### Optimization and Systems Theory Seminar

Friday, October 16 2009, 11.00, Room 3721, Lindstedtsvägen 25

Maja Karasalo, KTH

E-mail: karasalo at math.kth.se

####
Data Filtering and Control Design for Mobile Robots

In
this thesis, we consider problems connected to navigation and tracking for
autonomous robots under the assumption of constraints on sensors and kinematics.
We study formation control as well as techniques for filtering and smoothing of
noise contaminated input. The scientific contributions of the thesis comprise
five papers.
The focus of the talk will be on papers C, D and E, in which we investigate
theoretical properties and applications for control theoretic smoothing splines.

In
Paper C, we consider the problem of estimating a closed curve in the plane based
on noise contaminated samples. A recursive control theoretic smoothing spline
approach is proposed, that yields an initial estimate of the

curve and subsequently computes refinements of the estimate iteratively.
Periodic splines are generated by minimizing a cost function subject to
constraints imposed by a linear control system. The optimal control

problem is shown to be proper, and sufficient optimality conditions are derived
for a special case of

the problem using Hamilton-Jacobi-Bellman theory.

Paper D continues the study of recursive control theoretic smoothing splines. A
discretization of the problem is derived, yielding an unconstrained quadratic
programming problem. A proof of convexity for the discretized problem is
provided, and the recursive algorithm is evaluated in simulations and
experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia
Robotics.

Finally, in Paper E we explore the issue of optimal smoothing for control
theoretic smoothing splines. The output of the control theoretic smoothing
spline problem is essentially a tradeoff between faithfulness to measurement
data and smoothness. This tradeoff is regulated by the so-called smoothing
parameter. In Paper E, a method is developed for estimating the optimal value of
this smoothing parameter. The procedure is based on general cross validation and
requires no a priori information about the underlying curve or level of noise in
the measurements.

Calendar of seminars
*Last update: September 17, 2009 by
Marie Lundin.
*