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Research Papers

Stabilization of a Rigid Body Payload With Multiple Cooperative Quadrotors

[+] Author and Article Information
Farhad A. Goodarzi

Department of Mechanical and
Aerospace Engineering,
George Washington University,
Washington, DC 20052
e-mail: fgoodarzi@gwu.edu

Taeyoung Lee

Associate Professor
Department of Mechanical and
Aerospace Engineering,
George Washington University,
Washington, DC 20052
e-mail: tylee@gwu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 6, 2015; final manuscript received June 7, 2016; published online August 10, 2016. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 138(12), 121001 (Aug 10, 2016) (17 pages) Paper No: DS-15-1557; doi: 10.1115/1.4033945 History: Received November 06, 2015; Revised June 07, 2016

This paper presents the full dynamics and control of arbitrary number of quadrotor unmanned aerial vehicles (UAVs) transporting a rigid body. The rigid body is connected to the quadrotors via flexible cables where each flexible cable is modeled as a system of arbitrary number of serially connected links. It is shown that a coordinate-free form of equations of motion can be derived for the complete model without any simplicity assumptions that commonly appear in other literature, according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. A rigorous mathematical stability proof is given and the desirable features of the proposed controller are illustrated by numerical examples and experimental results.

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Figures

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Fig. 1

Two quadrotors stabilizing a payload cooperatively

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Fig. 2

Quadrotor UAVs with a rigid body payload. Cables are modeled as a serial connection of an arbitrary number of links (only four quadrotors with five links in each cable are illustrated).

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Fig. 3

Stabilization of a rigid body connected to multiple quadrotors. (a) Payload position (x0: solid, x0d: dotted), (b) payload velocity (ν0: solid, ν0d: dotted), (c) payload angular velocity Ω0, (d) quadrotors angular velocity errors ei, (e) payload attitude error Ψ0, (f) quadrotors attitude errors Ψi, (g) quadrotors total thrust inputs fi, and (h) direction error eq, and angular velocity error eω for the links.

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Fig. 4

Snapshots of controlled maneuver. (a) Three-dimensional perspective, (b) side view, and (c) top view.

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Fig. 5

Stabilization of a payload with multiple quadrotors connected with flexible cables. (a) Payload position (x0: solid, x0d: dotted), (b) payload velocity (ν0: solid, ν0d: dotted), (c) payload angular velocity Ω0, (d) quadrotors angular velocity errors ei, (e) payload attitude error Ψ0, (f) quadrotors attitude errors Ψi, (g) quadrotors total thrust inputs fi, and (h) direction error eq, and angular velocity error eω for the links.

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Fig. 6

Snapshots of the controlled maneuver.1 (a) t = 0 s, (b) t = 0.14 s, (c) t = 0.30 s, (d) t = 0.68 s, (e) t = 1.10 s, (f) t = 1.36 s, (g) t = 1.98 s, (h) t = 3.48 s, and (i) t = 10 s.

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Fig. 7

Hardware development for each quadrotor UAV. (a) Hardware configuration and (b) motor calibration setup.

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Fig. 8

Information flow of the experiments

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Fig. 9

Computer-aided design (CAD) model

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Fig. 10

Two quadrotors transporting a rod. (a) Experiment and (b) simulation.

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Fig. 11

Benchmark: quadrotor position control system [21]. (a) Rod's actual and desired positions, x0,x0d, (b) quadrotor's positions, x0,x1, (c) first cable's direction, q1, and (d) second cable's direction, q2.

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Fig. 12

Proposed controller: two quadrotors with rigid body payload. (a) Rod's actual and desired positions, x0,x0d, (b) quadrotor's positions, x1,x2, (c) first cable's direction, q1, and (d) second cable's direction, q2.

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Fig. 13

Snapshots of experiments.2

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