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Reasoning about distance is indispensable for establishing or avoidingcontact in manipulation tasks. To this end, we present an online approach forlearning implicit representations of signed distance using piecewise polynomialbasis functions. Starting from an arbitrary prior shape, our methodincrementally constructs a continuous and smooth distance representation fromincoming surface points, with analytical access to gradient information. Theunderlying model does not store training data for prediction, and itsperformance can be balanced through interpretable hyperparameters such aspolynomial degree and number of segments. We assess the accuracy of theincrementally learned model on a set of household objects and compare it toneural network and Gaussian process counterparts. The utility of intermediateresults and analytical gradients is further demonstrated in a physicalexperiment. For code and video, see https://sites.google.com/view/pp-sdf/.

Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials