Geometric phases, anholonomy, and optimal movement
- 10 December 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 2185-2189
- https://doi.org/10.1109/robot.1991.131953
Abstract
In the search for useful strategies for movement of robotic systems (e.g., manipulators, platforms) in constrained environments (e.g., in space, underwater), there appear to be new principles emerging from a deeper geometric understanding of optimal movements of nonholonomically constrained systems. The authors have exploited some new formulas for geometric phase shifts to derive effective control strategies. The theory of connections in principal bundles provides the proper framework for questions of the type addressed. An outline is presented of the essentials of this theory. A related optimal control problem and its localizations are also considered.<>Keywords
This publication has 5 references indexed in Scilit:
- How much does the rigid body rotate? A Berry’s phase from the 18th centuryAmerican Journal of Physics, 1991
- Isoholonomic problems and some applicationsCommunications in Mathematical Physics, 1990
- Steering nonholonomic systems using sinusoidsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1990
- On the rectification of vibratory motionSensors and Actuators, 1989
- Geometry of self-propulsion at low Reynolds numberJournal of Fluid Mechanics, 1989