Multifidelity Sampling for Fast Bayesian Shape Estimation with Tactile Exploration

This article presents a novel multifidelity-based optimal sampling method to rapidly estimate the shape of an object from the touch-down points on its surface given a highly limited number of sampling trials. The proposed approach attempts to improve the existing shape estimation via tactile exploration, which uses Gaussian process regression for implicit surface modeling with sequential sampling. The main objective is to make the process of sample point selection more efficient and systematic such that the unknown shape can be estimated fast and accurately with highly limited sample points (e.g., less than 1% of the original dataset). Specifically, we propose to select the next best sample point based on two optimization criteria: 1) the mutual information (MI) for uncertainty reduction, and 2) the local curvature for fidelity enhancement. The combination of these two objectives leads to an optimal sampling process that balances between the exploration of the whole shape and the exploitation of the local area where the higher fidelity (or more sampling) is required. Simulation and experimental results successfully demonstrate the advantage of the proposed method in terms of estimation speed and accuracy over the conventional methods. Our approach allows us to reconstruct recognizable three dimensional shapes using only around optimally selected 0.4% of the original dataset.