To quantitatively evaluate the difference between the ground-truth data and the simulated trajectories, we use the Euclidean distance between two vectors:17\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=||{{\bf{T}}}^{g}-{{\bf{T}}}^{s}||$$\end{document}d=||Tg−Ts||where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{T}}}^{g}=[{T}_{1}^{g},{T}_{2}^{g},\cdots {T}_{n}^{g}],{{\bf{T}}}^{s}=[{T}_{1}^{s},{T}_{2}^{s},\cdots {T}_{n}^{s}]$$\end{document}Tg=[T1g,T2g,⋯Tng],Ts=[T1s,T2s,⋯Tns] are joint trajectories of rotation in one step cycle from the ground truth and simulated result respectively. Tg is computed as the average of all collected trajectories of real ants.