Natural frames and interacting particles in three dimensions
| dc.creator | Justh, E. W. | |
| dc.creator | Krishnaprasad, P. S. | |
| dc.date | 2005-03-18 | |
| dc.date.accessioned | 2026-07-07T05:18:07Z | |
| dc.date.available | 2026-07-07T05:18:07Z | |
| dc.description | Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and analyze. A Lie group formulation arises naturally, and we discuss the general problem of determining (relative) equilibria for arbitrary G-invariant controls (where G = SE(3) is a symmetry group for the control law). We then present global convergence (and non-collision) results for specific two-vehicle interaction laws in three dimensions, which lead to specific formations (i.e., relative equilibria). Generalizations of the interaction laws to n vehicles is also discussed, and simulation results presented. | |
| dc.description | 8 pages, submitted to 44th IEEE Conf. Decision and Control, 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0503390 | |
| dc.identifier | http://arxiv.org/abs/math/0503390 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74551 | |
| dc.subject | Optimization and Control | |
| dc.subject | 93C10 (Primary); 93D30 (Secondary) | |
| dc.title | Natural frames and interacting particles in three dimensions | |
| dc.type | text |