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In this paper, a real-time interactive high resolution soft tissue modeling is implemented that enriches a coarse model in a data-driven approach to produce a fine model. As a preprocess step, a set of corresponding coarse and fine models are simulated for the database. In the test step, by using a regressor, the coarse model in the test set is compared to the coarse models in the training set and the blending weights are assigned to the training coarse models. These weights are used for approximating the fine model as a linear combination of the corresponding fine models in the train set. To decrease the computational complexity, assuming that applying a force on the tissue results in a local deformation, a feature extraction algorithm is proposed that considers the displacements of the contact node and its neighbor nodes and ignores the rest. This results in a low dimensional feature vector and decreases the computational complexity. In order to compute the blending weights, a nonlinear regressor with Gaussian kernel is leveraged. To eliminate the artefacts resulting from negative weights, a nonnegative least square algorithm is used for regression. Simulation results of applying the proposed method on two soft tissue models are investigated regarding the reconstruction accuracy, computational complexity and running time.

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In this paper, formation control based on the virtual structure for the non-holonomic mobile robot system with two models of certain and uncertain kinematic equations is discussed. First, the formation equations of a certain model are calculated and then it is proved that it is possible to create a geometric shape and maintain that state by using the sliding model control theory for any two moving mobile robots. Then, after deriving the formation equations of the uncertain model, a sliding model controller is designed that is able to control the uncertain model provided that the uncertainty range of the kinematic equation is present. For each design, the stability of the system is guaranteed using the Lyapunov stability theorem. Finally, in order to compare the performance of the designed controllers, a pre-designed back-stepping controller is introduced and the results will be presented in the form of simulations. The simulation results show the effective performance of the designed controllers.