cooperative Differential Game (CDG) setup to explore scenarios where players could benefit mutually from cooperation, in contrast to the often sub-optimal Nash Equilibria of Non-Cooperative Games.
2. Methodological Approach: The authors implement a Linear Quadratic Cooperative Game Theory (LQ-CGT) for role arbitration in pHRI, distinguishing it from traditional IC methods by introducing a shared reference tracking that can respond to dynamically changing environments.
3. Exploration of Role Arbitration: This research emphasizes the significance of role arbitration—a process allowing deliberative decision-making in robot behavior modeling. It contrasts robot-assisted human leading with scenarios where robots must lead actions, providing insights into dynamically adaptive cooperative solutions.

Key Simulations and Results

The authors present a series of simulations examining the sensitivity of the proposed CGT approach to control parameters such as the weight parameter (α), state weight matrices, and control weight matrices. These illustrate:

• Sensitivity Analysis: Detailed analysis showcases how tuning α influences the equilibrium states achieved by the interacting human-robot pair, where high α values favor human leader roles.
• Comparative Evaluations: The significance of selecting CGT over LQR or NCGT was highlighted, offering superior performance in contexts requiring cooperative problem-solving.
• Real-world Applicability: Preliminary tests with trained human participants underscored the method's feasibility in real-world applications, yet identified areas for improving robustness to account for human variability.

Implications and Speculations

The implications of this work are multifaceted, affecting both theoretical and practical realms of human-robot collaboration. From a theoretical perspective, the enhancement of game-theoretical frameworks for pHRI can lead to the development of more sophisticated and adaptive control algorithms that leverage cooperative dynamics. Practically, these insights can transform how robots assist humans in tasks ranging from manufacturing to service industries, offering both efficiency gains and improved safety.

The insights gathered from this research pave the way for further explorations into adaptive human-robot control systems that can dynamically alternate roles based on real-time environmental feedback or human intention estimation. Future work encouraged by this paper may involve integrating predictive models of human intent into the CGT framework, thereby enhancing the interaction quality and adaptability of robots operating within human-centric environments.

In conclusion, this investigation contributes to the strategic deployment of game-theoretic approaches in pHRI, emphasizing the potential for cooperative frameworks to improve interactive outcomes substantially. It lays a foundation for further exploration into role fluidity and dynamic adaptability in human-robot teams.