Dual Quaternion Laplacian Matrix and Formation Control
arxiv(2024)
摘要
The dual quaternion Laplacian matrix of desired relative configurations in
multi-agent formation control is similar to the classical unweighted Laplacian
matrix via a dual quaternion diagonal unitary matrix. Its eigenvalues are all
positive numbers except one zero eigenvalue. A unit dual quaternion vector is a
desired formation vector if and only if it is in the null space of this dual
quaternion Laplacian matrix. We study a control law based upon dual quaternion
Laplacian. We also show that pairwise asymptotical stability can be reduced to
rank-one asymptotical stability.
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