Semi-global Output Feedback Asymptotic Tracking for an Under-actuated Variable Stiffness Mechanism

This paper presents the control synthesis for an under-actuated variable stiffness mechanism. The mech- anism, which is a simple arrangement of two springs, a lever arm and a pivot bar, has an effective stiffness that is a rational function of the horizontal distance d of the pivot bar from the center of mass O of the lever. The ef- fective stiffness is varied by changing d while keeping the point of application of external load constant. A Lyapunov based adaptive controller is designed to achieve an asymp- totic tracking on d while keeping the uncontrolled state of the system stable. Dynamic filters were used to estimate un- measurable states of the system. Numerical simulations are provided to demonstrate the performance of the resulting control system.