Anti-gravity control of free-joint manipulators by vibrational input

Free joint manipulators under gravity potential are considered. Those under gravitation are pendulum systems. The scope of the paper is to control to a configuration other than the gravitational equilibriums, namely straight up or down. The free joint manipulators can be dynamically stabilized onto a configuration other than the gravitational equilibriums using the artificial potential produced by vibrational input to the first joint against gravity. Dynamic behaviors with vibrational inputs are investigated via averaging analysis, and inclined equilibriums other than gravitational ones are clarified. A method to determine the amplitude and frequency of vibrational input to the first joint to realize the desired inclined configuration is formulated. A control method to stabilize the free-joint manipulators onto the desired configuration using sliding mode control is proposed.