Quadrotors have been used in many areas such as cargo transportation, agriculture, and search and rescue. The low energy density of power sources and the low energy efficiency of quadrotors have prevented quadrotors from a wider range of applications where a large payload has to be carried or long flight time is required. This paper optimizes the energy efficiency of a quadrotor via rotating its arms to proper positions calculated based on the dynamics model of the quadrotor and the power–thrust curve of rotors. The conditions that a quadrotor in steady-state can achieve the optimal energy efficiency are mathematically derived and the energy efficiency of a quadrotor in various scenarios is analyzed. Based on the analysis, an arm-rotation approach is proposed to optimize the energy efficiency of a quadrotor with a center-of-gravity offset in steady hovering. It is shown with simulation that an example quadrotor with rotatable arms can save up to 13% of energy. Experiments show that the same example quadrotor can save even more energy in practice, owing to the byproduct of the arm-rotation approach.
Issue Section:
Research Papers
References
1.
Driessens
, S.
, and Pounds
, P. E. I.
, 2013
, “Towards a More Efficient Quadrotor Configuration
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Tokyo, Japan, Nov. 3–7, pp. 1386
–1392
.2.
Pounds
, P.
, Mahony
, R.
, and Corke
, P.
, 2010
, “Modelling and Control of a Large Quadrotor Robot
,” Control Eng. Pract.
, 18
(7
), pp. 691
–699
.3.
Pounds
, P. E.
, Mahony
, R. E.
, and Corke
, P. I.
, 2009
, “Design of a Static Thruster for Microair Vehicle Rotorcraft
,” J. Aerosp. Eng.
, 22
(1
), pp. 85
–94
.4.
Aleksandrov
, D.
, and Penkov
, I.
, 2012
, “Energy Consumption of Mini UAV Helicopters With Different Number of Rotors
,” 11th International Symposium Topical Problems in the Field of Electrical and Power Engineering
, Pränu, Estonia, Jan. 16–21, pp. 259
–262
.5.
Foehn
, P.
, Falanga
, D.
, Kuppuswamy
, N.
, Tedrake
, R.
, and Scaramuzza
, D.
, 2017
, “Fast Trajectory Optimization for Agile Quadrotor Maneuvers With a Cable-Suspended Payload
,” Robotics: Science and Systems
, Cambridge, MA, July 12–16, pp. 1
–10
.http://www.roboticsproceedings.org/rss13/p30.pdf6.
Morbidi
, F.
, Cano
, R.
, and Lara
, D.
, 2016
, “Minimum-Energy Path Generation for a Quadrotor UAV
,” IEEE International Conference on Robotics and Automation
(ICRA
), Stockholm, Sweden, May 16–21, pp. 1492
–1498
.7.
Palunko
, I.
, Cruz
, P.
, and Fierro
, R.
, 2012
, “Agile Load Transportation: Safe and Efficient Load Manipulation With Aerial Robots
,” IEEE Robot. Autom. Mag.
, 19
(3
), pp. 69
–79
.8.
Miranda-Colorado
, R.
, Aguilar
, L. T.
, and Herrero-Brito
, J. E.
, 2018
, “Reduction of Power Consumption on Quadrotor Vehicles Via Trajectory Design and a Controller-Gains Tuning Stage
,” Aerosp. Sci. Technol.
, 78
, pp. 280
–296
.9.
Yacef
, F.
, Rizoug
, N.
, Degaa
, L.
, Bouhali
, O.
, and Hamerlain
, M.
, 2017
, “Trajectory Optimisation for a Quadrotor Helicopter Considering Energy Consumption
,” Fourth International Conference on Control, Decision and Information Technologies
(CoDIT
), Barcelona, Spain, April 5–7, pp. 1030
–1035
.10.
Bouzid
, Y.
, Bestaoui
, Y.
, and Siguerdidjane
, H.
, 2017
, “Quadrotor-UAV Optimal Coverage Path Planning in Cluttered Environment With a Limited Onboard Energy
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Vancouver, BC, Canada, Sept. 24–28, pp. 979
–984
.11.
Kreciglowa
, N.
, Karydis
, K.
, and Kumar
, V.
, 2017
, “Energy Efficiency of Trajectory Generation Methods for Stop-and-Go Aerial Robot Navigation
,” International Conference on Unmanned Aircraft Systems
(ICUAS
), Miami, FL, June 13–16, pp. 656
–662
.12.
Bezzo
, N.
, Mohta
, K.
, Nowzari
, C.
, Lee
, I.
, Kumar
, V.
, and Pappas
, G.
, 2016
, “Online Planning for Energy-Efficient and Disturbance-Aware UAV Operations
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Daejeon, Korea, Oct. 9–14, pp. 5027
–5033
.13.
David
, T.
, and Boris
, L.
, 2014
, “Cascaded Energy Based Trajectory Tracking Control of a Quadrotor
,” At–Automatisierungstechnik
, 62
(6), p. 408
.14.
Liu
, Z.
, Sengupta
, R.
, and Kurzhanskiy
, A.
, 2017
, “A Power Consumption Model for Multi-Rotor Small Unmanned Aircraft Systems
,” International Conference on Unmanned Aircraft Systems
(ICUAS
), Miami, FL, June 13–16, pp. 310
–315
.15.
Sumantri
, B.
, Uchiyama
, N.
, and Sano
, S.
, 2017
, “Generalized Super-Twisting Sliding Mode Control With a Nonlinear Sliding Surface for Robust and Energy-Efficient Controller of a Quad-Rotor Helicopter
,” Proc. Inst. Mech. Eng., Part C
, 231
(11
), pp. 2042
–2053
.16.
Sumantri
, B.
, Uchiyama
, N.
, and Sano
, S.
, 2016
, “Least Square Based Sliding Mode Control for a Quad-Rotor Helicopter and Energy Saving by Chattering Reduction
,” Mech. Syst. Signal Process.
, 66–67
, pp. 769
–784
.17.
Guerrero-Sánchez
, M. E.
, Abaunza
, H.
, Castillo
, P.
, Lozano
, R.
, and García-Beltrán
, C. D.
, 2017
, “Quadrotor Energy-Based Control Laws: A Unit-Quaternion Approach
,” J. Intell. Robot. Syst.
, 88
(2–4
), pp. 347
–377
.18.
Guerrero
, M. E.
, Abaunza
, H.
, Castillo
, P.
, Lozano
, R.
, and García
, C. D.
, 2016
, “Energy Based Control for a Quadrotor Using Unit Quaternions
,” International Conference on Unmanned Aircraft Systems
(ICUAS
), Arlington, VA, June 7–10, pp. 144
–151
.19.
Gandolfo
, D. C.
, Salinas
, L. R.
, Serrano
, M. E.
, and Toibero
, J. M.
, 2017
, “Energy Evaluation of Low-Level Control in UAVs Powered by Lithium Polymer Battery
,” ISA Trans.
, 71
(Pt 2
), pp. 563
–572
.20.
Bouzid
, Y.
, Siguerdidjane
, H.
, and Bestaoui
, Y.
, 2018
, “Energy Based 3D Trajectory Tracking Control of Quadrotors With Model-Free Based on-Line Disturbance Compensation
,” Chin. J. Aeronaut.
, 31
(7
), pp. 1568
–1578
.21.
Gandolfo
, D. C.
, Salinas
, L. R.
, Brandão
, A.
, and Toibero
, J. M.
, 2017
, “Stable Path-Following Control for a Quadrotor Helicopter Considering Energy Consumption
,” IEEE Trans. Control Syst. Technol.
, 25
(4
), pp. 1423
–1430
.22.
Aleksandrov
, D.
, and Penkov
, I.
, 2012
, “Optimal Gap Distance Between Rotors of Mini Quadrotor Helicopter
,” Eighth DAAAM Baltic Conference
, Tallinn, Estonia, April 19–21, pp. 251
–255
.http://innomet.ttu.ee/daaam_publications/2012/Aleksandrov.pdf23.
Penkov
, I.
, and Aleksandrov
, D.
, 2017
, “Analysis and Study of the Influence of the Geometrical Parameters of Mini Unmanned Quad-Rotor Helicopters to Optimise Energy Saving
,” Int. J. Automot. Mech. Eng.
, 14
(4
), pp. 4730
–4746
.http://ijame.ump.edu.my/images/Volume%2014%20Issue%204%202017/11_penkov%20and%20aleksandrov.pdf24.
Kamil
, Y. M.
, 2017
, “A New Model of Unmanned Aerial Vehicle Quadrotor Using the Variation in the Length of the Arm
,” International Conference on Artificial Life and Robotics (ICAROB), Miyazaki, Japan, Jan. 19–22, pp. 723
–726
.25.
Yasameen Kamil
, N.
, Hazry
, D.
, Wan
, K.
, and Razlan
, Z. M.
, 2016
, “A Novel VAL: Quadrotor Control Technique for Trajectory Tracking Based on Varying the Arm's Length
,” ARPN J. Eng. Appl. Sci.
, 11
(15
), pp. 9195
–9204
.https://www.researchgate.net/publication/307568309_A_novel_VAL_Quadrotor_control_technique_for_trajectory_tracking_based_on_varying_the_Arm's_Length26.
Sheng
, S.
, and Sun
, C.
, 2016
, “Control and Optimization of a Variable-Pitch Quadrotor With Minimum Power Consumption
,” Energies
, 9
(4
), p. 232
.27.
Du Plessis
, J.
, and Pounds
, P. E. I.
, 2014
, “Rotor Flapping for a Triangular Quadrotor
,” Australasian Conference on Robotics and Automation
(ACRA
), Melbourne, Australia, Dec. 2–4, p. 144.http://www.araa.asn.au/acra/acra2014/papers/pap144.pdf28.
Driessens
, S.
, and Pounds
, P.
, 2015
, “The Triangular Quadrotor: A More Efficient Quadrotor Configuration
,” IEEE Trans. Robot.
, 31
(6
), pp. 1517
–1526
.29.
Roberts
, J. F.
, Zufferey
, J.-C.
, and Floreano
, D.
, 2008
, “Energy Management for Indoor Hovering Robots
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Nice, France, Sept. 22–26, pp. 1242
–1247
.30.
Leishman
, G. J.
, 2006
, Principles of Helicopter Aerodynamics With CD Extra
, Cambridge University Press
, Cambridge, UK.31.
Baklacioglu
, T.
, Aydin
, H.
, and Turan
, O.
, 2016
, “Energetic and Exergetic Efficiency Modeling of a Cargo Aircraft by a Topology Improving Neuro-Evolution Algorithm
,” Energy
, 103
, pp. 630
–645
.32.
Lawrance
, N. R. J.
, and Sukkarieh
, S.
, 2009
, “Wind Energy Based Path Planning for a Small Gliding Unmanned Aerial Vehicle
,” AIAA
Paper No. 2009-6112. 33.
Al-Sabban
, W. H.
, Gonzalez
, L. F.
, and Smith
, R. N.
, 2013
, “Wind-Energy Based Path Planning for Unmanned Aerial Vehicles Using Markov Decision Processes
,” IEEE International Conference on Robotics and Automation
(ICRA
), Karlsruhe, Germany, May 6–10, pp. 784
–789
.34.
Kladis
, G. P.
, Economou
, J. T.
, Knowles
, K.
, Lauber
, J.
, and Guerra
, T.-M.
, 2011
, “Energy Conservation Based Fuzzy Tracking for Unmanned Aerial Vehicle Missions Under a Priori Known Wind Information
,” Eng. Appl. Artif. Intell.
, 24
(2
), pp. 278
–294
.35.
Şöhret
, Y.
, Dinç
, A.
, and Karakoç
, T. H.
, 2015
, “Exergy Analysis of a Turbofan Engine for an Unmanned Aerial Vehicle During a Surveillance Mission
,” Energy
, 93
, pp. 716
–729
.36.
Sliwinski
, J.
, Gardi
, A.
, Marino
, M.
, and Sabatini
, R.
, 2017
, “Hybrid-Electric Propulsion Integration in Unmanned Aircraft
,” Energy
, 140
, pp. 1407
–1416
.37.
Ma
, S.
, Wang
, S.
, Zhang
, C.
, and Zhang
, S.
, 2017
, “A Method to Improve the Efficiency of an Electric Aircraft Propulsion System
,” Energy
, 140
, pp. 436
–443
.38.
Atlam
, O.
, and Kolhe
, M.
, 2013
, “Performance Evaluation of Directly Photovoltaic Powered DC PM (Direct Current Permanent Magnet) Motor–Propeller Thrust System
,” Energy
, 57
, pp. 692
–698
.39.
Hoffmann
, G. M.
, Huang
, H.
, Waslander
, S. L.
, and Tomlin
, C. J.
, 2007
, “Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment
,” AIAA
Paper No. 2007-6461.40.
Sharkh
, S. M. A.
, Lai
, S. H.
, and Turnock
, S. R.
, 2004
, “Structurally Integrated Brushless PM Motor for Miniature Propeller Thrusters
,” IEE Proc. Elect. Power Appl.
, 151
(5
), pp. 513
–519
.41.
Adkins
, C. N.
, and Liebeck
, R. H.
, 1994
, “Design of Optimum Propellers
,” J. Propul. Power
, 10
(5
), pp. 676
–682
.42.
Hardy
, G. H.
, Littlewood
, J. E.
, and Pólya
, G.
, 1952
, Inequalities
, Cambridge University Press
, Cambridge, UK.43.
Chovancová
, A.
, Fico
, T.
, Chovanec
, Ľ.
, and Hubinsk
, P.
, 2014
, “Mathematical Modelling and Parameter Identification of Quadrotor (A Survey)
,” Procedia Eng.
, 96
, pp. 172
–181
.44.
Luukkonen
, T.
, 2011
, “Modelling and Control of Quadcopter
,” Independent Research Project in Applied Mathematics, Aalto University, Espoo, Finland, Report
.http://sal.aalto.fi/publications/pdf-files/eluu11_public.pdf45.
Bergamasco
, M.
, and Lovera
, M.
, 2014
, “Identification of Linear Models for the Dynamics of a Hovering Quadrotor
,” IEEE Trans. Control Syst. Technol.
, 22
(5
), pp. 1696
–1707
.46.
Derafa
, L.
, Madani
, T.
, and Benallegue
, A.
, 2006
, “Dynamic Modelling and Experimental Identification of Four Rotors Helicopter Parameters
,” IEEE International Conference on Industrial Technology
(ICIT
), Mumbai, India, Dec. 15–17, pp. 1834
–1839
.47.
Michael
, N.
, Mellinger
, D.
, Lindsey
, Q.
, and Kumar
, V.
, 2010
, “The Grasp Multiple Micro-UAV Testbed
,” IEEE Robot. Autom. Mag.
, 17
(3
), pp. 56
–65
.48.
Amezquita-Brooks
, L.
, Liceaga-Castro
, E.
, Gonzalez-Sanchez
, M.
, Garcia-Salazar
, O.
, and Martinez-Vazquez
, D.
, 2017
, “Towards a Standard Design Model for Quad-Rotors: A Review of Current Models, Their Accuracy and a Novel Simplified Model
,” Prog. Aerosp. Sci.
, 95
, p. 1
.49.
Ding
, X.
, Wang
, X.
, Yu
, Y.
, and Zha
, C.
, 2017
, “Dynamics Modeling and Trajectory Tracking Control of a Quadrotor Unmanned Aerial Vehicle
,” ASME J. Dyn. Syst., Meas., Control
, 139
(2
), p. 021004
.http://dynamicsystems.asmedigitalcollection.asme.org/article.aspx?articleid=255317350.
Sanz
, R.
, Garcia
, P.
, Zhong
, Q.-C.
, and Albertos
, P.
, 2016
, “Robust Control of Quadrotors Based on an Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst., Meas., Control
, 138
(7
), p. 071006
.51.
Xu
, Z.
, He
, F.
, Xing
, X.
, Qi
, H.
, and Huo
, X.
, 2017
, “Modelling and Control of a Quadrotor Equipped With an Unbalanced Load
,” 11th Asian Control Conference
(ASCC
), Gold Coast, Australia, Dec. 17–20, pp. 784
–789
.52.
Xian
, B.
, Zhao
, B.
, Zhang
, Y.
, and Zhang
, X.
, 2017
, “Nonlinear Control of a Quadrotor With Deviated Center of Gravity
,” ASME J. Dyn. Syst., Meas., Control
, 139
(1
), p. 011003
.http://dynamicsystems.asmedigitalcollection.asme.org/article.aspx?articleid=2543315&resultClick=353.
Islam
, S.
, Liu
, P. X.
, and El Saddik
, A.
, 2015
, “Robust Control of Four-Rotor Unmanned Aerial Vehicle With Disturbance Uncertainty
,” IEEE Trans. Ind. Electron.
, 62
(3
), pp. 1563
–1571
.54.
Haus
, T.
, Orsag
, M.
, and Bogdan
, S.
, 2017
, “Mathematical Modelling and Control of an Unmanned Aerial Vehicle With Moving Mass Control Concept
,” J. Intell. Robot. Syst.
, 88
(2–4
), pp. 219
–246
.55.
Tayebi
, A.
, and McGilvray
, S.
, 2006
, “Attitude Stabilization of a VTOL Quadrotor Aircraft
,” IEEE Trans. Control Syst. Technol.
, 14
(3
), pp. 562
–571
.56.
Basri
, M. A. M.
, Husain
, A. R.
, and Danapalasingam
, K. A.
, 2015
, “Enhanced Backstepping Controller Design With Application to Autonomous Quadrotor Unmanned Aerial Vehicle
,” J. Intell. Robot. Syst.
, 79
(2
), p. 295
.57.
Mahony
, R.
, Kumar
, V.
, and Corke
, P.
, 2012
, “Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor
,” IEEE Robot. Autom. Mag.
, 19
(3
), pp. 20
–32
.58.
Napolitano
, M. R.
, 2012
, Aircraft Dynamics: From Modeling to Simulation
, J. Wiley
, Hoboken, NJ.59.
Stengel
, R. F.
, 2015
, Flight Dynamics
, Princeton University Press
, Princeton, NJ.60.
Beard
, R. W.
, and McLain
, T. W.
, 2012
, Small Unmanned Aircraft: Theory and Practice
, Princeton University Press
, Princeton, NJ.61.
Rinaldi
, F.
, Chiesa
, S.
, and Quagliotti
, F.
, 2013
, “Linear Quadratic Control for Quadrotors UAVs Dynamics and Formation Flight
,” J. Intell. Robot. Syst.
, 70
(1–4
), pp. 203
–220
.62.
Alaimo
, A.
, Artale
, V.
, Milazzo
, C.
, Ricciardello
, A.
, and Trefiletti
, L.
, 2013
, “Mathematical Modeling and Control of a Hexacopter
,” International Conference on Unmanned Aircraft Systems (ICUAS)
, Atlanta, GA, May 28–31, pp. 1043
–1050
.63.
Barbaraci
, G.
, 2015
, “Modeling and Control of a Quadrotor With Variable Geometry Arms
,” J. Unmanned Veh. Syst.
, 3
(2
), pp. 35
–57
.64.
Goodarzi
, F. A.
, Lee
, D.
, and Lee
, T.
, 2015
, “Geometric Adaptive Tracking Control of a Quadrotor Unmanned Aerial Vehicle on SE (3) for Agile Maneuvers
,” J. Dyn. Syst., Meas., Control
, 137
(9
), p. 091007
.65.
Wallace
, D. A.
, 2016
, “Dynamics and Control of a Quadrotor With Active Geometric Morphing
,” Master's thesis
, University of Washington, Seattle, WAhttps://digital.lib.washington.edu/researchworks/handle/1773/35518.66.
Bai
, Y.
, 2017
, “Control and Simulation of Morphing Quadcopter
,” Master's thesis
, Saint Louis University
, St. Louis, MO.https://search.proquest.com/docview/2021984043?accountid=1336067.
Avant
, T.
, Lee
, U.
, Katona
, B.
, and Morgansen
, K.
, 2018
, “Dynamics, Hover Configurations, and Rotor Failure Restabilization of a Morphing Quadrotor
,” Annual American Control Conference
(ACC
), Milwaukee, WI, June 27–29, pp. 4855
–4862
.68.
Birk
, A.
, Wiggerich
, B.
, Bülow
, H.
, Pfingsthorn
, M.
, and Schwertfeger
, S.
, 2011
, “Safety, Security, and Rescue Missions With an Unmanned Aerial Vehicle (UAV)
,” J. Intell. Robot. Syst.
, 64
(1
), pp. 57
–76
.69.
Rosen
, A.
, Ronen
, T.
, and Raz
, R.
, 1989
, “Active Aerodynamic Stabilization of a Helicopter/Sling-Load System
,” J. Aircr.
, 26
(9
), pp. 822
–828
.Copyright © 2019 by ASME
You do not currently have access to this content.
