A bio-inspired scheme based on the human multi-joint arm (HMJA) viscoelastic properties is proposed to design a robust controller for the complex robot arm-and-hand system (RAHS) using the operator-based robust right coprime factorization (RRCF) approach. The RAHS mainly consists of two components, a robot arm and a micro-hand with three fingers. The fingers are made up of miniature pneumatic curling soft (MPCS) actuators, and are located in the endpoint of the robot arm. The aim is for a human to intuitively control the robot arm to perform a task under unknown environments from a remote location. We identify the main limitations of standard interaction control schemes in obtaining the learned information pairs, then propose a new control approach that is inspired by the biological model of HMJA viscoelasticity in voluntary movements. To achieve the precise position of the robot arm and obtain the desired force using the micro-hand for coping with the external environment or task involved, we propose a two-loop feedback control architecture using the operator-based RRCF approach. The bio-inspired inner-loop controller is designed based on HMJA viscoelastic properties to control the angular position of the robot arm. The outer-loop controller is designed to control the fingers force by considering the stable inner-loop as a right factorization. The robust tracking conditions and the realization of the proposed control system are also discussed. Finally, the effectiveness of the proposed control system is also verified by simulation results based on experimental data.