Uncoupled Stability and Achievable Impedance Extremes of Haptic Interaction: A Comprehensive Study

Uncoupled stability analysis is valuable for assessing the stability of haptic interaction, since the interaction between a stable haptic device and a human operator maintains stability. Previous analyses have primarily focused on the normalized parameter space, but they yield an incorrect stability region that may lead to instability in the case of large normalized physical damping (NPD). Additionally, these analyses have neglected to return to the real parameter space, which can result in misconceptions such as increasing the control period expands the stability region or incomplete notions such as increasing the physical inertia always enlarges the stability region. To address these issues, this article presents an uncoupled stability constraint in the normalized parameter space that is applicable for all NPDs. Furthermore, the study returns to the real parameter space and, for the first time, provides analytical expressions that demonstrate the impacts of control period, physical damping and physical inertia on the achievable extremes of virtual stiffness and damping. Remarkably, it is observed that four out of the six influences exhibit non-monotonic behaviors, characterized by an “increase-decrease-increase” pattern. The correctness of the developed uncoupled stability region in the normalized parameter space and the existence of the unconventional non-monotonic behaviors in the real parameter space are validated through simulations and experiments.