Abstract
In this paper we show how to use periodic forcing to solve the constructive controllability problem for drift-free, left-invariant systems on matrix Lie groups with fewer controls than states. In particular, we prove a second-order averaging theorem applicable to systems evolving on general matrix Lie groups. Using this theorem, we show how to construct open loop controls for complete controllability of systems that require up to depth-one Lie brackets to satisfy the Lie algebra controllability rank condition. We apply these results to the attitude control problem with only two controls available and to the unicycle motion planning problem.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the IEEE Conference on Decision and Control |
| Publisher | Publ by IEEE |
| Pages | 3098-3104 |
| Number of pages | 7 |
| Volume | 4 |
| ISBN (Print) | 0780312988 |
| State | Published - Dec 1 1993 |
| Externally published | Yes |
| Event | Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) - San Antonio, TX, USA Duration: Dec 15 1993 → Dec 17 1993 |
Other
| Other | Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) |
|---|---|
| City | San Antonio, TX, USA |
| Period | 12/15/93 → 12/17/93 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization