Telesurgical robot control is a significant example of an uncertain nonlinear system, as it involves various complexities, including unknown master/slave dynamics, environmental uncertainties, joint elasticities, and communication time delays. This problem becomes even more complicated when desirable properties such as stability, transparency, rigidity, accuracy, and fine manipulability are considered. We consider an elastic joint telesurgical robot architecture that combines two parallel and serial manipulators to achieve the desired rigidity, accuracy, and fine manipulability. For this purpose, we propose using Brain Emotional Learning (BEL) to estimate the robot’s uncertain nonlinear dynamics. In contrast to recent stability analyses of BEL-based systems, we employ Lyapunov theory to achieve the closed-loop system’s general stability independent of robot dynamics and chattering. Furthermore, the proposed control architecture implements two reference impedance models for the master and slave robots’ trajectory generation and makes a trade-off between transparency and stability by simultaneously considering optimal position synchronization and transparency conditions. In this regard, we extend these two conditions in absolute stability theory and Llewellyn’s criterion to obtain the allowable bound of communication time delay. The proposed robot is designed and experimentally implemented at the Robotics Laboratories at FUM and SUT Universities. Along with confirming the theoretical results, simulations and laboratory experiments demonstrate that a reasonable trade-off between stability and transparency is made in four realistic case studies with and without communication time delays.

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