Efficient Probabilistic Collision Detection for Non-Gaussian Noise Distributions
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We present algorithms to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are given in non-Gaussian forms. Our algorithms can efficiently compute the upper bounds of collision probability when the error distributions are given as Truncated Gaussian, weighted samples, and Truncated Gaussian Mixture Model. We create positional error models on static obstacles captured by noisy depth sensors and dynamic obstacles with complex motion models. We highlight the performance of our probabilistic collision detection algorithms under non-Gaussian positional errors for static and dynamic obstacles in simulated scenarios and real-world robot motion planning scenarios with a 7-DOF robot arm. We demonstrate the benefits of our probabilistic collision detection algorithms in the use of motion planning algorithm in terms of planning collision-free trajectories under environments with sensor and motion uncertainties.
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