Delay-Compensated Stiffness Estimation for Robot-Mediated Dyadic Interaction

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.

Stability Criteria and Motor Performance in Delayed Haptic Dyadic Interactions Mediated by Robots

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.