### Doctoral Thesis Defense, Optimization and Systems Theory

Tuesday, November 20, 2001, 10.00, Kollegiesalen, Administration building,
Valhallavägen 79, KTH

**Henrik Rehbinder**

####
State estimation and limited communication control for
nonlinear robotic systems

*
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan
framlägges till offentlig granskning för avläggande av teknologie
doktorsexamen tisdagen den 20 november 2001 kl 10.00 i Kollegiesalen,
Administrationsbyggnaden, Kungliga Tekniska Högskolan, Valhallavägen
79.
*
In this thesis, two different control theoretic topics are studied,
nonlinear observer design for orientation estimation and control
design under limited communication. The specific problems studied originate
from control of mobile robots in difficult terrain, especially walking
robots.

In Paper A, the fusion of rate gyro data and inclinometer data with a
high-gain observer and a time-varying observer is studied. The Euler
angle representation of rigid body motion is used. It is shown that
even in the process of rate gyro offsets and slow inclinometer
dynamics it is possible to derive exponentially convergent attitude
observers with arbitrarily small bounded errors. The high-gain
observer is evaluated experimentally.

In Paper B, rate gyro data and accelerometer data are fused in order
to obtain attitude estimates. Two exponentially convergent observers
are presented. The underlying kinematic model used for the observer
design is global and the state evolves on the unit sphere. The
observers are evaluated experimentally on a walking robot.

In Paper C, the use of inertial sensors and computer vision is
investigated. Orientation estimation is studied and it is shown that
orientation can be estimated in the presence of an unknown
time-varying position. The problem is phrased as an observer problem
for an implicit output system evolving on $SO(3)$. Observability is
studied and a generalization of the unobservable subspace, the
unobservable subgroup, is derived. A locally convergent exponential
observer is presented and the domain of attraction is estimated
numerically. It is shown that position estimation can be formulated as
a linear implicit output problem.

In Paper D, the problem of control design under limited communication
is studied. It is shown how a limited communication channel can be
modeled and how the constraint due to this limitation is incorporated
into the system model. An algorithm for computing optimal
communication schedules and corresponding LQ-controllers is given.

Calendar of seminars

*Last update: November 8, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*