Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm
| dc.contributor.author | Leonard, Naomi E. | en_US |
| dc.contributor.author | Krishnaprasad, Perinkulam S. | en_US |
| dc.contributor.department | ISR | en_US |
| dc.date.accessioned | 2007-05-23T09:56:08Z | |
| dc.date.available | 2007-05-23T09:56:08Z | |
| dc.date.issued | 1994 | en_US |
| dc.description.abstract | In this paper we present a general algorithm for constructing open-loop controls to solve the complete constructive controllability problem for drift-free invariant systems on Lie groups that satisfy the Lie algebra controllability rank condition with up to ( p - 1) iterations of Lie brackets, p = 1,2,3. Specifically, given only the structure constants of the given system, an initial condition Xi, a final condition Xf and a final time tf, the algorithm specifies open-loop, small (e) amplitude sinusoidal controls such that the system starting from Xi, reaches Xf at t = tf, with O (ep) accuracy. The algorithm is based on the formulas and geometric interpretation of the average approximations to the solution given in Part I to this paper. To illustrate the effectiveness of the algorithms, we apply it to three problems: the spacecraft attitude control problem with only two controls available, the unicycle motion planning problem and the autonomous underwater vehicle motion control problem with only three controls available. | en_US |
| dc.format.extent | 408314 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/5489 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | ISR; TR 1994-9 | en_US |
| dc.subject | geometric control | en_US |
| dc.subject | kinematics | en_US |
| dc.subject | nonlinear systems | en_US |
| dc.subject | robotics | en_US |
| dc.subject | Intelligent Servomechanisms | en_US |
| dc.title | Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm | en_US |
| dc.type | Technical Report | en_US |
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