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Research Papers

In-Ground-Effect Modeling and Nonlinear-Disturbance Observer for Multirotor Unmanned Aerial Vehicle Control

[+] Author and Article Information
Xiang He, Gordon Kou

Design, Automation, Robotics, and Control
(DARC) Lab,
Salt Lake City, UT 84112

Marc Calaf

Wind Energy and Turbulence Laboratory,
Salt Lake City, UT 84112

Kam K. Leang

Mem. ASME
Department of Mechanical Engineering,
Design, Automation, Robotics, and Control
(DARC) Lab,
University of Utah Robotics Center,
University of Utah,
Salt Lake City, UT 84112
e-mail: kam.k.leang@utah.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 5, 2018; final manuscript received March 15, 2019; published online May 2, 2019. Assoc. Editor: Vladimir Vantsevich.

J. Dyn. Sys., Meas., Control 141(7), 071013 (May 02, 2019) (11 pages) Paper No: DS-18-1218; doi: 10.1115/1.4043221 History: Received May 05, 2018; Revised March 15, 2019

This paper focuses on modeling and control of in-ground-effect (IGE) on multirotor unmanned aerial vehicles (UAVs). As the vehicle flies and hovers over, around, or underneath obstacles, such as the ground, ceiling, and other features, the IGE induces a change in thrust that drastically affects flight behavior. This effect on each rotor can be vastly different as the vehicle's attitude varies, and this phenomenon limits the ability for precision flight control, navigation, and landing in tight and confined spaces. An exponential model describing this effect is proposed, analyzed, and validated through experiments. The model accurately predicts the quasi-steady IGE for an experimental quadcopter UAV. To compensate for the IGE, a model-based feed-forward controller and a nonlinear-disturbance observer (NDO) are designed for closed-loop control. Both controllers are validated through physical experiments, where results show approximately 23% reduction in the tracking error using the NDO compared to the case when IGE is not compensated for.

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Figures

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Fig. 1

Custom-designed ground-effect test stand. A load cell is mounted on a platform, which can be driven up and down by a stepper motor at top of the stand. The load cell connects a lever arm to the platform and measures the force generated by the quadcopter mounted at the other end of the lever arm. Propellers are installed in an inverted configuration to allow the rotor-to-ground height to be varied between 0 m and 1 m. The height of the vehicle is computer controlled using a VICON motion capture system.

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Fig. 2

Thrust recorded at different PWM levels (ranges from 10,000 to 45,000 at 5000 intervals) and height (ranges from 0.015 m to 0.575 m at 0.03 m intervals). Integer representation of the PWM levels from 0 to 65,535 is linearly mapped to duty cycle from 40% to 80%.

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Fig. 3

Normalized ground effect (GE) with respect to different PWM levels and heights

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Fig. 4

Comparison of the ground effect experimental results, proposed IGE model, Cheeseman and Bennett's model [48], Hayden's model [42], Danjun's model [10], and Nobahari and Sharifi's model [21]. Box and whisker plots at different heights represent the distribution of the IGE ratio at different PWM levels. Comparison of single rotor and full quadcopter IGE ratio is shown in the upper-right plot. Results are taken from fitting models to the experimental data.

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Fig. 5

Multirotor aerial vehicle free body diagram

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Fig. 6

Time response of quadcopter attitude closed-loop system with cascade PID controller operating in-ground-effect (a1) regulation with different initial conditions and desired roll, pitch, yaw to 0; (a2) settling time at z =0.47 m; (a3) settling time at z =0.02 m; (b1) regulation with zero initial conditions and different desired attitude; (b2) settling time at z =0.47 m; and (b3) settling time at z =0.02 m

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Fig. 7

System block diagrams: (a) outer-loop PID control for position; (b) inner-loop cascade PID control combined with NDO; and (c) model for simulation of quadcopter IGE dynamics

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Fig. 8

Comparison of nominal tracking responses with and without IGE model: (a) well-tuned PID control without IGE model and (b) same PID gains with the ground effect in the dynamics

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Fig. 9

(a) Tracking result of quadcopter IGE with proposed NDO. (b) Comparison of height tracking error with PID control only (solid), with controller from Ref. [10] (light dashed), and with nonlinear disturbance observer (heavy dashed).

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Fig. 10

Quadcopter platform used in experiments

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Fig. 11

Experimental flight test results: (a) nominal PID tracking result of the spiral trajectory OGE; (b) nominal PID tracking result of the trajectory IGE; and (c) tracking results of quadcopter following trajectory IGE with the NDO

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Fig. 12

IGE trajectory tracking error on height with PID controller (solid) and NDO (dashed), evaluated for zd<0.3 m

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Fig. 13

Experimental results of IGE model-based feed-forward ground-effect compensation of quadcopter tracking helical trajectory

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