The compliant controller is an effective controller method widely used in order to perform surgical tasks. In this study, the interaction environment has two main properties. The first one is that the parameters of the environment such as the stiffness are unknown and the second one is that the position of the environment is not available. In this regard, the variable impedance controller is considered as the main compliant controller of this work. In order to interact with the unknown surgical environment, three challenges including robustness, adaptation, and stability of the variable impedance are considered as the main parts of the thesis. For the robustness of the variable impedance, we proposed the dynamic surface controller using the intelligent approach such as a fuzzy and wavelet neural network to eliminate the uncertainties and disturbances. As the second challenge and in order to interact with the unknown surgical environment, we presented a noble formulation for the impedance profile to update the impedance parameters using intelligent methods such as wavelet neural network and fuzzy mechanism. The last challenge is the stability of the variable impedance. Updating the impedance parameters makes the impedance profile as a time-varying system, which can lead to system instability. Therefore, we proposed approaches to guarantee the stability of the impedance profile as an important part of this study. Finally, we induce various simulations and implementation using da Vinci and IIWA robotic manipulators to evaluate the performance of the proposed approaches. Key Words : Variable Impedance Control, Compliant Control, Wavelet Neural Network, Unknown and Dynamic Environment, Dynamic Surface
