Optimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866916533649801216 |
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| author | Nayak, Aradhana de Almagro, Rodrigo Sato Martín Colombo, Leonardo de Diego, David Martín |
| author_facet | Nayak, Aradhana de Almagro, Rodrigo Sato Martín Colombo, Leonardo de Diego, David Martín |
| contents | We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory evolving on the distribution which defines the nonholonomic constraints. We prepose a geometric framework since it describes the class of nonlinear systems under study in a coordinate-free framework. Necessary conditions for the existence of extrema are determined by the Pontryagin Minimum Principle. A nonholonomic fully actuated particle is used as a benchmark example to show how the proposed method is applied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1901_10374 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Optimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach Nayak, Aradhana de Almagro, Rodrigo Sato Martín Colombo, Leonardo de Diego, David Martín Systems and Control Optimization and Control We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory evolving on the distribution which defines the nonholonomic constraints. We prepose a geometric framework since it describes the class of nonlinear systems under study in a coordinate-free framework. Necessary conditions for the existence of extrema are determined by the Pontryagin Minimum Principle. A nonholonomic fully actuated particle is used as a benchmark example to show how the proposed method is applied. |
| title | Optimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/1901.10374 |