Wireless Human-Machine Collaboration (WHMC) represents a critical advancement for Industry 5.0, enabling seamless interaction between humans and machines across geographically distributed systems. As the WHMC systems become increasingly important for achieving complex collaborative control tasks, ensuring their stability is essential for practical deployment and long-term operation. Stability analysis certifies how the closed-loop system will behave under model randomness, which is essential for systems operating with wireless communications. However, the fundamental stability analysis of the WHMC systems remains an unexplored challenge due to the intricate interplay between the stochastic nature of wireless communications, dynamic human operations, and the inherent complexities of control system dynamics. This paper establishes a fundamental WHMC model incorporating dual wireless loops for machine and human control. Our framework accounts for practical factors such as short-packet transmissions, fading channels, and advanced HARQ schemes. We model human control lag as a Markov process, which is crucial for capturing the stochastic nature of human interactions. Building on this model, we propose a stochastic cycle-cost-based approach to derive a stability condition for the WHMC system, expressed in terms of wireless channel statistics, human dynamics, and control parameters. Our findings are validated through extensive numerical simulations and a proof-of-concept experiment, where we developed and tested a novel wireless collaborative cart-pole control system. The results confirm the effectiveness of our approach and provide a robust framework for future research on WHMC systems in more complex environments.

翻译：无线人机协作（WHMC）是工业5.0领域的一项关键进展，它实现了跨地理分布式系统的人与机器之间的无缝交互。随着WHMC系统在实现复杂协同控制任务中变得日益重要，确保其稳定性对于实际部署和长期运行至关重要。稳定性分析能够验证闭环系统在模型随机性下的行为表现，这对于依赖无线通信运行的系统尤为关键。然而，由于无线通信的随机性、动态的人为操作以及控制系统动力学固有的复杂性之间错综复杂的相互作用，WHMC系统的基本稳定性分析仍是一个尚未被探索的挑战。本文建立了一个包含机器控制与人类控制双无线环路的基本WHMC模型。我们的框架考虑了短包传输、衰落信道和先进HARQ方案等实际因素。我们将人类控制滞后建模为马尔可夫过程，这对于捕捉人机交互的随机性至关重要。基于此模型，我们提出了一种基于随机周期成本的方法，推导出WHMC系统的稳定性条件，该条件以无线信道统计特性、人类动力学和控制参数表示。我们的研究结果通过大量数值模拟和概念验证实验得到了验证，其中我们开发并测试了一种新型无线协同小车-倒立摆控制系统。结果证实了我们方法的有效性，并为未来在更复杂环境中研究WHMC系统提供了一个稳健的框架。