The paper presents a solution to the problem of planar contour tracking with a force-controlled robot. The contour shape is unknown and is characterized at each time step by the curvature together with the orientation angle and arc length. The unknown contour curvature, continuously changing, is supposed to be within a preliminary given interval. An Interacting Multiple Model (IMM) filter is implemented to cope with the uncertainties. The interval of possible curvature values is discretized, i.e., a grid is formed and several Extended Kalman filters (EKFs) are run in parallel. The curvature estimate represents a fusion of the values from the grid with the IMM probabilities. The orientation angle estimate is also a fusion of the estimates, obtained from the separate Kalman filters with the mode probabilities. A single-model EKF is implemented to localize the unknown initial robot end-effector position over the contour. The performance of both algorithms is investigated and results, based on real data, are presented.