TY - JOUR
T1 - Path following for a Class of Underactuated Systems Using Global Parameterization
AU - Akhtar, Adeel
AU - Saleem, Sajid
AU - Waslander, Steven L.
N1 - Generated from Scopus record by KAUST IRTS on 2023-10-11
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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 coordinate-based representations. In this paper, we propose a global parameterization of the special orthogonal group, denoted by $ \mathsf {SO}(3)$ , to design path-following controllers for underactuated systems. In particular, we present a nine-dimensional representation of $ \mathsf {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.
AB - 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 coordinate-based representations. In this paper, we propose a global parameterization of the special orthogonal group, denoted by $ \mathsf {SO}(3)$ , to design path-following controllers for underactuated systems. In particular, we present a nine-dimensional representation of $ \mathsf {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.
UR - https://ieeexplore.ieee.org/document/8999577/
UR - http://www.scopus.com/inward/record.url?scp=85080966050&partnerID=8YFLogxK
U2 - 10.1109/ACCESS.2020.2974153
DO - 10.1109/ACCESS.2020.2974153
M3 - Article
SN - 2169-3536
VL - 8
SP - 34737
EP - 34749
JO - IEEE Access
JF - IEEE Access
ER -