Impedance Control Using a Cascaded Loop Force Control

In this letter, a cascaded loop force control is implemented on a robot while considering the flexibility of the force sensor connecting the end effector to the tool. A classical frequency approach using a bandwidth and a phase margin is used to tune this controller. The aim is to find an equivalence between the proposed control law and a classical impedance control law. The apparent impedance of this system is calculated and can be seen as the desired impedance for a classical impedance control law. Using this equivalence, the cascaded loop force controller can be tuned to an impedance controller, and can be shown to behave equivalently in simulations and experiments on a one degree of freedom robot.