Effective sampling and distance metrics for 3D rigid body path planning

By James J. Kuffner Jr.. 2004

311 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data (2020, methodology): “There are multiple easy methods to sample uniformly from SO( d ) given in (Kuffner, 2004), for example sampling uniformly from SO( 3 ) can be done by sampling a unit quaternion from the 3-sphere, and identifying it with the corresponding rotation matrix.”
Sampling-Based Robot Motion Planning: A Review (2014, methodology): “Similarly, accounting for rotation using Euler angles, or Quaternions, proved to be advantageous when planning with RRT in 3D [112].”
An enumerative stepwise ansatz enables atomic-accuracy RNA loop modeling (2011, methodology): “, in enumerative coarse-grained or stochastic all-atom search methods from Dill and coworkers (18, 19), pioneering peptide-modeling work from the 1980s by the Scheraga lab (17), and earlier computational explorations by Levinthal in 1968 (6).”
Semi-Supervised Learning via Generalized Maximum Entropy (2010, methodology): “In order to cope with the double cover property (Kuffner, 2004) of quaternions, we compute the rotational distance f(θab), as the smaller angle between the two unit length quaternions ra and rb.”
Metrics for 3D Rotations: Comparison and Analysis (2009, methodology): “This function was used in [9] for the distance measure between two Euclidean transformations.”
Planning algorithms (2006, background): “Sampling issues in the context of motion planning are considered in [382, 562, 603, 642, 987].”