Stabilisation of infinitesimally rigid formations of multi-robot networks

Distributed formation stabilization for mobile agents using virtual tensegrity structures

“…Even though a wide range of issues have been studied, and hence several theoretical frameworks have been established to design control strategies, see, for example, [4] [5] establishing estimation strategy for Euler-Lagrange systems with partial states available, [6] [7] using matrix theory and graph theory, [8] based on gradient-descent control approach, graph rigidity theory [9][10], networked small-gain theory [11], sample-data for circle formation [12], to name a few, it should be noted that the desired formation shape can only be guaranteed to be locally stable in most of the research. In particular, based on the graph rigidity approach, it is challenging to coordinate a group of mobile robots globally converging to the prescribed formation [13].…”

Bearing-only formation control using an SE(2) rigidity theory

“…The vector χ(V) ∈ SE (2) |V| is the stacked position and attitude vector for the complete framework. We also denote by χ x p ∈ R |V| (χ y p ) as the x-coordinate (y-coordinate) vector for the framework configuration.…”

“…Recently, there has been a growing interest in formation control problems using relative bearing sensing. Similar to problems in distance-constrained formation control [2]- [7], bearingconstrained formations employ a bearing rigidity theory (also referred to as parallel rigidity) for analysis. Whereas rigidity theory is useful for maintaining formations specified by fixed inter-agent distances, bearing rigidity attempts to keep the bearing vector between neighboring agents constant (with no constraints on the scale of the formation).…”

Leader–follower formation via complex Laplacian

“…Such an approach can be naturally applied to undirected graphs using the concept of graph rigidity (Olfati-Saber and Murray, 2002a;Eren et al, 2002;Krick et al, 2009), in which two neighboring agents work together to reach the specific distance between them. For directed graphs, a further concept termed persistence is introduced to characterize a planar formation Yu et al, 2007).…”

“…Roughly, three main approaches to formation control have been discussed in recent literature. The first approach describes a formation in terms of inter-agent distance measures (Eren et al, 2002;Yu et al, 2007;Hendrickx et al, 2007;Bai et al, 2008) and uses gradient descent control laws resulted from distance-based artificial potentials (Olfati-Saber and Murray, 2002a;Cao et al, 2008;Yu et al, 2009;Krick et al, 2009;Cao et al, 2011). The second approach describes a formation in terms of inter-agent bearing measures (Eren, 2007) and uses angle only control laws (Basiri et al, 2010;Guo et al, 2011).…”