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Berglund, Tomas

Open this publication in new window or tab >>Planning smooth and obstacle-avoiding b-spline paths for autonomous mining vehicles### Berglund, Tomas

### Brodnik, Andrej

### Jonsson, Håkan

### Staffansson, Mats

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); ### Söderkvist, Inge

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_0_j_idt188_j_idt202",{id:"formSmash:j_idt184:0:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2010 (English)In: IEEE Transactions on Automation Science and Engineering, ISSN 1545-5955, E-ISSN 1558-3783, Vol. 7, no 1, p. 167-172Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Computational Mathematics Computer Sciences
##### Research subject

Scientific Computing; Dependable Communication and Computation Systems
##### Identifiers

urn:nbn:se:ltu:diva-5437 (URN)10.1109/TASE.2009.2015886 (DOI)000273133300017 ()2-s2.0-73849111744 (Scopus ID)38ae9f20-38bf-11dd-8721-000ea68e967b (Local ID)38ae9f20-38bf-11dd-8721-000ea68e967b (Archive number)38ae9f20-38bf-11dd-8721-000ea68e967b (OAI)
#####

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#####

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#####

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#####

##### Note

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science. University of Primorska, Slovenia. .

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.

Luleå tekniska universitet.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

We study the problem of automatic generation of smooth and obstacle-avoiding planar paths for efficient guidance of autonomous mining vehicles. Fast traversal of a path is of special interest. We consider four-wheel four-gear articulated vehicles and assume that we have an a priori knowledge of the mine wall environment in the form of polygonal chains. Computing quartic uniform B-spline curves, minimizing curvature variation, staying at least at a proposed safety margin distance from the mine walls, we plan high speed paths.

Validerad; 2010; Bibliografisk uppgift: Paper id:: T-ASE-2008-162; 20080612 (tb)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>snowBOTS: a mobile robot on snow covered ice### Fredriksson, Håkan

### Rönnbäck, Sven

### Berglund, Tomas

### Wernersson, Åke

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); ### Hyyppä, Kalevi

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_1_j_idt188_j_idt202",{id:"formSmash:j_idt184:1:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2007 (English)In: Proceedings of the 13th IASTED International Conference on Robotics and Applications: August 29 - 31, 2007, Würzburg, Germany / [ed] K. Schilling, Anaheim, Calif.: ACTA Press, 2007, p. 222-228Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Anaheim, Calif.: ACTA Press, 2007
##### National Category

Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Industrial Electronics
##### Identifiers

urn:nbn:se:ltu:diva-31828 (URN)61ef13e0-5f9b-11dc-807a-000ea68e967b (Local ID)9780889866850 (ISBN)61ef13e0-5f9b-11dc-807a-000ea68e967b (Archive number)61ef13e0-5f9b-11dc-807a-000ea68e967b (OAI)
##### Conference

IASTED International Conference on Robotics and Applications : 29/08/2007 - 31/08/2007
#####

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#####

##### Projects

CASTT - Centre for Automotive Systems Technologies and Testing
##### Note

Validerad; 2007; 20070910 (hf)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-25Bibliographically approved

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.

We introduce snowBOTs as a generic name for robots working in snow. This paper is a study on using scan ning range measuring lasers towards an autonomous snow cleaning robot, working in an environment consisting al most entirely of snow and ice. The problem addressed here is using lasers for detecting the edges generated by "the snow meeting the road". First the laser data were ﬁltered using his togram/median to discriminate against falling snowﬂakes and small objects. Then the road surface was extracted us ing the range weighted Hough/Radon transform. Finally the left and right edges of the road was detected by thresh olding. Tests have been made with a laser on top of a car driven in an automobile test range just south of the Arctic Circle. Moreover, in the campus area, the algorithms were tested in closed loop with the laser on board a robotized wheelchair.

Open this publication in new window or tab >>A semi-autonomous wheelchair towards user-centered design### Rönnbäck, Sven

### Piekkari, Jouni

### Hyyppä, Kalevi

### Berglund, Tomas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); ### Koskinen, Simo

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_2_j_idt188_j_idt202",{id:"formSmash:j_idt184:2:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2006 (English)In: Computers helping people with special needs: 10th international conference, ICCHP 2006, Linz, Austria, July 11-13, 2006 ; proceedings / [ed] Klaus Miesenberger, Berlin: Encyclopedia of Global Archaeology/Springer Verlag, 2006, p. 701-708Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Berlin: Encyclopedia of Global Archaeology/Springer Verlag, 2006
##### Series

Lecture Notes in Computer Science, ISSN 0302-9743 ; 4061
##### National Category

Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Industrial Electronics
##### Identifiers

urn:nbn:se:ltu:diva-36989 (URN)10.1007/11788713_103 (DOI)adc4e1d0-0509-11df-bae5-000ea68e967b (Local ID)978-3-540-36020-9 (ISBN)adc4e1d0-0509-11df-bae5-000ea68e967b (Archive number)adc4e1d0-0509-11df-bae5-000ea68e967b (OAI)
##### Conference

International Conference on Computers Helping People with Special Needs : 11/07/2006 - 13/07/2006
#####

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#####

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#####

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#####

##### Note

Validerad; 2006; 20100119 (ysko)Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2017-11-25Bibliographically approved

Faculty of Art and Design, University of Lapland, Rovaniemi.

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.

Faculty of Social Science, University of Lapland, Rovaniemi.

Research on assistive technology for impaired and elderly is of great importance and it is intended to grow as society undergoes an age shift in its population. Research on assistive technology leads to the development of aids for individual users. These aids can be made more or less autonomous in order to fit an individuals specific needs. Aids can be designed not only to please a user from a technical perspective, but also from a psychological perspective. Based on knowledge about a user, from for example interviews, the design of an aid can be improved. We present a semi-autonomous wheelchair which can be controlled using head-mounted sensors. Control is also possible by sensors placed on the hand of a user. The wheelchair hand control was tested by a user and the feedback from the user is included. Through an interface suitable for specific users, the wheelchair can perform certain tasks autonomously. One such task is moving to a certain location pointed out by a user looking at a map of the surrounding which is presented on a computer screen. With a user centered perspective based on interviews, direct contact, and knowledge about users, we show results for improving the design of assistive technology.

Open this publication in new window or tab >>Circle sector expansions for on-line exploration### Rönnbäck, Sven

### Berglund, Tomas

### Fredriksson, Håkan

### Hyyppä, Kalevi

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2006 (English)In: 2006 IEEE International Conference on Robotics and Biomimetics: Kunming, China, 17 - 20 December 2006, Piscataway, NJ: IEEE Communications Society, 2006, p. 1227-1232Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Piscataway, NJ: IEEE Communications Society, 2006
##### National Category

Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Industrial Electronics
##### Identifiers

urn:nbn:se:ltu:diva-27658 (URN)10.1109/ROBIO.2006.340103 (DOI)000245907302018 ()2-s2.0-46249089814 (Scopus ID)12c2d210-96bb-11db-8975-000ea68e967b (Local ID)1-424-40570-X (ISBN)12c2d210-96bb-11db-8975-000ea68e967b (Archive number)12c2d210-96bb-11db-8975-000ea68e967b (OAI)
##### Conference

IEEE International Conference on Robotics and Biomimetics : 17/12/2006 - 20/12/2006
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt359",{id:"formSmash:j_idt184:3:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt359",multiple:true});
#####

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#####

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#####

##### Projects

CASTT - Centre for Automotive Systems Technologies and Testing
##### Note

Godkänd; 2006; 20061228 (ysko)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-07-10Bibliographically approved

A novel and effective method denoted circle sector expansion (CSE) is presented that can be used to generate reduced Voronoi diagrams. It is intuitive and can be used to efficiently compute possible paths for a vehicle. The idea is to model free space instead of the features in the environment. It is easy to implement and can be used while a vehicle moves and collects new data of its surrounding. The method is directly applicable and has properties for fast computations of safety margins while at the same time having low complexity. We have successfully implemented the algorithm and its methods and performed real-life tests using an autonomous wheelchair equipped with a range scanning laser, a rate gyro, and wheel-encoders. Tests showed good results for supporting the use of CSE. The results are applicable for example to improve assistive technology for wheelchair users.

Open this publication in new window or tab >>Signature graphs for effective localization### Rönnbäck, Sven

### Berglund, Tomas

### Fredriksson, Håkan

### Hyyppä, Kalevi

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2006 (English)In: 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems: Beijing, China, 9 - 13 October 2006, Piscataway, NJ: IEEE Communications Society, 2006, p. 288-293Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Piscataway, NJ: IEEE Communications Society, 2006
##### National Category

Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Industrial Electronics
##### Identifiers

urn:nbn:se:ltu:diva-29956 (URN)10.1109/IROS.2006.282150 (DOI)000245452400048 ()2-s2.0-34250660455 (Scopus ID)3981b590-d619-11db-8550-000ea68e967b (Local ID)1-424-40258-1 (ISBN)3981b590-d619-11db-8550-000ea68e967b (Archive number)3981b590-d619-11db-8550-000ea68e967b (OAI)
##### Conference

IEEE/RSJ International Conference on Intelligent Robots and Systems : 09/10/2006 - 15/10/2006
#####

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#####

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#####

##### Projects

CASTT - Centre for Automotive Systems Technologies and Testing
##### Note

Godkänd; 2006; 20061228 (ysko)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-07-10Bibliographically approved

We present a novel method for the localization of an autonomous vehicle in two dimensions. Instead of focussing on properties of obstacles, we emphasize the description of free-space. We introduce the concept of signature graphs which is a compact data structure describing available free-space of an environment. It therefore also represents a map of the environment. A signature is an edge in the graph and is defined by seven parameters. An edge indicates that it is possible for the vehicle to move between two graph nodes. The signature graph is flexible and can easily be updated as new information about the environment is collected. We have with an autonomous wheelchair implemented our methods and tests them with successful results.

Open this publication in new window or tab >>Minimum curvature variation B-splines: validation of a path-planning model### Berglund, Tomas

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.### Brodnik, Andrej

### Jonsson, Håkan

### Mrozek, Kent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); ### Staffansson, Mats

### Söderkvist, Inge

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_5_j_idt188_j_idt202",{id:"formSmash:j_idt184:5:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2004 (English)Report (Other academic)
##### Place, publisher, year, edition, pages

Ljubljana, Slovenia: Institute for Mathematics, Physics and Mechanics, 2004. p. 19
##### Series

Preprint series, Institute for Mathematics, Physics and Mechanics, Ljubljana ; IMFM-(2004)-PS-917
##### National Category

Computational Mathematics Computer Sciences
##### Research subject

Scientific Computing; Dependable Communication and Computation Systems
##### Identifiers

urn:nbn:se:ltu:diva-22977 (URN)51c9ea90-38bb-11dd-8721-000ea68e967b (Local ID)51c9ea90-38bb-11dd-8721-000ea68e967b (Archive number)51c9ea90-38bb-11dd-8721-000ea68e967b (OAI)
#####

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##### Note

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.

Luleå tekniska universitet.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Godkänd; 2004; 20080612 (tb)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approvedOpen this publication in new window or tab >>An obstacle-avoiding minimum variation B-spline problem### Berglund, Tomas

### Jonsson, Håkan

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.### Söderkvist, Inge

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2003 (English)In: Proceedings: 2003 International Conference on Geometric Modeling and Graphics, GMAG 2003 ; 16 - 18 July 2003, London, England, Los Alamitos, Calif: IEEE Communications Society, 2003, p. 156-161Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Los Alamitos, Calif: IEEE Communications Society, 2003
##### National Category

Computational Mathematics Computer Sciences
##### Research subject

Scientific Computing; Dependable Communication and Computation Systems
##### Identifiers

urn:nbn:se:ltu:diva-36963 (URN)10.1109/GMAG.2003.1219681 (DOI)000184696400024 ()2-s2.0-84943595578 (Scopus ID)ad094930-c7d5-11db-98d9-000ea68e967b (Local ID)0-7695-1985-7 (ISBN)ad094930-c7d5-11db-98d9-000ea68e967b (Archive number)ad094930-c7d5-11db-98d9-000ea68e967b (OAI)
##### Conference

International Conference on Geometric Modeling and Graphics : 16/07/2003 - 18/07/2003
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_j_idt371",{id:"formSmash:j_idt184:6:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_j_idt371",multiple:true});
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##### Note

Godkänd; 2003; 20070301 (evan)Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

Open this publication in new window or tab >>Epi-convergence of minimum curvature variation B-splines### Berglund, Tomas

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.### Strömberg, Thomas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Jonsson, Håkan

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.### Söderkvist, Inge

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2003 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2003. p. 12
##### Series

Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:14
##### National Category

Mathematical Analysis Computer Sciences Computational Mathematics
##### Research subject

Mathematics; Dependable Communication and Computation Systems; Scientific Computing
##### Identifiers

urn:nbn:se:ltu:diva-23274 (URN)65571df0-2bc6-11dd-8657-000ea68e967b (Local ID)65571df0-2bc6-11dd-8657-000ea68e967b (Archive number)65571df0-2bc6-11dd-8657-000ea68e967b (OAI)
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##### Note

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.

Godkänd; 2003; 20080527 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approvedOpen this publication in new window or tab >>Path-planning with obstacle-avoiding minimum curvature variation B-splines### Berglund, Tomas

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2003 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2003. p. 64
##### Series

Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2003:36
##### National Category

Other Electrical Engineering, Electronic Engineering, Information Engineering
##### Research subject

Industrial Electronics
##### Identifiers

urn:nbn:se:ltu:diva-17432 (URN)360c7a70-bdfb-11db-9be7-000ea68e967b (Local ID)360c7a70-bdfb-11db-9be7-000ea68e967b (Archive number)360c7a70-bdfb-11db-9be7-000ea68e967b (OAI)
#####

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##### Note

Godkänd; 2003; 20070216 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

We study the general problem of computing an obstacle-avoiding path that, for a prescribed weight, minimizes the weighted sum of a smoothness measure and a safety measure of the path. We consider planar curvature-continuous paths, that are functions on an interval of a room axis, for a point-size vehicle amidst obstacles. The obstacles are two disjoint continuous functions on the same interval. A path is found as a minimizer of the weighted sum of two costs, namely 1) the integral of the square of arc- length derivative of curvature along the path (smoothness), and 2) the distance in L2 norm between the path and the point-wise arithmetic mean of the obstacles (safety). We formulate a variant of this problem in which we restrict the path to be a B-spline function and the obstacles to be piece-wise linear functions. Through implementations, we demonstrate that it is possible to compute paths, for different choices of weights, and use them in practical industrial applications, in our case for use by the ore transport vehicles operated by the Swedish mining company Luossavaara-Kiirunavaara AB (LKAB). Assuming that the constraint set is non-empty, we show that, if only safety is considered, this problem is trivially solved. We also show that properties of the problem, for an arbitrary weight, can be studied by investigating the problem when only smoothness is considered. The uniqueness of the solution is studied by the convexity properties of the problem. We prove that the convexity properties of the problem are preserved due to a scaling and translation of the knot sequence defining the B-spline. Furthermore, we prove that a convexity investigation of the problem amounts to investigating the convexity properties of an unconstrained variant of the problem. An empirical investigation of the problem indicates that it has one unique solution. When only smoothness is considered, the approximation properties of a B-spline solution are investigated. We prove that, if there exists a sequence of B-spline minimizers that converge to a path as the number of B-spline basis functions tends to infinity, then this path is a solution to the general problem. We provide an example of such a converging sequence.

Open this publication in new window or tab >>The problem of computing an obstacle-avoiding minimum variation B-spline### Berglund, Tomas

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.### Jonsson, Håkan

Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.### Söderkvist, Inge

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2003 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2003
##### Series

Technical report / Luleå University of Technology, ISSN 1402-1536 ; 2003:06
##### National Category

Computational Mathematics Computer Sciences
##### Research subject

Scientific Computing; Dependable Communication and Computation Systems
##### Identifiers

urn:nbn:se:ltu:diva-23772 (URN)859d9350-2b44-11dd-8657-000ea68e967b (Local ID)859d9350-2b44-11dd-8657-000ea68e967b (Archive number)859d9350-2b44-11dd-8657-000ea68e967b (OAI)
#####

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#####

##### Note

Godkänd; 2003; 20080526 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved

We study the problem of computing a planar curve restricted to lie between two given polygonal chains such that the integral of the square of arc- length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.