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Despite decades of research on efficient swept volume computation for robotics, computing the exact swept volume is intractable and approximate swept volume algorithms have been computationally prohibitive for applications such as motion and task planning. In this work, we employ deep neural networks (DNNs) for fast swept volume estimation. Since swept volume is a property of robot kinematics, a DNN can be trained off-line once in a supervised manner and deployed in any environment. The trained DNN is fast during on-line swept volume geometry or size inferences. Results show that DNNs can accurately and rapidly estimate swept volumes caused by rotational, translational, and prismatic joint motions. Sampling-based planners using the learned distance are up to five times more efficient and identify paths with smaller swept volumes on simulated and physical robots. Results also show that swept …