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Multi-Aerial-Robot Planning
Published in Yasmina Bestaoui Sebbane, Multi-UAV Planning and Task Allocation, 2020
If n aerial robots communicate according to a time-invariant undirected communication graph G = (I, E) where I = {1,..., n}, E = {(i, j)∈ I × I|i and j communicate } and Ni = {j ∈ I|(i, j) ∈ E} is the set of neighbors of node I. A path graph is a graph in which there are only nodes of degree 2 except for two nodes of degree 1. The nodes of degree 1 are called external nodes and denoted 1 and n, while the others are called internal nodes [438]. A cycle graph is a graph in which all the nodes have degree 2. The aerial robots are modeled as single integrators running on a consensus algorithm based on a Laplacian control law [76]. The continuous time dynamics of the agents are given by x˙i(t)=-∑j∈Nixi(t)-xj(t)i∈(1,…,n)
Graphs with logarithmic scales
Published in John Bird, Basic Engineering Mathematics, 2017
Since p=cvn $ p = cv^{n} $ , then lgp=nlgv+lgc $ \lg p = n\; \lg v + \lg c $ , which is of the form Y=mX+c $ Y\,{=}~mX + c $ , showing that to produce a straight line graph lgp $ \lg p $ is plotted vertically against lg v horizontally. The co-ordinates are plotted on ‘log 3 cycle×2 $ \,\times 2 $ cycle’ graph paper as shown in Fig. 4. With the data expressed in standard form, the axes are marked in standard form also. Since a straight line results the law p=cvn $ p = cv^{n} $ is verified.
Introduction to Graph Models
Published in Jonathan L. Gross, Jay Yellen, Mark Anderson, Graph Theory and Its Applications, 2018
Jonathan L. Gross, Jay Yellen, Mark Anderson
definition: A cycle graph is a single vertex with a self-loop or a simple graph C with |VC| = |EC| that can be drawn so that all of its vertices and edges lie on a single circle. An n-vertex cycle graph is denoted Cn.
6-DOF consensus control of multi-agent rigid body systems using rotation matrices
Published in International Journal of Control, 2022
Mohammad Maadani, Eric A. Butcher
Suppose there are three rigid bodies with a cycle graph. One non-consensus equilibrium for this configuration is 120 rotation about a single axis (e.g. x-axis ) between each pair of the agents. As shown in Figure 9, the initial relative rotations about x-axis do not result in consensus because of the symmetric orientation of the agents. This configuration causes the summation in (29) be equal to zero although is not equal to zero individually. However, by perturbing the initial attitude of agent 2, the orientation of the agents is no longer symmetric, hence, the rigid bodies reach consensus, as depicted in the right plot of Figure 9. Two different values of 121 and are considered as the initial perturbation of agent 2 where the latter causes a larger settling time.
Dependability analysis of instrumented linear static systems based on their observability
Published in International Journal of Systems Science: Operations & Logistics, 2019
In this example, cycles C1, C2, C3 and C4 are independent and form a basis of fundamental cycles. Two fundamental cycles sharing at least one edge can be combined, by removing the common edge, to produce a new cycle. In that way, eight new cycles C5, C6, C7, C8, C9, C10, C11 and C12 are produced from the previous four fundamental cycles. For example, C5 is obtained from the combination of C1 and C2 by removing arc 3. The cycle matrix can be deduced from the cycle graph, where the lines correspond to cycles and columns to the variables (Table 1). The column Nmc of this table gives number of measured variables for each cycle. Measured variables are reported in bold type.
Monitoring edge-geodetic numbers of convex polytopes and four networks
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Ao Tan, Wen Li, Xiumin Wang, Xin Li
Given an n-cycle graph , for n = 3 and , . Moreover, . For n = 3 and , with the vertices of from to , the set is a MEG-set of .