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Data Filtering and Control Design for Mobile Robots
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. (Optimeringslära och Systemteori, Optimization and Systems Theory)
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, we consider problems connected to navigation and tracking for autonomousrobots under the assumption of constraints on sensors and kinematics. We study formation controlas 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 rangesensors. The resulting formation is a leader-follower system, where each follower agent tracksits leader agent at a specified angle and distance. No inter-agent communication is required toexecute the controls. A switching Kalman filter is introduced for active sensing, and robustnessis demonstrated in experiments and simulations with Khepera II robots.In Paper B, an optimization-based adaptive Kalman filteringmethod is proposed. The methodproduces an estimate of the process noise covariance matrix Q by solving an optimization problemover a short window of data. The algorithm recovers the observations h(x) from a system˙ x = f (x), y = h(x)+v without a priori knowledge of system dynamics. The algorithm is evaluatedin simulations and a tracking example is included, for a target with coupled and nonlinearkinematics. In Paper C, we consider the problem of estimating a closed curve in R2 based on noisecontaminated samples. A recursive control theoretic smoothing spline approach is proposed, thatyields an initial estimate of the curve and subsequently computes refinements of the estimateiteratively. Periodic splines are generated by minimizing a cost function subject to constraintsimposed by a linear control system. The optimal control problem is shown to be proper, andsufficient 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 discretizationof the problem is derived, yielding an unconstrained quadratic programming problem. Aproof of convexity for the discretized problem is provided, and the recursive algorithm is evaluatedin 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 smoothingsplines. 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 socalled smoothing parameter. In Paper E, a method is developed for estimating the optimal valueof this smoothing parameter. The procedure is based on general cross validation and requires noa priori information about the underlying curve or level of noise in the measurements.

Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , xii, 30 p.
Series
Trita-MAT. OS, ISSN 1401-2294
Keyword [en]
formation control, tracking, nonlinear control, optimal smoothing, adaptive filtering
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-11011ISBN: 978-91-7415-432-0 (print)OAI: oai:DiVA.org:kth-11011DiVA: diva2:236785
Public defence
2009-10-22, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100722Available from: 2009-10-01 Created: 2009-09-08 Last updated: 2010-07-22Bibliographically approved
List of papers
1. Robust Formation Control using Switching Range Sensors
Open this publication in new window or tab >>Robust Formation Control using Switching Range Sensors
2010 (English)In: Robotics and Autonomous Systems, ISSN 0921-8890, E-ISSN 1872-793X, Vol. 58, no 8, 1003-1016 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, control algorithms are presented for formation keeping and path followingfor non-holonomic platforms. The controls are based on feedback from onboard directional range sensors, and a switching Kalman filter is introduced for active sensing.Stability is analyzed theoretically and robustness isdemonstrated in experiments and simulations.

Keyword
Formation control, multi-agent systems, path following, sensor-based feedback control
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11142 (URN)10.1016/j.robot.2010.03.015 (DOI)000280511200007 ()2-s2.0-80052702996 (Scopus ID)
Note
QC 20100722Available from: 2009-10-01 Created: 2009-09-22 Last updated: 2017-12-13Bibliographically approved
2. An Optimization Approach to Adaptive Kalman Filtering
Open this publication in new window or tab >>An Optimization Approach to Adaptive Kalman Filtering
2009 (English)In: 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009; Shanghai; 15 December 2009 through 18 December 2009; Category number 09CH38112; Code 79678, 2009, 2333-2338 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, 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 shortwindow 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. Potential applications include target tracking using a network of nonlinear sensors, servoing, mapping, and localization. The algorithm isdemonstrated in simulations on a tracking example for a target with coupled and nonlinear kinematics.Simulations indicate superiority overa standard MMAE algorithm for a large class of systems.

Keyword
Adaptive filtering, optimization, tracking
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11145 (URN)10.1109/CDC.2009.5400877 (DOI)000336893602136 ()2-s2.0-77950856267 (Scopus ID)
Conference
Joint 48th IEEE Conference on Decision and Control (CDC) / 28th Chinese Control Conference (CCC), Shanghai, PEOPLES R CHINA
Note

Uppdaterad till från manuskript till konferensbidrag: 20100722 QC 20100722

Available from: 2009-10-01 Created: 2009-09-22 Last updated: 2015-06-10Bibliographically approved
3. Periodic and Recursive Control Theoretic Smoothing Splines
Open this publication in new window or tab >>Periodic and Recursive Control Theoretic Smoothing Splines
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, a recursive control theoretic smoothing spline approach is proposed forreconstructing a closed contour.Periodic splines are generated by minimizing a cost function subjectto constraints imposed by a linear control system. The optimal controlproblem is shown to be proper, andsufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.

The filtering effect of the smoothing splines allows for usageof noisy sensor data. An important feature of the method is thatseveral data sets for the same closed contour can be processedrecursively so that the accuracy is improved stepwiseas new data becomes available.

Keyword
Smoothing splines, optimal control, Hamilton-Jacobi-Bellman theory, periodic solutions
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11147 (URN)
Note
QC 20100722Available from: 2009-10-01 Created: 2009-09-22 Last updated: 2010-07-22Bibliographically approved
4. Contour Reconstruction using Recursive Smoothing Splines - Algorithms and Experimental Validation
Open this publication in new window or tab >>Contour Reconstruction using Recursive Smoothing Splines - Algorithms and Experimental Validation
2009 (English)In: Robotics and Autonomous Systems, ISSN 0921-8890, E-ISSN 1872-793X, Vol. 57, no 6-7, 617-628 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, a recursive smoothing splineapproach for contour reconstruction is studied and evaluated.  Periodic smoothing splines areused by a robot to approximate the contour of encountered obstaclesin the environment.  The splines are generated through minimizing acost function subject to constraints imposed by a linear controlsystem and accuracy is improved iteratively using a recursive splinealgorithm.  The filtering effect of the smoothing splines allows forusage of noisy sensor data and the method is robust with respect to odometrydrift. The algorithm is extensively evaluated in simulationsfor various contours and in experiments using a SICK laser scanner mounted on a PowerBot fromActivMedia Robotics

Keyword
mapping, optimal control, recursive smoothing splines, implementation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11148 (URN)10.1016/j.robot.2009.01.003 (DOI)000271434100005 ()2-s2.0-67349156757 (Scopus ID)
Note
Uppdaterad från manuskript till artikel: 20100722 QC 20100722Available from: 2009-10-01 Created: 2009-09-22 Last updated: 2017-12-13Bibliographically approved
5. An estimated general cross validation function for periodic control theoretic smoothing splines
Open this publication in new window or tab >>An estimated general cross validation function for periodic control theoretic smoothing splines
2010 (English)In: Lecture notes in control and information sciences, ISSN 0170-8643, E-ISSN 1610-7411, Vol. 398, 95-104 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, a method is developed for estimating the optimal smoothing parameter for periodic control theoretic smoothing splines.The procedure is based on general cross validation (GCV) and requires no a priori information about the underlyingcurve or level of noise in the measurements.The optimal smoothin parameter is the minimizer of a GCV cost function, which is derived based on a discretizationof the L2 smoothing problem for periodic control theoretic smoothing splines.

Keyword
general cross validation, optimal smoothing, influence matrix, periodic control theoretic smoothing splines
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-11150 (URN)10.1007/978-3-540-93918-4_9 (DOI)000281198800009 ()2-s2.0-77950266700 (Scopus ID)
Note
Tidigare titel: An Estimated GCV Function for Periodic Control Theoretic Smoothing Splines Uppdaterad från manuskript till artikel: 20100722 QC 20100722Available from: 2009-10-01 Created: 2009-09-22 Last updated: 2017-12-13Bibliographically approved

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