Maja Karasalo: 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 Power-Bot 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.