Contact-Force Control of a Flexible Timoshenko Arm in Rigid/Soft Environment

This technical note discusses a contact-force control problem of a one-link flexible arm. This flexible arm includes a Timoshenko beam, and thus we call it the flexible Timoshenko arm. The primary aim is to control the contact force at the contact point. To do so, we first apply our previously proposed force controller, which exponentially stabilizes the closed-loop system of a flexible Euler-Bernoulli arm, to the force-control problem of the flexible Timoshenko arm. We then show that our previously proposed force controller cannot exponentially stabilize the flexible Timoshenko arm. Next, we consider the flexible Timoshenko arm, which is making contact with a soft environment. By utilizing the damping force in the soft environment, as well as the controller, we try to overcome the problem. We then prove the exponential stability of the closed-loop system. Finally, we provide simulation results, and consider the validity of our force controller.