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For mobile robots driving across soft soils, such as sand, loose dirt, or snow, it is critical that the dynamic effects occurring at the wheel-terrain interface be taken into account. One of the most prevalent of these effects is wheel sinkage. Wheels can sink in soft soils to depths sufficient to prohibit further motion, leading to danger of entrapment with consequent mission failure. This paper presents an algorithm for visual estimation of wheel sinkage in deformable terrain. We call it the visual sinkage estimation (VSE) method. It assumes the presence of a monocular camera mounted on the wheel assembly, with a field of view containing the wheel-terrain interface. An artificial pattern, composed of concentric circumferences equally spaced apart on a white background, is attached to the wheel side in order to determine the contact angle with the terrain, following an edge detection strategy. The paper also introduces an analytical model for wheel sinkage in soft, deformable terrain based on terramechanics. In order to validate the VSE module, several tests were, first, performed on a single-wheel test bed, under different operating conditions including non-flat terrains, variable lighting conditions, and terrain with and without rocks. Successively, the effectiveness of the proposed approach in real context was proved, employing an all-terrain rover traveling on a sandy beach.