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Swing-Up of a Weakly Actuated Double Pendulum via Nonlinear Normal Modes

2024-04-12 13:55:29
Arne Sachtler, Davide Calzolari, Maximilian Raff, Annika Schmidt, Yannik P. Wotte, Cosimo Della Santina, C. David Remy, Alin Albu-Schäffer

Abstract

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.

Abstract (translated)

我们通过分析双摆动系统的非线性正交模(NMO)在重力下的稳定平衡状态,确定了它们与同构轨道的连接,并通过不稳定直立位置随能量增加而建立联系。这一结果被用于设计一种有效的双摆动系统弱、饱和式执行器的摆动提升策略。我们的方法包括在能量逐渐注入的同时,通过稳定系统到与非线性模相关的周期轨道来稳定系统。由于这些模是自组织的系统演化,所以所需的控制努力为最小。即使双摆动系统的执行器限制小于1%的最大重力扭矩,所提出的技术也能通过允许足够的时间来实现摆动提升。

URL

https://arxiv.org/abs/2404.08478

PDF

https://arxiv.org/pdf/2404.08478.pdf


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