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

TL;DR

This paper develops coordinate-free, differentially-flat models for various quadrotor systems with suspended payloads, enabling feasible trajectory planning and control using linear quadratic regulators.

Contribution

It introduces novel differentially-flat models for complex quadrotor payload systems and demonstrates trajectory planning and control strategies.

Findings

Models are differentially-flat, facilitating trajectory planning.

LQ regulator effectively tracks trajectories with large attraction regions.

Applicable to single and multiple quadrotors with flexible or rigid payloads.

Abstract

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.