## 2 Related Works  
Table 1 offers a summary categorization of the relevant literature. Discrete DLO models tackle the problem by breaking down the structure into a number of rigid rod elements of finite length, which can be physically simulated as pendulums, curve segments or by a network of masses and springs, so called lumped-mass models. These models require the representation of forces and moments at each element so that it is possible to model the motion of each and all of them. A study comparing several modeling methods concluded that the lumped-mass representation is the most versatile method, despite the large amount of computational resources required for its implementation [22]. Alternatively, some approaches propose the modeling of the DLO as a chain of rigid links allowing the differentially flat control [23] of the team carrying the DLO transportation under quasi-stationary conditions [15]. Nevertheless, comparative studies on cable structure modeling show the superior numerical efficiency of catenaries for the study of different force situations, vibrations and torsions [24; 25; 26]. Catenaries are widely accepted as accurate cable models, for instance, in mooring cable simulations [32; 36; 39], and in the design of civil cable structures [28; 50]. Continuous cable \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & **Year** & **DvC** & **Paradigm** & **Applications** \\ \hline [27] & 1971 & continuous & catenary & cable towed by aircraft \\ \hline [22] & 1973 & both & Analytical methods (survey) & Ocean Science \\ \hline [28] & 1981 & continuous & catenary & cable structures \\ \hline [29] & 1995 & continuous & catenary & cable towed by aircraft \\ \hline [30] & 1999 & both & catenary vs. rod elements & – \\ \hline [31] & 2000 & continuous & catenary & underwater towing \\ \hline [32] & 2001 & continuous & catenary & ocean sciences, mooring \\ \hline [33] & 2001 & continuous & catenary & underwater towing \\ \hline [24] & 2006 & continuous & catenary & designs of nets of cables \\ \hline [34] & 2007 & continuoys & rigid link & tethered UAV \\ \hline [35] & 2008 & continuous & parabola & cable structures \\ \hline [36] & 2008 & continuous & catenary & ocean sciences, mooring \\ \hline [37] & 2009 & continuous & rigid link & cooperating UAV payload transport \\ \hline [38] & 2010 & continuous & rigid link & cooperating UAV payload transport \\ \hline [39] & 2012 & continuous & catenary & cable-driven parallel robot \\ \hline [40] & 2012 & continuous & rigid link & cooperating UAV payload transport \\ \hline [41] & 2013 & continuous & rigid link & tethered UAV \\ \hline [42] & 2013 & continuous & catenary & cable-driven parallel robot \\ \hline [43] & 2015 & continuous & rigid link & tethered surveillance UAV \\ \hline [44] & 2015 & discrete & series of rigid links & cooperating UAV payload transport \\ \hline [18; 45] & 2015, 2017 & continuous & catenary & DLO transportation by \(n\geq 2\) UAVs \\ \hline [46] & 2016 & continuous & catenary & tethered UAV \\ \hline [47] & 2017 & continuous & catenary & tethered UAVs \\ \hline [48] & 2017 & continuous & catenary & cable transportation by 2 UAVs \\ \hline [25] & 2018 & continuous & catenary & suspension bridges \\ \hline [26] & 2018 & continuous & catenary & suspension bridges \\ \hline [49] & 2018 & continuous & catenary and parabola & cable vibrations \\ \hline [15] & 2020 & discrete & chain of rigid links & hose transportation by 2 UAVs \\ \hline \end{tabular}
\end{table} 
Table 1: Summary comparison of DLO related research. DvC = Discrete versus continuous model. modeling by catenaries is more accurate and less computationally demanding [30] than discretization approaches.