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We introduce a novel approach to long-range path planning that relies on a learned model to predict the outcome of local motions using possibly partial knowledge. The model is trained from a dataset of trajectories acquired in a self-supervised way. Sampling-based path planners use this component to evaluate edges to be added to the planning tree. We illustrate the application of this pipeline with two robots: a complex, simulated, quadruped robot (ANYmal) moving on rough terrains; and a simple, real, differential-drive robot (Mighty Thymio), whose geometry is assumed unknown, moving among obstacles. We quantitatively evaluate the model performance in predicting the outcome of short moves and long-range paths; finally, we show that planning results in reasonable paths.