%0 Generic %1 bloesch2016primer %A Bloesch, Michael %A Sommer, Hannes %A Laidlow, Tristan %A Burri, Michael %A Nuetzi, Gabriel %A Fankhauser, Péter %A Bellicoso, Dario %A Gehring, Christian %A Leutenegger, Stefan %A Hutter, Marco %A Siegwart, Roland %D 2016 %K 2016 3D arxiv calculus robotics rotation tutorial %T A Primer on the Differential Calculus of 3D Orientations %U http://arxiv.org/abs/1606.05285 %X The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal solutions. The existence of many different conventions further complicates this issue, especially when interfacing multiple differing implementations. This document discusses an alternative approach which makes use of a more abstract notion of 3D orientations. The relative orientation between two coordinate systems is primarily identified by the coordinate mapping it induces. This is combined with the standard exponential map in order to introduce representation-independent and minimal differentials, which are very convenient in optimization based methods.

@misc{bloesch2016primer, abstract = {The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal solutions. The existence of many different conventions further complicates this issue, especially when interfacing multiple differing implementations. This document discusses an alternative approach which makes use of a more abstract notion of 3D orientations. The relative orientation between two coordinate systems is primarily identified by the coordinate mapping it induces. This is combined with the standard exponential map in order to introduce representation-independent and minimal differentials, which are very convenient in optimization based methods.}, added-at = {2018-03-15T16:21:53.000+0100}, author = {Bloesch, Michael and Sommer, Hannes and Laidlow, Tristan and Burri, Michael and Nuetzi, Gabriel and Fankhauser, Péter and Bellicoso, Dario and Gehring, Christian and Leutenegger, Stefan and Hutter, Marco and Siegwart, Roland}, biburl = {https://www.bibsonomy.org/bibtex/20b6104445e34b884e7a9fda428ef88a8/achakraborty}, description = {[1606.05285] A Primer on the Differential Calculus of 3D Orientations}, interhash = {f52140f594107bba4a873f71b524b245}, intrahash = {0b6104445e34b884e7a9fda428ef88a8}, keywords = {2016 3D arxiv calculus robotics rotation tutorial}, note = {cite arxiv:1606.05285}, timestamp = {2018-03-15T16:22:29.000+0100}, title = {A Primer on the Differential Calculus of 3D Orientations}, url = {http://arxiv.org/abs/1606.05285}, year = 2016 }