Online Learning of Piecewise Polynomial Signed Distance Fields for Manipulation Tasks

Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online method for learning implicit representations of signed distance using piecewise polynomial basis functions. Starting from an arbitrary prior shape, our approach incrementally constructs a continuous representation from incoming point cloud data. It offers fast access to distance and analytical gradients without the need to store training data. We assess the accuracy of our model on a diverse set of household objects and compare it to neural network and Gaussian process counterparts. Distance reconstruction and real-time updates are further evaluated in a physical experiment by simultaneously collecting sparse point cloud data and using the evolving model to control a manipulator.