The key to robot-assisted rehabilitation lies in the design of the human-machine interface, which must accommodate the needs of both patients and machines. Current interface designs primarily focus on machine control algorithms, often requiring patients to spend considerable time adapting. In this paper, we introduce a novel approach based on the Cooperative Adaptive Markov Decision Process (CAMDPs) model to address the fundamental aspects of the interactive learning process, offering theoretical insights and practical guidance. We establish sufficient conditions for the convergence of CAMDPs and ensure the uniqueness of Nash equilibrium points. Leveraging these conditions, we guarantee the system's convergence to a unique Nash equilibrium point. Furthermore, we explore scenarios with multiple Nash equilibrium points, devising strategies to adjust both Value Evaluation and Policy Improvement algorithms to enhance the likelihood of converging to the global minimal Nash equilibrium point. Through numerical experiments, we illustrate the effectiveness of the proposed conditions and algorithms, demonstrating their applicability and robustness in practical settings. The proposed conditions for convergence and the identification of a unique optimal Nash equilibrium contribute to the development of more effective adaptive systems for human users in robot-assisted rehabilitation.

本研究针对目前机器人辅助康复中的人机界面设计问题，提出一种基于合作自适应马尔可夫决策过程（CAMDP）的新方法，解决了交互学习过程中的基本问题。研究表明，在特定条件下，系统能收敛至独特的纳什均衡点，进而为机器人辅助康复中的自适应系统设计提供了理论指导和实践应用。 

人机共同适应模型及其收敛分析