# Differential-Flatness and Control of Quadrotor(s) with a Payload Suspended through Flexible Cable(s)

arXiv: https://arxiv.org/abs/1711.04895 · HTML: https://mlsanity.com/paper/1711.04895/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2017.

## Built on by (most cited first, 1 of 1)

- [RoVerFly: Robust and Versatile Implicit Hybrid Control of Quadrotor-Payload Systems](https://mlsanity.com/paper/2509.11149/) (2025)

## Abstract (arXiv)

We present the coordinate-free dynamics of three different quadrotor systems : (a) single quadrotor with a point-mass payload suspended through a flexible cable; (b) multiple quadrotors with a shared point-mass payload suspended through flexible cables; and (c) multiple quadrotors with a shared rigid-body payload suspended through flexible cables. We model the flexible cable(s) as a finite series of links with spherical joints with mass concentrated at the end of each link. The resulting systems are thus high-dimensional with high degree-of-underactuation. For each of these systems, we show that the dynamics are differentially-flat, enabling planning of dynamically feasible trajectories. For the single quadrotor with a point-mass payload suspended through a flexible cable with five links (16 degrees-of-freedom and 12 degrees-of-underactuation), we use the coordinate-free dynamics to develop a geometric variation-based linearized equations of motion about a desired trajectory. We show that a finite-horizon linear quadratic regulator can be used to track a desired trajectory with a relatively large region of attraction.