Title: Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach,
Abstract: In the multi-agent systems setting, this paper addresses continuous-time
distributed synchronization of columns of rotation matrices. More precisely, k
specific columns shall be synchronized and only the corresponding k columns of
the relative rotations between the agents are assumed to be available for the
control design. When one specific column is considered, the problem is
equivalent to synchronization on the (d-1)-dimensional unit sphere and when all
the columns are considered, the problem is equivalent to synchronization on
SO(d). We design dynamic control laws for these synchronization problems. The
control laws are based on the introduction of auxiliary variables in
combination with a QR-factorization approach. The benefit of this
QR-factorization approach is that we can decouple the dynamics for the k
columns from the remaining d-k ones. Under the control scheme, the closed loop
system achieves almost global convergence to synchronization for quasi-strong
interaction graph topologies.