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CEAS EuroGNC 2022

Quaternion based LQR for Free-Floating Robots Without Gravity
Shubham Vyas Researcher, Robotics Innovation Center, Deutsches Forschungszentrum für Künstliche Intelligenz GmbH, 28359, Bremen, Germany.
Bilal Wehbe Researcher, Robotics Innovation Center, Deutsches Forschungszentrum für Künstliche Intelligenz GmbH, 28359, Bremen, Germany.
Shivesh Kumar Researcher, Robotics Innovation Center, Deutsches Forschungszentrum für Künstliche Intelligenz GmbH, 28359, Bremen, Germany.
Abstract:
Quaternions are commonly used for rotation representation as they avoid the singularities found in the Euler angles representation and are more compact than using rotation matrices (for storage, operations, and constraints required). However, it is difficult to use quaternions in linear control approaches due to the inherent unit length constraint of the representation. Quaternion-based linear control has been previously used for single rigid body control such as quadrotors and satellite attitude control. In this paper, we provide an analytical method for linearizing multibody free-floating robotic systems without gravity using a quaternion-based rotation representation for the floating base. This linearization is then used for deriving a Linear Quadratic Regulator (LQR) based controller. The LQR is optimal in the local neighbourhood of the linearization and is globally asymptotically stable for such systems. The utility of this method is demonstrated using two examples from different robotic domains: space and underwater robotics.
Keywords: Robotics; Space Robotics; Underwater Robotics; LQR; Linear Optimal Control; Quaternions
 View PDF CEAS-GNC-2022-024


Shubham Vyas, Bilal Wehbe, Shivesh Kumar: Quaternion based LQR for Free-Floating Robots Without Gravity. Proceedings of the 2022 CEAS EuroGNC conference. Berlin, Germany. May 2022. CEAS-GNC-2022-024.
BibTeX entry:

@Incollection{CEAS-GNC-2022-024,
    authors = {Vyas, Shubham and Wehbe, Bilal and Kumar, Shivesh},
    title = {Quaternion based LQR for Free-Floating Robots Without Gravity},
    booktitle = {Proceedings of the 2022 {CEAS EuroGNC} conference},
    address = {Berlin, Germany},
    month = may,
    year = {2022},
    note = {CEAS-GNC-2022-024}
}