Path Following for a Class of Underactuated Systems Using Global Parameterization

Abstract

A large number of both aerial and underwater mobile robots fall in the category of underactuated systems that are defined on a manifold, which is not isomorphic to Euclidean space. Traditional approaches to designing controllers for such systems include geometric approaches and local coordinatebased representations. In this paper, we propose a global parameterization of the special orthogonal group, denoted by SO(3), to design path-following controllers for underactuated systems. In particular, we present a nine-dimensional representation of SO(3) that leads to controllers achieving path-invariance for a large class of both closed and non-closed embedded curves. On the one hand, this over-parameterization leads to a simple set of differential equations and provides a global non-ambiguous representation of systems as compared to other local or minimal parametric approaches. On the other hand, this over-parameterization also leads to uncontrolled internal dynamics, which we prove to be bounded and stable. The proposed controller, when applied to a quadrotor system, is capable of recovering the system from challenging situations such as initial upside-down orientation and also capable of performing multiple flips. INDEX TERMS Feedback linearization, nonlinear control, path following, quadrotor, underactuated system.

Attitude Control of a Quadrotor with Fuzzy Logic Controller on SO(3)

“…The class of underactuated systems involves a large class of systems, such as tail-sitting robots, quadrotors, underwater vehicles, satellites, and many others. The rotational dynamics of each system belonging to the underactuated systems are defined on a smooth manifold 𝑆𝑂(3) × ℝ 3 [20]. Jen-Te Yu [21] system.…”