Strict Modes Everywhere - Bringing Order Into Dynamics of Mechanical Systems by a Potential Compatible With the Geodesic Flow

Abstract:Strict nonlinear normal modes provide very regular families of oscillations within conservative mechanical systems. However, a strict normal mode will generally be an isolated curve within the configuration space of the system. In this letter, we design a potential that will densely fill the configuration space with strict normal modes such that each configuration belongs to one mode and each mode passes through a common point, the equilibrium. As the potential can be realized by (nonlinear) elastic elements it can be used to execute a variety of periodic trajectories very efficiently. Most of the required torques will come from the elastic elements in the system and not from the actuators. We also design a controller stabilizing the system to a desired target mode and a controller performing swing-up and compensating dissipated energy. Finally, we showcase the approach for a two DoF manipulator. The experiments show that the approach performed well for the example system.

Robotics (cs.RO)

arXiv:2609.04817 [cs.RO]

(or arXiv:2609.04817v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.04817 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 2337-2344, April 2022

https://doi.org/10.1109/LRA.2022.3142921 Focus to learn more DOI(s) linking to related resources

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