Stability margins and passivity for the control of robots operating in varying-impedance environments

It is well-known that iff the robot with its endeffector force control is passive, the closed loop system consisting of the robot and an arbitrary passive environment is asymptotically stable. Passive robot control, however, limits the achievable robot impedance reduction. Recently, (Buerger and Hogan, 2007) investigated what performance can be achieved with non-passive control when uncertainty bounds for the environment are known, but unfortunately neglected stability margins. Here we present a robust force control design with stability margins for Buerger and Hogan's example. Furthermore, we perform experiments on a full scale industrial robot in order to identify six transfer functions from the control input to the inner velocity loop, i.e. from the velocity reference to the end effector force output for five different environments, from solid wall to air. The experimental data also makes it possible to compute the impedance of the controlled robot. Two controllers are designed and compared experimentally: one marginally stable but with non-passive controlled robot impedance that is low for low frequencies, and the other controller respecting the closed loop stability margin of IS(s)l<; 6 dB, where S(s) is the closed loop sensitivity function, but giving a passive controlled robot impedance that is higher for low frequencies. The paper is concluded by a short discussion of the role of stability margins and passivity for robots operating in varying impedance environments.