Model Abstraction in Dynamical Systems: Application to Mobile Robot Control

To reduce complexity of system analysis and control design, simplified models that capture the behavior of interest in the original system can be obtained. These simplified models, called abstractions, can be analyzed more easily than the original complex model. Hierarchies of consistent abstractions can significantly reduce the complexity in determining the reachability properties of nonlinear systems. Such consistent hierarchies of reachability-preserving nonlinear abstractions are considered for the robotic car. Not only can these abstractions be analyzed with respect to some behavior of interest, they can also be used to transfer control design for the complex model to the simplified model. In this work, the abstraction is applied to the car/unicycle system. Working towards control design, it is seen that there are certain classes of trajectories that exist in the rolling disk system that cannot be achieved by the robotic car. In order to account for these cases, the new concepts of traceability and &#949-traceability are introduced. This work also studies the relationship between the evolution of uncertain initial conditions in abstracted control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. Abstracted control systems with stochastic initial conditions show the same behavior as systems with deterministic initial conditions. A conservation law is applied to the probability density function (pdf) requiring that the area under it be unity. Application of the conservation law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Department dc:contributor.department

Electrical and Computer Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Mellodge, Patricia

Chair dc:contributor.committeechair

• Kachroo, Pushkin

Committee members dc:contributor.committeemember

• Day, Martin V.
• Stilwell, Daniel J.
• Baumann, William T.
• Abbott, A. Lynn

• abstraction
• traceability
• mobile robots
• nonholonomic systems
• feedback control

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05172007-112915

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/27758