| Title | Steering Algorithm for Drift Free Control Systems |
| Publication Type | Journal Article |
| Year of Publication | 2007 |
| Authors | -UR-REHMAN, FAZAR, Ahmed, MM, Moiz, SA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 11 |
| Issue | 4 |
| Start Page | 485 |
| Pagination | 514 |
| Date Published | 12/2007 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34.K25, 34B 15, 34KlO |
| Abstract | This paper presents a simple steering algorithm for nonholonomic control systems without drift. The effectiveness of the algorithm is tested on four different nonholonomic control systems: a spacecraft, a front wheel drive car, a fire truck model, and a model of mobile robot with trailer. The controllability Lie Algebra of the spacecraft model contains Lie bracket of depth one while the model of a front wheel drive car and a rue truck model contain Lie brackets of depth one and two. The controllability Lie Algebra of the model of mobile robot with trailer contains Lie brackets of depth one, two, and three. The feedback controls are piecewise constant, states dependent and the method is based on the construction of a cost function V which is sum of the two semi positive definite functions VI and V2, where VI consists of the function of the first m state variables which can be steered along the given vector fields and V2 is the function of the remaining n - m state variables which can be steered along the missing Lie brackets. The values of the functions VI and V2 allow in determining a desired direction of system motion and permit to construct a sequence of controls such that the sum of these functions decreases in an average sense. This approach does not necessitate the conversion of the system model into a "chained form", and thus does not rely on any special transformation techniques.
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| URL | http://www.acadsol.eu/en/articles/11/4/5.pdf |
| Short Title | DRIFT FREE CONTOL SYSTEMS |
| Refereed Designation | Refereed |
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