High-Order Averaging on Lie Groups and Control of an Autonomous Underwater Vehicle
Abstract
In this paper, the authors extend their earlier results on the use of periodic forcing and averaging to solve the constructive controllability problem for drift-free left-invariant systems on Lie groups with fewer controls than state variables. In particular, they prove a third-order averaging theorem applicable to systems evolving on general matrix Lie groups and show how to use the resulting approximations to construct open-loop controls for complete controllability of systems that require up to depth-two Lie brackets to satisfy the Lie algebra controllability rank condition. The motion control problem for an autonomous underwater vehicle is modelled as a drift-free, left-invariant system on the matrix Lie group SE(3). In the general case, when only one translational and two angular control inputs are available, this system satisfies the controllability rank condition using depth-two Lie brackets. They use the third-order averaging result and its geometric interpretation to construct open loop controls to arbitrarily translate and orient an autonomous underwater vehicle.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1993
- Accession Number
- ADA454917
Entities
People
- Naomi Ehrich Leonard
- P.S.Krishnaprasad
Organizations
- University of Maryland