M-Width: Stability, noise characterization, and accuracy of rendering virtual mass

In certain robot control and physical human-robot interaction scenarios, it is desirable to carefully control the apparent mass of a robot. Manipulating the apparent mass can be accomplished through virtual mass rendering, where the actuators of the robot produce forces proportional to measured acceleration. Many factors influence mass rendering, including device mechanical properties, sample rate, control structure, filtering, environment dynamic coupling parameters, and delay. Inspired by the “Z-Width” approach to sampled-data robotic system passivity, which represents the infinite-dimensional passive impedances of a robotic haptic display, we establish “M-Width”: the passive range of pure virtual mass. In this paper, we identify important parameters for system passivity and stability, present passivity and stability boundaries, predict noise limit cycles and establish conditions for their existence, and describe the expected accuracy of rendered virtual mass. We construct explicit parameter regions to describe the three-way trade-off that occurs between passivity/stability, noise, and accuracy. Experimental data gathered with a Phantom Premium 1.5 robot validates the theoretical analysis. These results serve as a general design tool for manipulating the effective mass of a robot, which is particularly relevant for rehabilitation robotics, robotic exoskeletons, and haptic display applications.