Dynamics and control of an MRI compatible master-slave system with hydrostatic transmission

Abstract

We analyze the dynamics of an MR-compatible hydrostatic transmission designed to transfer power over distances of up to 10 m. In this system, a master actuates a passive slave connected by two hydrostatic lines in a cyclic arrangement. We derive a nonlinear model of this system and use it to analyze the system's behavior and the design parameters. The transmission acts as a low-pass filter with cut-off frequency decreasing for longer hoses. Even for a length of 10 m the cut-off frequency is about 20 Hz, resulting in a bandwidth that suffices for haptic interfaces interacting with human motion as well as for medical robots. A pragmatic control delivered free movements, position and velocity dependent force fields and trajectory control suitable to investigate how the brain controls movements in interaction with the environment. For short hose lengths (≤1m) the dynamics can be well approximated by a linear model, and the system is dynamic and stiff. The hydraulic transmission can produce force and motion in any orientation, enabling a more flexible design than other types of transmissions such as by cables.