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Quantizing Euclidean Motions via Double-Coset Decomposition

Research 2019年第1期2019卷 525-540页

作者： Christian Wülker sipu ruan Gregory S.Chirikjian Johns Hopkins University BaltimoreMDUSA Department of Mechanical Engineering National University of SingaporeSingapore

Concepts from mathematical crystallography and group theory are used here to quantize the group of rigid-body motions,resulting in a“motion alphabet”with which robot motion primitives are *** these primitives it is possible to develop a dictionary of physical *** with an alphabet of the sort developed here,intelligent actions of robots in the world can be approximated with fnite sequences of characters,thereby forming the foundation of a language in which robot motion is *** particular,we use the discrete handedness-preserving symmetries of macromolecular crystals(known in mathematical crystallography as Sohncke space groups)to form a coarse discretization of the space SE(3)of rigid-body *** discretization is made fner by subdividing using the concept of double-coset *** specifcally,a very efcient,equivolumetric quantization of spatial motion can be defned using the group-theoretic concept of a double-coset decomposition of the formΓ\SE(3)/Δ,whereΓis a Sohncke space group andΔis a fnite group of rotational symmetries such as those of the *** resulting discrete alphabet is based on a very uniform sampling of SE(3)and is a tool for describing the continuous trajectories of robots and *** efcient coarse-to-fne search algorithm is presented to round of any motion sampled from the continuous group of motions to the nearest element of our *** is shown that our alphabet and this efcient rounding algorithm can be used as a geometric data structure to accelerate the performance of other sampling schemes designed for desirable dispersion or discrepancy ***,the general“signals to symbols”problem in artifcial intelligence is cast in this framework for robots moving continuously in the world.

关键词： robot primitive thereby

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