Absolute Stability Of3-DOF Bilateral Haptic Systems

A 3-degrees-of-freedom (DOF) bilateral haptic system can be modeled as a 2- port network where each port connects to a termination defined by 3 inputs and 3 outputs. The stability analysis of such systems is not trivial due to dynamic coupling across the different DOFs of the robots, the human operators, and the physical/virtual environments, and unknown dynamics of the human operators and the environments exacerbate the problem. Llewellyn's criterion only allows for absolute stability analysis of 1-DOF bilateral haptic systems, which can be modeled as 2-port networks. The absolute stability of a general 3-DOF bilateral haptic system cannot be obtained from the application of Llewellyn's criterion to each DOF of the bilateral system. In this paper, we present a straightforward and convenient criterion for absolute stability analysis of a class of 3-DOF bilateral haptic systems. As a case study, a 3-DOF bilateral haptic system is studied for absolute stability with simulations confirming the theoretical stability conditions.