Designing Multirate Controller for Optimal Tracking of Nonholonomic Laparoscopic Robotic Arm in a Telesurgery System

This paper presents the stability analysis of telesurgery systems regarding to the Nonholonomic Constraints and bandwidth limitations. The exponential stability of the sampled-data telesurgery system is satisfied by using Lyapunov-Krasovskii based stability criteria for non-uniform sampling rates. Calculating the maximum duration of two successive sampling times is proposed by linear matrix inequalities. The proposed multirate structure indicates that choosing proper periods for samplers and adequate refresh rates for actuators has a noticeable effect on the stability of the telesurgery system. Taking into account the nonholonomic conditions for the grasper of the surgical system and applying the Ritz approximation, the optimal steering problem has been evaluated. In order to verify the stability criteria, the performance of the multirate sampling for nonholonomic constraints is evaluated by simulation results, and the allowable sampling intervals are calculated to preserve the exponential stability of the system.