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Single and Multi-UAV Trajectory Optimization and Simulation

Jiecheng (Jerry) Zhang1

Vinayak Suresh2, Dr. David J Love2

1School of Aeronautics and Astronautics

2School of Electrical and Computer Engineering

Purdue University

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SURF ID: 255

This material is based upon work supported by the IoT4Ag Engineering Research Center funded by the National Science Foundation (NSF) under NSF Cooperative Agreement Number EEC-1941529.  Any opinions, findings and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect those of the NSF.

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Reference: https://internetofbusiness.com/accuracy-drone-data-agriculture/

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Introduction and Problem Statement

  • UAV-aided information dissemination/data collection, applicable in IoT4Ag. (Thrust 2)
  • UAVs are versatile, efficient, portable, cost-effective… but could be energy consuming.

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Source: https://iot4ag.us/research/thrust-2/

https://www.embention.com/news/nmand-f300-fixed-wing-uav/

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Introduction and Problem Statement

  • Goal: optimize trajectory of single- & multi- UAV systems with moving Ground Terminals for maximizing energy efficiency.
  • Energy Efficiency (EE): total amount of information transferred / total amount of consumed power.

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  • Key info:
  • Fixed Wing UAV
  • Customizable Starting and Ending Point
  • Moving Ground Terminal(s)
  • Employ Constraints

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Reference: Y. Zeng and R. Zhang, “Energy-efficient UAV communication with

trajectory optimization,” IEEE Trans. Wireless Commun., vol. 16, no.6, pp. 3747–3760, Jun. 2017.

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GT Movement

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Overview of the Technical Approach

  •  

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Reference: Y. Zeng and R. Zhang, “Energy-efficient UAV communication with

trajectory optimization,” IEEE Trans. Wireless Commun., vol. 16, no.6, pp. 3747–3760, Jun. 2017.

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Overview of the Technical Approach

  • Optimization with Matlab (cvx package) to optimize trajectory with single UAV for maximization of energy efficiency.

1. Discretize Integral

2. Reformulate nonconvex constraints

3. Use fractional programming techniques

  • Expand simulation with multiple UAVs with the addition of collision avoidance constraints.

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Constraints:

  1. Fixed Starting & Ending Point
  2. Max. acceleration & velocity
  3. Min. Velocity (Only for fixed-wing UAV)
  4. Kinematic equations
  5. Collision Avoidance (Multi-UAV only)

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Assume:

  • Same initial & final velocity
  • Constant Altitude
  • Defined UAV dynamics
  • Defined telecommunication constants
  • Known GT trajectory

Reference: Y. Zeng and R. Zhang, “Energy-efficient UAV communication with

trajectory optimization,” IEEE Trans. Wireless Commun., vol. 16, no.6, pp. 3747–3760, Jun. 2017.

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Results – Trajectory Analysis (Single UAV Single GT)

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Table II

Comparison of Various Cases of Simulation

UAV Starting Point

UAV Ending Point

GT Movement

Left to Right at 2 m/s

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Results (Single UAV)

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Table II

Comparison of Various Cases of Simulation

 

Avg. Speed (m/s)

Avg. Rate (Mbps)

Avg. Power (Watts)

EE (kbits/J)

Straight flight

5.125

5.617

447.880

12.54

Maximize Rate

6.293

9.500

823.19

11.54

Minimize Power

29.58

3.436

100.57

34.16

Maximize EE

25.50

7.437

117.07

63.53

Optimal Cruise Speed for UAV – 30 m/s

(From UAV dynamics)

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Results (Multi UAV) – Grouping & Collision Avoidance

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Table II

Comparison of Various Cases of Simulation

(UAV1,3) Starting Point

(UAV2,4) Starting Point

Ending Point

Group

Avg. Rate (per UAV, Mbps)

Avg. Power (per UAV, W)

EE (kbits/J)

1

6.933

113.58

61.04

2

7.458

117.57

63.43

Avg.

7.196

115.58

62.24

Group 1 serving GT1: UAV 1 & 2 (Upper left)

Group 2 serving GT2: UAV 3 & 4 (Lower right)

Min Separation: 2 m

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Conclusions

  • Energy Efficiency increased vastly compared to benchmarks.
  • Widely customizable, thus applicable to different fields. Would enable us to perform various UAV-related tasks with optimal efficiency.
  • Applicable to IoT4Ag – have potential to develop more efficient and enduring agricultural sensing drones.

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  • Future Potentials:

- Involve analysis of interference

- Environmental variables

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References

  • Y. Zeng and R. Zhang, “Energy-efficient UAV communication with

trajectory optimization,” IEEE Trans. Wireless Commun., vol. 16, no.6, pp. 3747–3760, Jun. 2017.

  • Wu, Q., Zeng, Y. and Zhang, R., 2018. Joint trajectory and communication design for multi-UAV enabled wireless networks. IEEE Transactions on Wireless Communications, 17(3), pp.2109-2121.
  • S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.:Cambridge Univ. Press, 2004.
  • K. Shen and W. Yu, "Fractional Programming for Communication Systems—Part I: Power Control and Beamforming," in IEEE Transactions on Signal Processing, vol. 66, no. 10, pp. 2616-2630, 15 May15, 2018, doi: 10.1109/TSP.2018.2812733.
  • Y. Zeng, R. Zhang, and T. J. Lim, “Wireless communications with unmanned aerial vehicles: Opportunities and challenges,” IEEE Commun.Mag., vol. 54, no. 5, pp. 36–42, May 2016.

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Acknowledgment

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Many thanks to Mr. Vinayak Suresh & Dr. David Love for instruction and guidance!

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Questions？

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