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With the introduction of telerobotic systems, it has become possible for surgeons to perform medical operations at greater physical distances from their patients. Whether in an adjacent room or on another continent, these systems enable greater flexibility in mitigating adverse surgical conditions. These ideas originally came from the space research, where further needs emerged to advance robots that could resolve surgical cases previously not treatable. The concept of providing surgical aid to astronauts in outer space yielded to telerobotic surgical care on Earth, benefiting around 1 million patients per year. As the field continues to develop and becomes more prevalent, it is worth looking back to the origins of the technology and the early days of robotic telesurgery. While many of the early prototypes and technologies never reached patients, their engineering components and innovative concepts directly lead to the birth of modern surgical robots.

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Rheological soft tissue models play an important role in designing control methods for modern teleoperation systems. In the meanwhile, these models are also essential for creating a realistic virtual environment for surgical training. The implementation of model-based control in teleoperation has been a frequently discussed topic in the past decades, offering solutions for the loss of stability caused by time delay, which is one of the major issues in long-distance force control. In this paper, mass-spring-damper soft tissue models are investigated, showing that the widely used linear models do not represent realistic behavior under surgical manipulations. A novel, nonlinear model is proposed, where mechanical parameters are estimated using curve fitting methods. Theoretical reaction force curves are estimated using the proposed model, and the results are verified using measurement results from uniaxial indentation. The model is extended with force estimation by nonuniform surface deformation, where the surface deformation function is approximated according to visual data. Results show that using the proposed nonlinear model, a good estimation of reaction force can be achieved within the range of 0-4 mm, provided that the tissue deformation shape function is appropriately approximated.