Nonlinear trilateral teleoperation stability analysis subjected to time-varying delays

A trilateral teleoperation system facilitates the collaboration of two users to share control of a single robot in a remote environment. While various applications of shared-control trilateral haptic teleoperation systems have recently emerged, they have mostly been studied in the context of single-DOF, LTI robotic systems. On the other hand, robotic manipulators with multiple degrees of freedom (DOF) and therefore nonlinear dynamics have recently found many applications such as in robotic-assisted surgery and therapy, space exploration and navigation systems. In this paper, considering the full nonlinear dynamical models of multi-DOF robots, stability analysis of a dual-user haptic teleoperation system is considered over a communication network subjected to asymmetrical time varying delays and through a dominance factor suitable for trainer-trainee applications. Stability in free motion and contact motion and asymptotic position tracking of the trilateral haptic teleoperation system in free motion are proven via Lyapunov stability analysis and Barbalat's lemma where operators and the environment are assumed to be passive. Simulation and experimental results concerning robot position tracking and user-perceived forces for three 2-DOF robots and experimental analysis of user-perceived stiffnesses for three 3-DOF robots validate the theoretical findings pertaining to the system stability and demonstrate the efficiency of the proposed controller.