Towards developing a coupled stability theory for haptic systems, we study the interaction of operators with time-delayed force feedback. In this work, we analyzed and validated experimentally the stability boundaries of an uncoupled system - without considering the human. We then designed an experiment in which the participants used a haptic device to interact with virtual elastic force fields in a stiffness discrimination task. We compared the performance and kinematics of users in uncoupled-unstable and uncoupled-stable conditions and characterized the stabilizing contribution of the users. We found that the users were able to perform the task regardless of the uncoupled-stability conditions. In addition, in uncoupled-unstable conditions, users maintained movement characteristics that were important for exploratory mediation, such as depth and duration of the movement, whereas other characteristics were not preserved. The results were reproduced in a simulation of the human controller that combined an inverse model and an optimal feedback controller. Adequate performance under the uncoupled-unstable yet coupled-stable conditions supports the potential benefit of designing for coupled stability of haptic systems. This could lead to the use of less conservative controllers than state-of-the-art solutions in haptic and teleoperation systems, and advance the fidelity of haptic feedback.
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