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

2026-09-04

AI Summary

通过设计一种与系统几何流兼容的势能，密集填充配置空间以实现严格非线性正常模式，从而高效执行周期轨迹并减少所需驱动扭矩。

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.

Problem

• strict normal modes
• configuration space
• potential
• geodesic flow
• elastic elements

Innovation

• strict nonlinear normal modes
• potential design
• elastic elements
• torque generation
• controller design