Quaternion based LQR for Free-Floating Robots without Gravity
Shubham Vyas, Bilal Wehbe, Shivesh Kumar
In 6th CEAS Conference on Guidance, Navigation, and Control, (EuroGNC-2022), 3.5.-5.5.2022, Berlin, CEAS, May/2022.
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 freefloating 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.
Robotics;Space Robotics; Underwater Robotics; LQR; Linear Optimal Control; Quaternions