240 research outputs found
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
Complete spelling rules for the Monster tower over three-space
The Monster tower, also known as the Semple tower, is a sequence of manifolds
with distributions of interest to both differential and algebraic geometers.
Each manifold is a projective bundle over the previous. Moreover, each level is
a fiber compactified jet bundle equipped with an action of finite jets of the
diffeomorphism group. There is a correspondence between points in the tower and
curves in the base manifold. These points admit a stratification which can be
encoded by a word called the RVT code. Here, we derive the spelling rules for
these words in the case of a three dimensional base. That is, we determine
precisely which words are realized by points in the tower. To this end, we
study the incidence relations between certain subtowers, called Baby Monsters,
and present a general method for determining the level at which each Baby
Monster is born. Here, we focus on the case where the base manifold is three
dimensional, but all the methods presented generalize to bases of arbitrary
dimension.Comment: 14 pages, 4 figures; new titl
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Regelungstheorie
The workshop āRegelungstheorieā (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering
AUTONOMOUS SPACECRAFT RENDEZVOUS WITH A TUMBLING OBJECT: APPLIED REACHABILITY ANALYSIS AND GUIDANCE AND CONTROL STRATEGIES
Rendezvous and proximity operations are an essential component of both military and commercial space missions and are rising in complexity. This dissertation presents an applied reachability analysis and develops a computationally feasible autonomous guidance algorithm for the purpose of spacecraft rendezvous and proximity maneuvers around a tumbling object. Recent advancements enable the use of more sophisticated, computation-based algorithms, instead of traditional control methods. These algorithms are desirable for autonomous applications due to their ability to optimize performance and explicitly handle constraints (e.g., safety, control limits). In an autonomous setting, however, some important questions must be answered before an algorithm implementation can be realized. First, the feasibility of a maneuver is addressed by analyzing the fundamental spacecraft relative dynamics. Particularly, a set of initial relative states is computed and visualized from which the desired rendezvous state can be reached (i.e., backward reachability analysis). Second, with the knowledge that a maneuver is feasible, the Model Predictive Control (MPC) framework is utilized to design a stabilizing feedback control law that optimizes performance and incorporates constraints such as control saturation limits and collision avoidance. The MPC algorithm offers a computationally efficient guidance strategy that could potentially be implemented in real-time on-board a spacecraft.http://archive.org/details/autonomousspacec1094560364Major, United States Air ForceApproved for public release; distribution is unlimited
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