Haptic robotic exploration aims to control the movements of a robot with the objective of touching an object and retrieving physical information about it. In this work, we present an innovative exploration strategy to simultaneously detect symmetries in a 3-D object and use this information to enhance shape estimation. This is achieved by leveraging a novel formulation of Gaussian process models that allows the modeling of symmetric surfaces. Our procedure does not assume any prior knowledge about the object, neither about its shape nor about the presence and type of symmetry, necessitating only an approximate estimate of the size and boundaries (bounding box). We report experimental results both in simulation and in the real world, showing that using symmetric models leads to a reduction in shape estimation error, exploration time, and in the number of physical contacts performed by a robot when exploring objects that have symmetries.

The shapes of most real-world objects are symmetric with respect to at least one plane of symmetry. This information is unconsciously used by humans when they attempt to estimate the shape of an object in presence of uncertainty or missing evidence, for example if the object is partially occluded or if they are exploring the object by touch (i.e. haptic exploration). In robotics, this concept has been used for the visual estimation of object shape. However, no attempt has been made so far to incorporate this idea into haptic-based estimation. This work presents a method for the haptic exploration of object shape that includes the assumption that a symmetry could exist. The approach combines a tailored version of Gaussian Processes and a novel exploratory procedure that is able to detect the position and orientation of any plane of symmetry. Our results show that, if one or more symmetries exist, the object shape can be estimated faster and more accurately. Interestingly, in the case that no symmetry is present, the exploration process is only slightly slower, and the final accuracy of the shape estimation is not compromised.