### Thesis defense in Optimization and Systems Theory Thursday, October 22 2009, 10.00, Room F3, Lindstedtsvägen 26

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. In Paper A, we propose three cascaded, stabilizing formation controls for multi-agent systems. We consider platforms with non-holonomic kinematic constraints and directional range sensors. The resulting formation is a leader-follower system, where each follower agent tracks its leader agent at a specified angle and distance. No inter-agent communication is required to execute the controls. A switching Kalman filter is introduced for active sensing, and robustness is demonstrated in experiments and simulations with Khepera II robots. In Paper B, an optimization-based adaptive Kalman filtering method is proposed. The method produces an estimate of the process noise covariance matrix $Q$ by solving an optimization problem over a short window of data. The algorithm recovers the observations $h(x)$ from a system $\dot x = f(x),~y = h(x) + v$ without a priori knowledge of system dynamics. The algorithm is evaluated in simulations and a tracking example is included, for a target with coupled and nonlinear kinematics. In Paper C, we consider the problem of estimating a closed curve in $\mathbb{R}^2$ 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 \textit{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 18, 2009 by Marie Lundin.