Stable Non-linear Force/Position Mapping for Enhanced Telemanipulation of Soft Environments

The performance index in bilateral teleoperation, transparency, is often defined as linear scaling between the master and slave positions, as well as the operator and environment forces. Motivated by applications involving soft tissue manipulation such as robotic surgery, the transparency objective is generalized to include monotonic nonlinear mappings between the master/slave position and force signals. Modified Lyapunov-based adaptive motion/force controllers are presented that can guarantee the convergence of position and force tracking errors in the presence of dynamic uncertainty. Given a priori known bounds on the unknown operator and environment mass-spring-damper parameters, the closed-loop stability is analyzed using an off-axis circle criterion and the Nyquist envelope of interval plant systems. This approach produces far less conservative stability margins than those achievable by the passivity analysis. Experimental results with a two-axis teleoperation setup are provided.