Haptic-enabled Collaborative Training with Generalized Force and Position Mappings

A control framework is introduced for collaborative training in haptic-enabled virtual environments. To increase the versatility of the proposed approach, the haptic interface control is separated from the virtual environment simulation, which can be of either impedance or admittance-type. Adaptive nonlinear controllers are developed to enforce desired linear-time-invariant and/or nonlinear static mappings among the users and the virtual task environment positions and forces. The controllers account for nonlinear models of the haptic devices and can cope with uncertainties present in the users and haptic devices dynamics. The performance and closed-loop stability of the proposed methods are demonstrated in two steps. First, using a Lyapunov analysis, the tracking behavior of the system is shown. Then given a priori known bounds on the users and environment parameters, the robust stability of the closed-loop system is analyzed based on the Nyquist envelops of interval plants and an off-axis circle criterion. Experimental results demonstrate the effectiveness of the proposed controllers.