Transparent, High-Force, and High-Stiffness Control of Haptic Actuators with Backlash: A Multi Degree of Freedom Approach

Actuators with speed reducers have desirable increased force and impedance rendering capabilities due to the mechanical transformer which magnifies their output force or torque and enables increased rendering capability. Unfortunately, the same mechanical transformer also magnifies the inertia of the actuator. The equivalent inertia of an actuator grows with the reduction ratio squared while the force capability only increases linearly. The increased open loop output impedance of an actuator with a speed reducer impedes the use of highly geared actuators in haptics. Recent work shows that backlash (i.e. mechanical play) and a control topology referred to here as relative motion control helps to overcome this limitation in actuators utilizing speed reducers. This work focuses on scaling this single degree of freedom control approach to a multi degree of freedom haptic device. Free space rendering, which is enabled by the presence of backlash is scaled into multiple degrees of freedom. Furthermore, we present a novel multi degree of freedom haptic rendering approach which allows the haptic device to render high impedances while smoothly sliding along an arbitrary virtual surface. We experimentally validate the approach with a two degree of freedom pantograph style haptic device and discuss its considerations and limitations.