This dissertation addresses three diverse research problems pertaining to
rigid body attitude stabilization and control. The problems addressed result in
theoretical development for the topics of cooperative control, delayed feedback, and
state estimation, through the formulation of a novel class of switching observers.
In the area of consensus management for cooperative control, the problem
of designing torque control laws that synchronize the attitude of a team of rigid
bodies under constant, unknown communication time delays is addressed. Directed
communication graphs are considered, which encompass both leader-follower and
leaderless architectures. A feedback linearization result involving the Modified
Rodrigues parameter (MRP) representation of attitude kinematics reduces the attitude
dynamics equations to double integrator agents and the remainder of the
control effort achieves position consensus. New necessary and sufficient delay dependent stability conditions for the system of double integrator agents are presented.
This dissertation also considers the problem of stabilizing attitude dynamics
with unknown piecewise-constant delayed feedback. The problem is addressed
through stability analysis of switched linear time-invariant and nonlinear timedelay
systems. In the case of linear systems with switched delay feedback, a new
sufficiency condition for average dwell time result is presented using a complete
type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding
switched system with nonlinear perturbations is proven to be exponentially stable
inside a well characterized region of attraction for an appropriately chosen average
dwell time.
Finally, this dissertation provides a new switching angular velocity observer
formulation to the classical problem of rigid body attitude tracking in the absence
of angular rate measurements. Exponential convergence of the angular velocity
state estimation errors is proven independent of control design by using a novel
error signal definition through this switching-type observer. The switching ensures
C0 continuity for all the estimated states. Further, the maximum number of
switches required by the observer is shown to be finite and that zeno-type behavior
cannot occur. A “separation property” type result in the absence of actual angular
rate measurements is established, wherein a linear and nonlinear controller
utilizes angular velocity estimates from the proposed observer to achieve attitude
tracking. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2012-12-6725 |
| Date | 29 January 2013 |
| Creators | Chunodkar, Apurva Arvind |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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