### Doctoral Thesis Defense, Optimization and Systems Theory

Friday, April 14, 2000, 10.00, Kollegiesalen, Administration building,
Valhallavägen 79, KTH

**Magnus Egerstedt**

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Motion planning and control of mobile robots

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Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan
framlägges till offentlig granskning för avläggande av teknologie
doktorsexamen fredagen den 14 april 2000 kl 10.00 i Kollegiesalen,
Administrationsbyggnaden, Kungl Tekniska Högskolan, Valhallavägen 79.
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In this thesis various control theoretic questions from the field of
autonomous robotics are investigated. Those questions range from
motion planning and control to modeling and analysis of complex
control systems based on hybrid automata theory.

A path planning method is proposed for generating smoothing splines
that are optimal with respect to an energy functional at the same time
as they drive the output of a given, linear control system close to
desired waypoints. These curves are furthermore numerically
inexpensive to produce, which suggests that they can be used on-line
for refining or updating paths as a reaction to unexpected events in
the environment.

A stable and model-independent control strategy for making mobile
platforms track reference paths is also proposed. The control
algorithm is based on a parameterization of the reference trajectory
in such a way that the motion of the point on the trajectory, tracked
by the robot, is governed by a differential equation containing error
feedback. This makes the method robust to disturbances and measurement
errors.

The third topic covered in this thesis concerns the integration of
continuous controllers into one, complex control system. These types
of complex control architectures can for instance be found in a
behavior based robot system, where different continuous robot
behaviors are influenced by events in the environment or controlled
transitions between different behaviors. This combination of
continuous and discrete phenomena makes it possible to model the
system as a hybrid automaton. It is furthermore shown in this thesis
how chattering between different behaviors can be avoided within this
framework by exploiting regularization techniques that basically
involves adding extra nodes to the hybrid automaton.

Calendar of seminars

*Last update: March 30, 2000 by
Anders Forsgren,
anders.forsgren@math.kth.se.
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