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Energy-Optimal Planning of Waypoint-Based UAV Missions -- Does Minimum Distance Mean Minimum Energy?

Nicolas Michel, Ayush Patnaik, Zhaodan Kong, Xinfan Lin

TL;DR

This paper tackles the problem of energy-efficient mission planning for 3D waypoint-based UAVs by proving that the order of visiting waypoints need not follow the shortest path. It introduces a physics-based, system-level energy model that captures rotor aerodynamics, motor/ESC dynamics, battery dynamics, and rigid-body motion, and uses precomputed, interpolated energy costs between waypoint pairs to optimize the overall mission energy via exhaustive search or MILP. Across extensive simulations and real-world experiments, the study finds that the energy-optimal waypoint order differs from traditional minimum-distance orders in the majority of cases and can yield up to 14.9% energy savings. The analysis reveals that minimizing vertical transitions and leveraging diagonal motion—thereby improving rotor efficiency—are key drivers of energy savings, with experimental validation corroborating the model’s predictions and practical impact for extending UAV endurance.

Abstract

Multirotor unmanned aerial vehicle is a prevailing type of aerial robots with wide real-world applications. The energy efficiency of the robot is a critical aspect of its performance, determining the range and duration of the missions that can be performed. This paper studies the energy-optimal planning of the multirotor, which aims at finding the optimal ordering of waypoints with the minimum energy consumption for missions in 3D space. The study is performed based on a previously developed model capturing first-principle energy dynamics of the multirotor. We found that in majority of the cases (up to 95%) the solutions of the energy-optimal planning are different from those of the traditional traveling salesman problem which minimizes the total distance. The difference can be as high as 14.9%, with the average at 1.6%-3.3% and 90th percentile at 3.7%-6.5% depending on the range and number of waypoints in the mission. We then identified and explained the key features of the minimum-energy order by correlating to the underlying flight energy dynamics. It is shown that instead of minimizing the distance, coordination of vertical and horizontal motion to promote aerodynamic efficiency is the key to optimizing energy consumption.

Energy-Optimal Planning of Waypoint-Based UAV Missions -- Does Minimum Distance Mean Minimum Energy?

TL;DR

This paper tackles the problem of energy-efficient mission planning for 3D waypoint-based UAVs by proving that the order of visiting waypoints need not follow the shortest path. It introduces a physics-based, system-level energy model that captures rotor aerodynamics, motor/ESC dynamics, battery dynamics, and rigid-body motion, and uses precomputed, interpolated energy costs between waypoint pairs to optimize the overall mission energy via exhaustive search or MILP. Across extensive simulations and real-world experiments, the study finds that the energy-optimal waypoint order differs from traditional minimum-distance orders in the majority of cases and can yield up to 14.9% energy savings. The analysis reveals that minimizing vertical transitions and leveraging diagonal motion—thereby improving rotor efficiency—are key drivers of energy savings, with experimental validation corroborating the model’s predictions and practical impact for extending UAV endurance.

Abstract

Multirotor unmanned aerial vehicle is a prevailing type of aerial robots with wide real-world applications. The energy efficiency of the robot is a critical aspect of its performance, determining the range and duration of the missions that can be performed. This paper studies the energy-optimal planning of the multirotor, which aims at finding the optimal ordering of waypoints with the minimum energy consumption for missions in 3D space. The study is performed based on a previously developed model capturing first-principle energy dynamics of the multirotor. We found that in majority of the cases (up to 95%) the solutions of the energy-optimal planning are different from those of the traditional traveling salesman problem which minimizes the total distance. The difference can be as high as 14.9%, with the average at 1.6%-3.3% and 90th percentile at 3.7%-6.5% depending on the range and number of waypoints in the mission. We then identified and explained the key features of the minimum-energy order by correlating to the underlying flight energy dynamics. It is shown that instead of minimizing the distance, coordination of vertical and horizontal motion to promote aerodynamic efficiency is the key to optimizing energy consumption.

Paper Structure

This paper contains 14 sections, 5 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Modeling of Multirotor Energy Dynamics
  3. Key Subsystem Dynamics
  4. Rigid Body Kinetics
  5. Propeller Aerodynamics
  6. Model-Based Energy Efficiency Analysis
  7. Problem Formulation for Mission Planning
  8. Result Analysis
  9. Energy Performance of Different Orders
  10. Analysis of Sample Missions
  11. Experimental Validation
  12. Validation of 3-Waypoint Mission
  13. Validation of Diagonal Descent
  14. Conclusions

Figures (7)

  • Figure 1: Block diagram of System-Level Model Architecture
  • Figure 2: Geometries of a Blade Cross-section
  • Figure 3: Reference Table for Optimal Energy Costs between Waypoints over a Range of Horizontal and Vertical Displacements
  • Figure 4: Histograms of Ratio of Energy Cost of Baseline Orders (Min-$X_M$, $Z_M$, and $D_M$) over Min-Energy Order for 5000 Randomized Missions, with $N_W=8$ and Ranges of $-30m<X<30m$, $-30m<Y<30m$, $-25m<Z<25m$
  • Figure 5: Minimum-Energy (Solid) and Minimum-Distance (Dashed) Orders for 8-Waypoint Sample Mission, Including Multiple Viewing Angles.
  • ...and 2 more figures