Motion control of drift-free, left-invariant systems on Lie groups
- 1 January 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 40 (9) , 1539-1554
- https://doi.org/10.1109/9.412625
Abstract
In this paper we address the constructive controllability problem for drift-free, leftinvariantsystems on finite-dimensional Lie groups with fewer controls than state dimension.We consider small (ffl) amplitude, low-frequency, periodically time-varying controls andderive average solutions for system behavior. We show how the pth-order average formulacan be used to construct open-loop controls for point-to-point maneuvering of systems thatrequire up to (p \Gamma 1) iterations of Lie...Keywords
This publication has 27 references indexed in Scilit:
- Averaging for attitude control and motion planningPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Geometric phases, anholonomy, and optimal movementPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- On reorienting linked rigid bodies using internal motionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Limits of highly oscillatory controls and the approximation of general paths by admissible trajectoriesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Control problems on principal bundles and nonholonomic mechanicsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Control synthesis and adaptation for an underactuated autonomous underwater vehicleIEEE Journal of Oceanic Engineering, 1995
- Infinite products and T products of exponentialsTheoretical and Mathematical Physics, 1976
- Control systems on Lie groupsJournal of Differential Equations, 1972
- Domaines d'injectivité de l'application exponentielleTopology, 1966
- On global representations of the solutions of linear differential equations as a product of exponentialsProceedings of the American Mathematical Society, 1964