In a haptic teleoperation system, which interacts with unknown and hybrid environments, it is important to achieve stability and transparency. In medical usages, the utilization of knowledge on the tissues behavior in a controller design can improve the performance of the surgery in a robot-assisted telesurgery. Simultaneous interaction with hard and soft tissues makes it difficult to achieve stability and transparency. To deal with this difficulty, two controller schemes are designed. At first, a nonlinear mathematical model (inspired by the Hunt-Crossley (HC) model), which has the properties of soft and hard tissues, is combined with the slave side dynamic. In the second approach, the reaction force applied by hybrid tissues during the transition between tissues of different properties is modeled as an unknown force acting on the slave side. In a four-channel (4-CH) architecture, nonlinear adaptive controllers are designed without any knowledge about the parameters of the master, the slave robot, and the environment. For both control schemes, Lyapunov candidate functions provide a way to ensure the stability and transparency in the presence of uncertainties. The testbed comprises two Novint Falcon robots functioning as master and slave robots. Moreover, the experiments are performed on various objects, including a soft cube, a hard cube, and a phantom tissue. This paper rigorously evaluates the performances of the proposed methods, comparing them with each other and other previous schemes. Experimental and numerical results demonstrate the effectiveness of the proposed control schemes.

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