Exclusive production of $omega$ mesons was studied at the COMPASS experiment by scattering $160~mathrm{GeV}/mathit{c}$ muons off transversely polarised protons. Five single-spin and three double-spin azimuthal asymmetries were measured in the range of photon virtuality $1~(mathrm{GeV}/mathit{c})^2 < Q^2 < 10~(mathrm{GeV}/mathit{c})^2$, Bjorken scaling variable $0.003 < x_{mathit{Bj}} < 0.3$ and transverse momentum squared of the $omega$ meson $0.05~(mathrm{GeV}/mathit{c})^2 < p_{T}^{2} < 0.5~(mathrm{GeV}/mathit{c})^2$. The measured asymmetries are sensitive to the nucleon helicity-flip Generalised Parton Distributions (GPD) $E$ that are related to the orbital angular momentum of quarks, the chiral-odd GPDs $H_{T}$ that are related to the transversity Parton Distribution Functions, and the sign of the $piomega$ transition form factor. The results are compared to recent calculations of a GPD-based model.
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