Abstract

Electric vertical-take-off-and-landing multirotor aircraft has been emerging as a revolutionary transportation mode for both manned and unmanned applications, but this technology is limited by flight time and range restrictions. In this work, an energy-efficient model-based trajectory planning and feedback control framework is developed to improve the energy performance of a multirotor unmanned aerial vehicle. Target vehicle trajectories are planned by solving a formulated energy consumption optimization problem based on a system-level model, which accommodates the integrated dynamics of key vehicle subsystems. In order to implement the generated target trajectories, the framework also includes a PID feedback control architecture for real-time trajectory following. The framework is first verified under simulation, and shows an average reduction of 10.7% in energy consumption over a range of typical hover-to-hover operations, compared to the commonly used baseline flight control architecture. Through model-based analysis, key relationships that contribute to the improvements are identified and analyzed. These results demonstrate the importance of considering and coordinating all relevant system dynamics for efficient and holistic trajectory planning and control, which is absent in existing literature. The framework also demonstrates similar performance improvement under experimental validation, with an average energy reduction of 10.2% over the baseline controller despite the presence of significant real-world disturbances including wind effect.

References

1.
Hoffmann
,
G.
,
Huang
,
H.
,
Waslander
,
S.
, and
Tomlin
,
C.
,
2007
, “
Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment
,”
AIAA
Paper No. 2007-6461.10.2514/6.2007-6461
2.
Kasliwal
,
A.
,
Furbush
,
N. J.
,
Gawron
,
J. H.
,
McBride
,
J. R.
,
Wallington
,
T. J.
,
De Kleine
,
R. D.
,
Kim
,
H. C.
, and
Keoleian
,
G. A.
,
2019
, “
Role of Flying Cars in Sustainable Mobility
,”
Nat. Commun.
,
10
(
1
), p.
1555
.10.1038/s41467-019-09426-0
3.
Li
,
B.
,
Li
,
Q.
,
Zeng
,
Y.
,
Rong
,
Y.
, and
Zhang
,
R.
,
2021
, “
3D Trajectory Optimization for Energy-Efficient UAV Communication: A Control Design Perspective
,”
IEEE Trans. Wireless Commun.
,
21
(
6
), pp.
4579
4593
.10.1109/TWC.2021.3131384
4.
Lambey
,
V.
, and
Prasad
,
A. D.
,
2021
, “
A Review on Air Quality Measurement Using an Unmanned Aerial Vehicle
,”
Water, Air, Soil Pollut.
,
232
(
3
), p.
109
.
5.
Liu
,
W.
,
Sanders
,
M.
,
Barit
,
D.
,
Akagi
,
J.
,
Harding
,
S.
, and
Tadekawa
,
S.
,
2021
, “
Towards METOC UAS for Measuring Evaporative Duct Profiles
,”
OCEANS
, San Diego–Porto, Sept. 20-23, pp.
1
3
.10.23919/OCEANS44145.2021.9705891
6.
Garrow
,
L. A.
,
German
,
B. J.
, and
Leonard
,
C. E.
,
2021
, “
Urban Air Mobility: A Comprehensive Review and Comparative Analysis With Autonomous and Electric Ground Transportation for Informing Future Research
,”
Transp. Res. Part C: Emerging Technol.
,
132
, p.
103377
.10.1016/j.trc.2021.103377
7.
Polaczyk
,
N.
,
Trombino
,
E.
,
Wei
,
P.
, and
Mitici
,
M.
,
2019
, “
A Review of Current Technology and Research in Urban on-Demand Air Mobility Applications
,”
8th Biennial Autonomous VTOL Technical Meeting and 6th Annual Electric VTOL Symposium
, Mesa, AZ, Jan. 28–Feb. 1, pp.
333
343
.https://www.aere.iastate.edu/~pwei/proceedings/vfs19_nick.pdf
8.
Murray
,
C. C.
, and
Chu
,
A. G.
,
2015
, “
The Flying Sidekick Traveling Salesman Problem: Optimization of Drone-Assisted Parcel Delivery
,”
Transp. Res. Part C: Emerging Technol.
,
54
, pp.
86
109
.10.1016/j.trc.2015.03.005
9.
Goodchild
,
A.
, and
Toy
,
J.
,
2018
, “
Delivery by Drone: An Evaluation of Unmanned Aerial Vehicle Technology in Reducing CO2 Emissions in the Delivery Service Industry
,”
Transp. Res. Part D: Transp. Environ.
,
61
, pp.
58
67
.10.1016/j.trd.2017.02.017
10.
Hackenberg
,
D. L.
,
2018
, “
NASA Aeronautics Research Mission Directorate (ARMD) UAS and UAM Research Visions
,” accessed Jan. 4, 2023, https://ntrs.nasa.gov/citations/20180008493
11.
Fredericks
,
W. L.
,
Sripad
,
S.
,
Bower
,
G. C.
, and
Viswanathan
,
V.
,
2018
, “
Performance Metrics Required of Next-Generation Batteries to Electrify Vertical Takeoff and Landing (VTOL) Aircraft
,”
ACS Energy Lett.
,
3
(
12
), pp.
2989
2994
.10.1021/acsenergylett.8b02195
12.
Morbidi
,
F.
,
Cano
,
R.
, and
Lara
,
D.
,
2016
, “
Minimum-Energy Path Generation for a Quadrotor UAV
,” 2016 IEEE International Conference on Robotics and Automation (
ICRA
), Stockholm, Sweden, May 16-21, pp.
1492
1498
.10.1109/ICRA.2016.7487285
13.
Kreciglowa
,
N.
,
Karydis
,
K.
, and
Kumar
,
V.
,
2017
, “
Energy Efficiency of Trajectory Generation Methods for Stop-and-Go Aerial Robot Navigation
,” 2017 International Conference on Unmanned Aircraft Systems (
ICUAS
), Miami, FL, June 13–16, pp.
656
662
.10.1109/ICUAS.2017.7991496
14.
Han
,
T.
,
Hu
,
Q.
, and
Xin
,
M.
,
2022
, “
Three-Dimensional Approach Angle Guidance Under Varying Velocity and Field-of-View Limit Without Using Line-of-Sight Rate
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
52
(
11
), pp.
7148
7159
.10.1109/TSMC.2022.3150299
15.
Liu
,
Z.
,
Kurzhanskiy
,
A.
, and
Sengupta
,
R.
,
2017
, “
An Energy-Based Optimal Control Problem for Unmanned Aircraft Systems Flight Planning
,” 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (
SICE
), Kanazawa, Japan, Sept. 19–22, pp.
1320
1325
.10.23919/SICE.2017.8105434
16.
She
,
X. T. P.
,
Lin
,
X.
, and
Lang
,
H.
,
2020
, “
A Data-Driven Power Consumption Model for Electric UAVs
,” 2020 American Control Conference (
ACC
), Denver, CO, July 1–3, pp.
4957
4962
.10.23919/ACC45564.2020.9147622
17.
Liu
,
Z.
,
Sengupta
,
R.
, and
Kurzhanskiy
,
A.
,
2017
, “
A Power Consumption Model for Multi-Rotor Small Unmanned Aircraft Systems
,” 2017 International Conference on Unmanned Aircraft Systems (
ICUAS
), Miami, FL, June 13–16, pp.
310
315
.10.1109/ICUAS.2017.7991310
18.
Liu
,
Z.
, and
Sengupta
,
R.
,
2017
, “
An Energy-Based Flight Planning System for Unmanned Traffic Management
,” 2017 Annual IEEE International Systems Conference (
SysCon
), Montreal, QC, Canada, Apr. 24–27, pp.
1
7
.10.1109/SYSCON.2017.7934784
19.
Morbidi
,
F.
, and
Pisarski
,
D.
,
2021
, “
Practical and Accurate Generation of Energy-Optimal Trajectories for a Planar Quadrotor
,”
IEEE International Conference on Robotics and Automation
, Xi'an, China, May 30–June 5, pp.
355
361
.10.1109/ICRA48506.2021.9561395
20.
Fouad
,
Y.
,
Rizoug
,
N.
,
Bouhali
,
O.
, and
Hamerlain
,
M.
,
2017
, “
Optimization of Energy Consumption for Quadrotor UAV
,”
International Micro Air Vehicle Conference and Flight Competition (IMAV)
, Toulouse, France, Sept. 18–21, pp.
355
361
.
21.
Yacef
,
F.
,
Rizoug
,
N.
,
Degaa
,
L.
, and
Hamerlain
,
M.
,
2020
, “
Energy-Efficiency Path Planning for Quadrotor UAV Under Wind Conditions
,” 2020 7th International Conference on Control, Decision and Information Technologies (
CoDIT
), Prague, Czech Republic, June 29–July 2, pp.
1133
1138
.10.1109/CoDIT49905.2020.9263968
22.
Yacef
,
F.
,
Rizoug
,
N.
,
Degaa
,
L.
,
Bouhali
,
O.
, and
Hamerlain
,
M.
,
2021
, “
Energy Efficiency Path Planning for a Quadrotor Aerial Vehicle
,”
Trans. Inst. Meas. Control.
, epub.10.1177/01423312211058560
23.
Podhradský
,
M.
,
Coopmans
,
C.
, and
Jensen
,
A.
,
2014
, “
Battery State-Of-Charge Based Altitude Controller for Small, Low Cost Multirotor Unmanned Aerial Vehicles
,”
J. Intell. Rob. Syst.
,
74
(
1–2
), pp.
193
207
.10.1007/s10846-013-9894-7
24.
Schacht-Rodríguez
,
R.
,
Ponsart
,
J.-C.
,
García-Beltrán
,
C.-D.
,
Astorga-Zaragoza
,
C.-M.
,
Theilliol
,
D.
, and
Zhang
,
Y.
,
2018
, “
Path Planning Generation Algorithm for a Class of UAV Multirotor Based on State of Health of Lithium Polymer Battery
,”
J. Intell. Rob. Syst.
,
91
(
1
), pp.
115
131
.10.1007/s10846-018-0870-0
25.
Schacht-Rodríguez
,
R.
,
Ponsart
,
J. C.
,
García-Beltrán
,
C. D.
,
Astorga-Zaragoza
,
C. M.
, and
Theilliol
,
D.
,
2019
, “
Mission Planning Strategy for Multirotor UAV Based on Flight Endurance Estimation
,” 2019 International Conference on Unmanned Aircraft Systems (
ICUAS
), Atlanta, GA, June 11–14, pp.
778
786
.10.1109/ICUAS.2019.8798292
26.
Michel
,
N.
, and
Kong
,
Z.
, and
Lin
,
X.
,
2020
, “
Optimal Control of a Multirotor Unmanned Aerial Vehicle Based on a Multiphysical Model
,”
ASME
Paper No. DSCC2020-3239.10.1115/DSCC2020-3239
27.
Michel
,
N.
,
Wei
,
P.
,
Kong
,
Z.
,
Sinha
,
A. K.
, and
Lin
,
X.
,
2022
, “
Modeling and Validation of Electric Multirotor Unmanned Aerial Vehicle System Energy Dynamics
,”
eTransportation
,
12
, p.
100173
.10.1016/j.etran.2022.100173
28.
Wu
,
X.
, and
Mueller
,
M. W.
,
2020
, “
In-Flight Range Optimization of Multicopters Using Multivariable Extremum Seeking With Adaptive Step Size
,” 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), IEEE, Las Vegas, NV, Oct. 25–29, pp.
1545
1550
.10.1109/IROS45743.2020.9340762
29.
Wu
,
X.
,
Zeng
,
J.
,
Tagliabue
,
A.
, and
Mueller
,
M. W.
,
2021
, “
Model-Free Online Motion Adaptation for Energy Efficient Flights of Multicopters
,” CoRR, arXiv:abs/2108.03807.
30.
Lin
,
X.
,
Perez
,
H. E.
,
Mohan
,
S.
,
Siegel
,
J. B.
,
Stefanopoulou
,
A. G.
,
Ding
,
Y.
, and
Castanier
,
M. P.
,
2014
, “
A Lumped-Parameter Electro-Thermal Model for Cylindrical Batteries
,”
J. Power Sources
,
257
, pp.
1
11
.10.1016/j.jpowsour.2014.01.097
31.
Lin
,
X.
,
Kim
,
Y.
,
Mohan
,
S.
,
Siegel
,
J. B.
, and
Stefanopoulou
,
A. G.
,
2019
, “
Modeling and Estimation for Advanced Battery Management
,”
Annu. Rev. Control, Rob., Auton. Syst.
,
2
(
1
), pp.
393
426
.10.1146/annurev-control-053018-023643
32.
Michel
,
N.
,
Sinha
,
A. K.
,
Kong
,
Z.
, and
Lin
,
X.
,
2019
, “
Multiphysical Modeling of Energy Dynamics for Multirotor Unmanned Aerial Vehicles
,” 2019 International Conference on Unmanned Aircraft Systems (
ICUAS
), Atlanta, GA. June 11–14, pp.
738
747
.10.1109/ICUAS.2019.8797747
33.
Johnson
,
W.
,
1994
,
Helicopter Theory
,
Dover Publications
,
New York
.
34.
Gur
,
O.
, and
Rosen
,
A.
,
2009
, “
Optimizing Electric Propulsion Systems for Unmanned Aerial Vehicles
,”
J. Aircraft
,
46
(
4
), pp.
1340
1353
.10.2514/1.41027
35.
Thurlbeck
,
A. P.
, and
Cao
,
Y.
,
2019
, “
Analysis and Modeling of UAV Power System Architectures
,” IEEE Transportation Electrification Conference and Expo (
ITEC
), Novi, MI, June 17–19, pp.
1
8
.10.1109/ITEC.2019.8790566
36.
Lin
,
X.
,
2018
, “
Theoretical Analysis of Battery SOC Estimation Errors Under Sensor Bias and Variance
,”
IEEE Trans. Ind. Electron.
,
65
(
9
), pp.
7138
7148
.10.1109/TIE.2018.2795521
37.
Lin
,
X.
,
2017
, “
Analytic Analysis of the Data-Dependent Estimation Accuracy of Battery Equivalent Circuit Dynamics
,”
IEEE Control Syst. Lett.
,
1
(
2
), pp.
304
309
.10.1109/LCSYS.2017.2715821
38.
Powers
,
C.
,
Mellinger
,
D.
, and
Kumar
,
V.
,
2015
,
Quadrotor Kinematics and Dynamics
,
Springer
,
Dordrecht
, The Netherlands, pp.
307
328
.
39.
Cao
,
Y.
, and
Thurlbeck
,
A. P.
,
2019
, “
Heavy-Duty UAV Electrical Propulsion Architectures and Multitimescale Multi-Physics Modeling
,” AIAA/IEEE Electric Aircraft Technologies Symposium (
EATS
), Indianapolis, IN, Aug. 22–24, pp.
1
13
.10.2514/6.2019-4404
40.
Lawrence
,
D.
, and
Mohseni
,
K.
,
2005
, “
Efficiency Analysis for Long Duration Electric MAVs
,”
AIAA
Paper No. 2005-7090.10.2514/6.2005-7090
41.
Lin
,
X.
,
Perez
,
H. E.
,
Siegel
,
J. B.
,
Stefanopoulou
,
A. G.
,
Li
,
Y.
,
Anderson
,
R. D.
,
Ding
,
Y.
, and
Castanier
,
M. P.
,
2013
, “
Online Parameterization of Lumped Thermal Dynamics in Cylindrical Lithium Ion Batteries for Core Temperature Estimation and Health Monitoring
,”
IEEE Trans. Control Syst. Technol.
,
21
(
5
), pp.
1745
1755
.10.1109/TCST.2012.2217143
42.
Lin
,
X.
,
Fu
,
H.
,
Perez
,
H. E.
,
Siege
,
J. B.
,
Stefanopoulou
,
A. G.
,
Ding
,
Y.
, and
Castanier
,
M. P.
,
2013
, “
Parameterization and Observability Analysis of Scalable Battery Clusters for Onboard Thermal Management
,”
Oil Gas Sci. Technol.–Revue d'IFP Energies Nouvelles
,
68
(
1
), pp.
165
178
.10.2516/ogst/2012075
43.
Michel
,
N.
,
Kong
,
Z.
, and
Lin
,
X.
,
2022
, “
Energy-Efficient UAV Trajectory Generation Based on System-Level Modeling of Multi-Physical Dynamics
,”
American Control Conference
, Atlanta, GA, June 8–10.10.23919/ACC53348.2022.9867646
You do not currently have access to this content.