M-Width: Stability and Accuracy of Haptic Rendering of Virtual Mass

In many physical human-robot interaction scenarios, such as haptic virtual environments for training and rehabilitation, it is desirable to carefully control the apparent inertia of a robot. Inertia compensation can be used to mitigate forces felt by the user during free-space motion, and rendering of additional inertia is desired for particular rehabilitation and training procedures. Many factors influence the stability and accuracy of rendering for haptic display of a pure mass, including device mechanical properties, sample rate, control structure, and human behavior. Inspired by the “Z-Width” approach to haptic device stability and performance analysis, we introduce “M-width”, which we define as the dynamic range of virtual masses renderable in a stable manner. We identify the important parameters for system stability, find stability boundaries, and describe the expected accuracy of the haptic rendering for a canonical haptic system. These results serve as a design tool for creating stable and accurate haptic virtual environments, establish limits of performance, and lay the groundwork for new controllers to improve mass rendering.