Swing-Up of a Weakly Actuated Double Pendulum via Nonlinear Normal Modes
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909274753466368 |
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| author | Sachtler, Arne Calzolari, Davide Raff, Maximilian Schmidt, Annika Wotte, Yannik P. Della Santina, Cosimo Remy, C. David Albu-Schäffer, Alin |
| author_facet | Sachtler, Arne Calzolari, Davide Raff, Maximilian Schmidt, Annika Wotte, Yannik P. Della Santina, Cosimo Remy, C. David Albu-Schäffer, Alin |
| contents | We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is exploited to devise an efficient swing-up strategy for a double pendulum with weak, saturating actuators. Our approach involves stabilizing the system onto periodic orbits associated with the nonlinear modes while gradually injecting energy. Since these modes are autonomous system evolutions, the required control effort for stabilization is minimal. Even with actuator limitations of less than 1% of the maximum gravitational torque, the proposed method accomplishes the swing-up of the double pendulum by allowing sufficient time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Swing-Up of a Weakly Actuated Double Pendulum via Nonlinear Normal Modes Sachtler, Arne Calzolari, Davide Raff, Maximilian Schmidt, Annika Wotte, Yannik P. Della Santina, Cosimo Remy, C. David Albu-Schäffer, Alin Systems and Control Robotics We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is exploited to devise an efficient swing-up strategy for a double pendulum with weak, saturating actuators. Our approach involves stabilizing the system onto periodic orbits associated with the nonlinear modes while gradually injecting energy. Since these modes are autonomous system evolutions, the required control effort for stabilization is minimal. Even with actuator limitations of less than 1% of the maximum gravitational torque, the proposed method accomplishes the swing-up of the double pendulum by allowing sufficient time. |
| title | Swing-Up of a Weakly Actuated Double Pendulum via Nonlinear Normal Modes |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2404.08478 |