Robot-mediated human-human (dyadic) interactions enable therapists to provide physical therapy remotely, yet an accurate perception of patient stiffness remains challenging due to network-induced haptic delays. Conventional stiffness estimation methods, which neglect delay, suffer from temporal misalignment between force and position signals, leading to significant estimation errors as delays increase. To address this, we propose a robust, delay-compensated stiffness estimation framework by deriving an algebraic estimator based on quasi-static equilibrium that explicitly accounts for temporally aligning the expert's input with the novice's response. A Normalised Weighted Least Squares (NWLS) implementation is then introduced to robustly filter dynamic bias resulting from the algebraic derivation. Experiments using commercial rehabilitation robots (H-MAN) as the platform demonstrate that the proposed method significantly outperforms the standard estimator, maintaining consistent tracking accuracy under multiple introduced delays. These findings offer a promising solution for achieving high-fidelity haptic perception in remote dyadic interaction, potentially facilitating reliable stiffness assessment in therapeutic settings across networks.

翻译：机器人中介的人类双人交互使治疗师能够远程提供物理治疗，但由于网络引起的触觉延迟，准确感知患者刚度仍然具有挑战性。传统的刚度估计方法忽略延迟，导致力与位置信号之间的时间错位，随着延迟增加会产生显著的估计误差。为解决此问题，我们提出了一种鲁棒的延迟补偿刚度估计框架，通过基于准静态平衡推导代数估计器，该估计器明确考虑了将专家输入与新手响应进行时间对齐。随后引入归一化加权最小二乘（NWLS）实现，以鲁棒地滤除由代数推导产生的动态偏差。使用商用康复机器人（H-MAN）作为平台的实验表明，所提方法显著优于标准估计器，在多种引入的延迟下保持一致的跟踪精度。这些发现为实现远程双人交互中的高保真触觉感知提供了有前景的解决方案，有望促进跨网络治疗环境中可靠的刚度评估。