Controller Design for Systems on Manifolds in Euclidean Space
For control engineers working with systems on manifolds, this offers a simpler global coordinate approach, but the contribution is incremental as it extends existing embedding techniques.
The paper develops a theory for designing controllers on manifolds embedded in Euclidean space by modifying system dynamics outside the manifold to add attractiveness, and applies it to fully actuated rigid body stabilization and tracking.
Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on the manifold or coordinate-free tools from differential geometry. In this paper, we develop a theory about this and apply it to the fully actuated rigid body system for stabilization and tracking. A noteworthy point in this theory is that we legitimately modify the system dynamics outside its state-space manifold before controller design so as to add attractiveness to the manifold in the resulting dynamics.