On Controller Design for Systems on Manifolds in Euclidean Space

Abstract

A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state-space manifold $M$ of a given control system into some Euclidean space ${\mathbb{R}}^n$, extend the system from $M$ to the ambient space ${\mathbb{R}}^n$, and modify it outside $M$ to add transversal stability to $M$ in the final dynamics in ${\mathbb{R}}^n$. Controllers are designed for the final system in the ambient space ${\mathbb{R}}^n$. Then, their restriction to $M$ produces controllers for the original system on $M$. This method has the merit that only one single global Cartesian coordinate system in the ambient space ${\mathbb{R}}^n$ is used for controller synthesis, and any controller design method in ${\mathbb{R}}^n$, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.

International Journal of Robust and Nonlinear Control (Accepted July 2018

References in corpus (2)

• Geometric Adaptive Tracking Control of a Quadrotor UAV on SE(3) for Agile Maneuvers
• Feedback Integrators

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