相关论文: Dual Quaternion Matrices in Multi-Agent Formation …

This paper studies the integrated position and attitude control problem for multi-agent systems of 3D rigid bodies. While the state-of-the-art method in [Olfati-Saber and Murray, 2004] established the theoretical foundation for rigid-body…

We propose a supplement matrix method for computing eigenvalues of a dual Hermitian matrix, and discuss its application in multi-agent formation control. Suppose we have a ring, which can be the real field, the complex field, or the…

Dual quaternion matrices have important applications in multi-agent formation control. In this paper, we first address the concept of spectral norm of dual quaternion matrices. Then, we introduce a von Neumann type trace inequality and a…

Dual quaternions can represent rigid body motion in 3D spaces, and have found wide applications in robotics, 3D motion modelling and control, and computer graphics. In this paper, we introduce three different right linear independency for a…

We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…

Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…

We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field…

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the…

Dual quaternion/complex matrices have important applications in brain science and multi-agent formation control. In this paper, we first study some basic properties of determinants of dual complex matrices, including Sturm theorem and…

Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half…

Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and…

This paper proposes a novel formation maneuver control method for both 2-D and 3-D space, which enables the formation to translate, scale, and rotate with arbitrary orientation. The core innovation is the novel design of weights in the…

This paper presents a control strategy based on dual quaternions for the coordinated formation flying of small UAV groups. A virtual structure is employed to define the desired formation, enabling unified control of its position,…

We consider the localization problem between agents while they run a formation control algorithm. These algorithms typically demand from the agents the information about their relative positions with respect to their neighbors. We assume…

We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…

In formation control, triangular formations consisting of three autonomous agents serve as a class of benchmarks that can be used to test and compare the performances of different controllers. We present an algorithm that combines the…

The poses of $m$ robotics in $n$ time points may be represented by an $m \times n$ dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices. We introduce right and left eigenvalues for square dual…

In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications…

We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…

The concept of the integrated adjacency matrix for mixed graphs was first introduced in [9], where its spectral properties were analyzed in relation to the structural characteristics of the mixed graph. Building upon this foundation, this…