Nonlinear and Geometric Controllers for Rigid Body Vehicles
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Date
2018-10-18
Authors
Akhtar, Adeel
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
In this thesis we investigate the motion control problem for a class of vehicles C V , which includes
satellites, quadrotors, underwater vehicles, and tailsitters. Given a globally represented model of
C V , and a curve, the motion control problem entails following the curve using control inputs. In
this thesis the motion control problem is viewed under two settings, 1) as a local path following
problem, 2) as a geometric trajectory tracking problem. We provide solutions to both problems
by designing controllers based on the concept of feedback linearization.
In the local path following problem, the C V class of vehicles is represented by a local chart.
The problem is solved in a monolithic control setting, and the path that needs to be followed is
treated as a set to be stabilized. The nonlinear model under study is first dynamically extended
and then converted into a fully linear form through a coordinate transformation and smooth feed-
back. This approach achieves path invariance. We also design a fault tolerant local controller that
ensure path following and path invariance in the presence of a one rotor failure for a quadrotor.
The second major problem addressed is the geometric trajectory tracking problem, which is
treated in an inner-outer loop setting. Specifically, we design a controller class for the attitude dy-
namics of the C V class of vehicles. The novel notion of Lie algebra valued functions are defined
on the Special Orthogonal group SO(3), which constitutes a family of functions. This family
of functions induces a novel geometric controller class, which consists of almost globally stable
and locally stable controllers. This class is designed using the idea of feedback linearization, and
is proven to be asymptotically stable through a Lyapunov-like argument. This allows the system
to perform multiple flips. We also design geometric controllers for the position loop, which are
demonstrated to work with the attitude controller class through simulations with noisy sensor
data.
Description
Keywords
Nonlinear, control, quadrotors, rigid body, feedback linearization, lie groups, lie algebra, geometric