Dynamics Modeling of a Multi-UAV Slung Load System Using a Discrete-Link Cable Approach

Harvey Merton; Ian W. Hunter

cs.ROOct 5, 2026

Dynamics Modeling of a Multi-UAV Slung Load System Using a Discrete-Link Cable Approach

Authors: Harvey Merton, Ian W. Hunter

Organizations: The authors are with the BioInstrumentation Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America

Abstract

A common assumption to simplify the problem of controlling a multi-UAV slung load system (MUSLS) is that the flexible cables can be modeled as massless rigid rods. In this work, we propose an alternative Euler-Newton derived dynamical model which uses a series of rigid links to model the flexible cables. The model is specifically designed to allow efficient simulation using Featherstone's articulated body algorithm. We perform real-world validation of this model on gentle, aggressive, and tension-engagement maneuvers and run a parameter sweep to determine the number of links, joint damping, and joint friction to achieve the greatest model fidelity. The model closely matches real-world flight data with mean load translation errors below 132 mm (5.5% of the cable length) and orientation errors below 11.4 degrees. We make the real-world flight data publicly available for the development of future cable models.

Figures & tables

Fig. 1: A multi-UAV slung load system using a discrete-link cable model. This example features $p=3$ drones, where each cable attaching the $i^{\text{th}}$ drone to the load has $n_{i}$ links. The symbols used are defined in Section II .

Fig. 2: A model for cable $i$ comprised of $n_{i}$ cylindrical links each with mass $m_{ij}$ , length $l_{ij}$ and inertia $\bm{J}_{ij}$ . The labeled joint axes are fixed at the end of each link, while the purple axis represents a generic axis around which link $j+1$ can rotate relative to link $j$ using a universal joint.

Fig. 3: Key elements of a three-quadrotor MUSLS in simulation (left) and the real world (right).

Fig. 4: Block diagram of the full MUSLS used for testing the dynamics model. Each drone has an onboard lower-level pose controller and state estimator that closes the loop with an individual drone’s dynamics. The drones dynamics are coupled by the load and cables to form the full MUSLS. Measured quantities are indicated with $\overset{\sim}{.}$ , while estimated quantities are indicated with $\hat{\cdot}$ .

Load
Mass $m_{L}$ ( $\mathrm{kg}$ )	1.66
Inertia $\bm{J}_{L}$ ( $\mathrm{kg}\text{$ !\cdot! $}{\mathrm{m}}^{2}$ )	$\begin{bmatrix}0.0101956&0.0003278&-0.000108.0\\ 0.0003278&0.013750&-0.0003215\\ -0.0001080&-0.0003215&0.0209970\end{bmatrix}$
Cable 1 attach. pt. ${}^{L}\bm{r}_{1L}$ ( $\mathrm{m}$ )	$[0.1,0,0.03]^{\intercal}$
Cable 2 attach. pt. ${}^{L}\bm{r}_{2L}$ ( $\mathrm{m}$ )	$[-0.05,0.087,0.03]^{\intercal}$
Cable 3 attach. pt. ${}^{L}\bm{r}_{3L}$ ( $\mathrm{m}$ )	$[0.03]^{\intercal}$
Drones

TABLE I: MUSLS parameters.

Fig. 5: Comparison of mean drone and load trajectories in a MUSLS. ‘Real’ trajectories are generated experimentally in the real world, while ‘sim’ trajectories are generated in simulation using the tuned multi-rigid-link cable model. The three sets of trajectories shown are (from left to right): a quasi-static circle, one period of simple harmonic motion along the

Y

-axis, and one cycle of cable tension engagement.

Panel of Figure 7 — Fig. 6: Z position and yaw angle of the load during the tension engage trajectory while varying the simulated: (a) joint damping, (b) joint friction. The real-world load’s trajectory is provided in black for reference. All experiments are performed with 29 cable elements and $0\text{\,}\mathrm{N}\text{$ !\cdot! $}\mathrm{m}\text{/}\mathrm{rad}$ of joint stiffness.

* Tension engagement excluded: requires a timestep of
Setting	Realtime factor (approx.)
15 links, no friction	$99\text{\,}\mathrm{\%}$
15 links, with friction	$94\text{\,}\mathrm{\%}98\text{\,}\mathrm{\%}$
29 links, no friction	$99\text{\,}\mathrm{\%}$
29 links, with friction	$40\text{\,}\mathrm{\%}56\text{\,}\mathrm{\%}$
$2\text{\times}{10}^{-4}\text{\,}\mathrm{s}$ to maintain stability.

TABLE II: Run speed of the MUSLS simulator under different cable settings. Maximum step size

4\text{\times}{10}^{-3}\text{\,}\mathrm{s}

. *

Fig. 7: Mean distance (over each trajectory) of the mean simulated load’s pose to the mean real-world load’s pose under a varied number of cable elements. Joint damping:

2\text{\times}{10}^{-3}\text{\,}\mathrm{N}\text{

!\cdot!

}\mathrm{s}\text{/}\mathrm{rad}

, joint friction:

0\text{\,}\mathrm{N}\text{

!\cdot!

}\mathrm{m}

Fig. 8: Mean position and orientation of the load and drone 1 in the final tuned MUSLS model across the trajectories shown in Fig. 5 . For the circular trajectory, yaw is clipped for both the load and drone 1 to highlight roll and pitch. The shaded regions represent

95\text{\,}\mathrm{\%}

confidence intervals.

Agent	Trans. (mm)	Geo. (deg)	Trans. (mm)	Geo. (deg)
	Circle		SHM
Load	67.8	9.7	118.5	11.4
Drone 1	74.8	1.7	95.1	4.1
Drone 2	68.3	1.8	118.0	3.0
Drone 3	204.1	2.1	110.5	2.6
		Engage

TABLE III: Mean translational (Trans.) and geodesic (Geo.) error of the simulated MUSLS.

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Ana Maria Nascimento, Augusto Sales, Antonio Marcus Lima, Tiago Nascimento

Aerial Manipulation Quadrotor State Estimation Lagrangian Methods

Open paper AskPDF arXiv

This work proposes a novel control and estimation approach for aerial manipulation of a cable-suspended load using Unmanned Aerial Vehicles (UAVs). Common approaches in the state of the art have practical limitations, relying on direct load measurements and Lagrangian methods for dynamic modeling. The lack of a straightforward dynamic model of the system led us to propose adopting the Udwadia-Kalaba method to explicitly incorporate the cable's geometric constraints. This formulation allowed for the consistent derivation of the tension force and its direct integration into the NMPC prediction model. Additionally, we propose a sensorless load state estimation based on the same geometric constraints. Results from real-robot experiments demonstrated that the explicit inclusion of load dynamics in the optimization problem significantly reduces trajectory-tracking errors and yields better overall performance compared to strategies based on incomplete models.

Abstract

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