Wireless Human-Machine Collaboration in Industry 5.0

TL;DR

A stochastic cycle-cost-based approach is proposed to derive a stability condition for the WHMC system, expressed in terms of wireless channel statistics, human dynamics, and control parameters, and is validated through extensive numerical simulations and a proof-of-concept experiment.

Abstract

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.

Figures (7)

• Figure 1: Illustration of the WHMC system, consisting of two types of control loops, i.e., the machine control loop and the human control loop.
• Figure 2: Temporal operation of the two control loops.
• Figure 3: Illustration of the time horizon of plant dynamics between two adjacent closed human control loops. $\Delta(\cdot) = \tau_{SH}(\cdot) + \tau_{H}(\cdot) + \tau_{HA}$
• Figure 4: Illustration of the stability region boundaries.
• Figure 5: Numerical examples of the boundary of stability conditions: (a) Impacts of the human state transition matrix on the stability region in terms of $\alpha_{HM}$ and $\alpha_{H}$, where $\alpha=1.02$, $\alpha_{M}=1.01$, $N=3$, and TI-HARQ are adopted. (b) Impacts of HARQ schemes on the stability region in terms of $\alpha_{HM}$ and $\alpha_{H}$, where $\alpha=1.02$, $\alpha_{M}=1.01$, $\mathbf{M} = \mathbf{M}_l$, and $N=3$ are adopted. (c) Impacts of the maximum number of retransmissions on the stability region in terms of $\alpha_{HM}$ and $\alpha_{H}$, where $\alpha=1.02$, $\alpha_{M}=1.01$, $\mathbf{M} = \mathbf{M}_l$, and IR-HARQ are adopted. (d) The stability region in terms of $\alpha_{M}$ vs. $\alpha_{H}$ and $\alpha_{M}$ vs. $\alpha_{HM}$, where $\mathbf{M} = \mathbf{M}_l$, and IR-HARQ are adopted. (e) The stability region in terms of $\alpha_{HM}$ and $\alpha_{H}$, where $\alpha=1.02$, $\mathbf{M} = \mathbf{M}_l$, and IR-HARQ are adopted. (f) The stability region in terms of $\alpha_{M}$ and $\alpha_{H}$, where $\alpha_{HM}=0.3$, $\mathbf{M} = \mathbf{M}_l$, and IR-HARQ are adopted. Colourized areas are stable regions.

Theorems & Definitions (8)

• Definition 1: Stochastic Stability LiuStabilityAssumption1Assumption2
• Theorem 1
• proof
• Corollary 1
• proof
• Proposition 1
• proof
• Definition 2: Collaborative Control Performance