A Class of Explicitly Solvable Vehicle Motion Problems
Selig, JM (2015). A Class of Explicitly Solvable Vehicle Motion Problems. IEEE Transactions on Robotics. 31 (3), pp. 766 - 777 (11).
A small but interesting result of Brockett is extended to the Euclidean group SE(3) and is illustrated by several examples. The result concerns the explicit solution of an optimal control problem on Lie groups, where the control belongs to a Lie triple system in the Lie algebra. The extension allows for an objective function based on an indefinite quadratic form. Applying the result requires explicit knowledge of the Lie triple systems of the Lie algebra se(3). Hence, a complete classification of the Lie triple systems of this Lie algebra is derived. Examples are considered for optimal trajectories in three cases. The first case concerns cars moving in the plane. The second looks at motions that rigidly follow the Bishop frame to a space curve. The final example does not have a particular name as it does not seem to have been studied before. The appendix gives a brief introduction to Screw theory. This is essentially the study of the Lie algebra se(3).
|Journal||IEEE Transactions on Robotics|
|Journal citation||31 (3), pp. 766 - 777 (11)|
|Digital Object Identifier (DOI)||doi:10.1109/TRO.2015.2426471|
|15 May 2015|
|Publication process dates|
|Deposited||31 May 2016|
|Accepted author manuscript|
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