PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability

the Point-to-Point Case

Journal article (2021)

Authors

Davide Calzolari German Aerospace Center, Technische Universität München
C. Della Santina German Aerospace Center, Technische Universität München, Learning & Autonomous Control - Mechanical, Maritime and Materials Engineering
Alin Albu-Schaffer Technische Universität München, German Aerospace Center
Research Group
Learning & Autonomous Control (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2021 Davide Calzolari, C. Della Santina, Alin Albu-Schaffer
DOI: https://doi.org/10.1109/LCSYS.2020.3046538
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Published Date

2021

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Cognitive Robotics

Research Group

Learning & Autonomous Control

Abstract

This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on uni-dimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.

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