Estimating forces acting on Deformable Linear Objects (DLOs) is challenging due to their underactuated nature. However, reliable contact estimation is crucial to precisely control them and enable safe manipulation tasks. Differently from the various approaches presented in the literature, this work adopts a probabilistic formulation where the DLO state and sensor data are related through conditional distributions. In particular, factor graphs are used to determine the magnitude, direction, and location of a 3D force acting on a DLO, while simultaneously reconstructing its shape. Since DLOs are not actuated and are typically thin, like cables and wires, strain gauges and actuation readings are usually impractical. Therefore, to overcome this issue, this work is tested using one type of sensing information only, thus developing a generic technique suited for a wider variety of tasks. Realistic tests are performed by introducing noise into the measurements while the DLO follows a prescribed path in the presence of external forces that are accurately estimated.

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