Infinitesimal Weak Rigidity and Stability Analysis on Three-Agent Formations

Kwon, Seong-Ho; Trinh, Minh Hoang; Oh, Koog-Hwan; Zhao, Shiyu; Ahn, Hyo‐Sung

doi:10.23919/sice.2018.8492617

Cited by 20 publications

(19 citation statements)

References 16 publications

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“…In addition, we have d 12 ‰ 0 and d 13 ‰ 0. Substituting the correct bearing vectors g 12 " g ‹ 12 and g 13 " g ‹ 13 in the dynamics of R1 and rearranging the terms result in (11) with coefficients in (12). Next, we consider moving configurations.…”

Section: The (1d2b) Setup With Signed Area Control Termmentioning

confidence: 99%

“…Recently, approaches on realizing a formation shape using a mixed set of constraints have been considered. In [12], distance and angle constraints are employed; the paper [4] considers the combination of distance and bearing constraints, while the work in [11] use distance, bearing, and angle constraints to describe the desired formation shape. Furthermore, a series of works [1,7,16,17] focus on the combination of distance and signed area constraints.…”

Section: Introductionmentioning

confidence: 99%

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Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

Chan,

Jayawardhana,

de Marina

2021

Preprint

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This paper focuses on securing a triangular shape (up to translation) for a team of three mobile robots that uses heterogeneous sensing mechanism. Based on the available local information, each robot employs the popular gradient-based control law to attain the assigned individual task(s). In the current work, robots are assigned either distance and signed area task(s) or bearing task(s). We provide a sufficient condition on the gain ratio R Ad between the signed area and the distance control term such that the desired formation shape, an isosceles triangle, is reached from all feasible starting positions. Numerical simulations are provided to support the theoretical analyses.

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Section: The (1d2b) Setup With Signed Area Control Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

Chan,

Jayawardhana,

de Marina

2021

Preprint

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“…Different from [15], in this article, the desired formation shape is realized using only angle measurements. In addition, weak rigidity with mixed distance and angle constraints has been investigated in [22]- [24], under which the formation control algorithms are also designed for agents by using the measurements of relative position.…”

mentioning

confidence: 99%

Angle Rigidity and Its Usage to Stabilize Multiagent Formations in 2-D

Chen

Cao

2021

IEEE Trans. Automat. Contr.

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Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multipoint framework, named "angularity", consisting of a set of nodes embedded in a Euclidean space, and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame, and are signed according to the counter-clockwise direction. Here, angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate, or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient conditions for infinitesimal angle rigidity by checking the rank of an angularity's rigidity matrix. We develop a combinatorial necessary condition for infinitesimal minimal angle rigidity. Using the developed theories, a formation stabilization algorithm is designed for a robotic team to achieve an angle rigid formation, in which only angle measurements are needed. Simulation examples demonstrate the advantages of the proposed angle-only formation control approach.

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“…Recently, approaches to realize a desired geometrical shape using a mixed set of constraints have also been considered. In [31], distance and angle constraints have been employed; the paper in [10] has considered the combination of distance and bearing constraints, while the work in [29] has used distance, bearing, and angle constraints to provide a description of the desired shape. Furthermore, a series of works [3,15,44,45] has focused on the combination of distance and signed area constraints.…”

Section: Review Of Multi-agent Formation Controlmentioning

confidence: 99%

“…Gradient-based control laws are a popular approach for realizing the formation shape specified by distance [48] or bearing constraints [53]. A formation shape can also be realized by a set of mixed constraints; see, among others, [9,29,31]. In distance-constrained and also distance-and-angle-constrained formation control, flip and flex ambiguities occur.…”

Section: Introductionmentioning

confidence: 99%

Securing and Maneuvering Heterogeneous Mobile Robot Formations: Distributed Control Design and Stability Analysis

Chan¹

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At last! The train ride labeled 'PhD' is coming to an end. Let me sit here for some more moments to recall the past 4`years while the train is at the destination, but not yet standing still. While doing so, allow me to address a few words to some particular individuals.The first on my list is Bayu. Bayu, terima kasih! I am grateful you have taken me under your wing in the past period. You have given me freedom to explore but also make sure I stay on the rails. You always have a smile on your face during our meetings which were not limited to only discussing research. I also thank you for the support you have shown me when I asked you for permission to conduct additional teaching duties after my involvement in the course 'Signals & Systems'.Dear Jacquelien, I am grateful to you for the discussions we had during the start of my PhD which led to Chapter 6 of the thesis and the good time we spent in Hong Kong! Needless to mention, the annual group outing we have and the 'nieuwjaarsrolletjes' with cream you bring at the start of each year.Gracias también to Hector with whom I have collaborated on different chapters of the thesis. Hector, your cheerful appearance during our e-meetings made them light-hearted.Who is next on the list? Yes, it is you Frederika, my favorite secretary! Dankjewel 1 for bringing a smile to my face whenever I see you. I look back with joy to starting the day in the secretary office with you and the other colleagues while having a sip of coffee or tea, and I will remember the stories you shared with me.I would like to express gratitude to my reading committee members. Thank you Ming Cao, Kanat Ç amlibel, and Dimos Dimarogonas for your time and effort.To all my former and current colleagues at DTPA, SMS, and ODS, thanks for having me! I am happy to be in your midst and occasionally also enjoy the group dynamics evolving from a spectator's view. Special mention goes to Xiaodong, 1 'u' is not preferred :) vii Hadi, Lulu, Hongyu, Wouter and of course my office mates Zaki, Bao, Carmen, Tábitha, and Liangming.I came to Groningen with the knowledge that I have to start from zero in terms of building a social circle. I am fortunate to say I will still be connected to Groningen by means of the following individuals: Jeroen, Jan, Mark, and Michel. Each of you has been a source of support when I needed to talk to somebody and you have allowed me to focus on stuff non-RUG related.I would also like to address some words to Ignaas Jimidar and Cyrano Vaseur, the two friends I have met since our Bachelor period in Suriname and with whom I enjoyed my Master period in Enschede. Thank you both for agreeing to be my paranymphs and more than that, thanks for being my friend. While we are some train hours apart, we always have lots to discuss when being together. My gratitude also to all the other people whom I have not mentioned.爸爸，妈妈，姐姐，很感谢你们给我机会和自由去做我想做的事，走自己的路。爸爸，妈妈, 儿子快毕业了，您们不需要操心了。 Last on my list is Maarten. Dankjewel for having my back, and for regularly pulling me out of my work environment to discover the...

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Infinitesimal Weak Rigidity and Stability Analysis on Three-Agent Formations

Cited by 20 publications

References 16 publications

Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

Angle Rigidity and Its Usage to Stabilize Multiagent Formations in 2-D

Securing and Maneuvering Heterogeneous Mobile Robot Formations: Distributed Control Design and Stability Analysis

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