This paper establishes analytical stability criteria for robot-mediated human-human (dyadic) interaction systems, focusing on haptic communication under network-induced time delays. Through frequency-domain analysis supported by numerical simulations, we identify both delay-independent and delay-dependent stability criteria. The delay-independent criterion guarantees stability irrespective of the delay, whereas the delay-dependent criterion is characterised by a maximum tolerable delay before instability occurs. The criteria demonstrate dependence on controller and robot dynamic parameters, where increasing stiffness reduces the maximum tolerable delay in a non-linear manner, thereby heightening system vulnerability. The proposed criteria can be generalised to a wide range of robot-mediated interactions and serve as design guidelines for stable remote dyadic systems. Experiments with robots performing human-like movements further illustrate the correlation between stability and motor performance. The findings of this paper suggest the prerequisites for effective delay-compensation strategies.

翻译：本文针对网络诱导时延下的触觉交互系统，建立了机器人介导人-人（双人）交互系统的解析稳定性判据。通过数值仿真支持的频域分析，我们识别了与时延无关及与时延相关的稳定性判据。与时延无关的判据保证系统在任何时延下均保持稳定，而与时延相关的判据则表现为系统失稳前可容忍的最大时延阈值。分析表明，这些判据依赖于控制器及机器人动力学参数，其中刚度增加会以非线性方式降低最大可容忍时延，从而加剧系统脆弱性。所提出的判据可推广至各类机器人介导的交互系统，并为设计稳定的远程双人系统提供指导原则。通过机器人执行类人运动的实验进一步阐明了稳定性与运动表现之间的关联。本文的研究结果为设计有效的时延补偿策略提供了理论基础。