We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy datasets from depth sensors, whose distributions may correspond to Truncated Gaussian, Weighted Samples, or Truncated Gaussian Mixture Model. We derive tight probability bounds for convex shapes and extend them to non-convex shapes using hierarchical representations. We highlight the benefits of our approach over prior probabilistic collision detection algorithms in terms of tighter bounds (10x) and improved running time (3x). Moreover, we use our tight bounds to design an efficient and accurate motion planning algorithm for a 7-DOF robot arm operating in tight scenarios with sensor and motion uncertainties.
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