Range, Endurance, and Optimal Speed Estimates for Multicopters

TL;DR

This work addresses the challenge of accurately estimating range, endurance, and optimal flight speed for multicopters by integrating a first-principles blade-element-momentum theory (BEM) aerodynamic model with a graybox motor-efficiency model and a one-time-constant Thevenin (OTC) battery model. The authors validate the approach with real-world and lab data, achieving thrust-error and power-prediction RMSEs of roughly 0.91 N and 2.7% respectively, and battery-voltage RMSE around 61 mV. They also provide a practical pen-and-paper algorithm that, using only mass, propulsion, and battery characteristics, delivers endurance and range estimates within about 10% of manufacturer specifications for several drones. The combination of high-fidelity physics-based modeling and a lightweight estimation method enables designers and policymakers to reason about performance, tradeoffs, and regulatory implications for aerial robots with improved confidence and efficiency.

Abstract

Multicopters are among the most versatile mobile robots. Their applications range from inspection and mapping tasks to providing vital reconnaissance in disaster zones and to package delivery. The range, endurance, and speed a multirotor vehicle can achieve while performing its task is a decisive factor not only for vehicle design and mission planning, but also for policy makers deciding on the rules and regulations for aerial robots. To the best of the authors' knowledge, this work proposes the first approach to estimate the range, endurance, and optimal flight speed for a wide variety of multicopters. This advance is made possible by combining a state-of-the-art first-principles aerodynamic multicopter model based on blade-element-momentum theory with an electric-motor model and a graybox battery model. This model predicts the cell voltage with only 1.3% relative error (43.1 mV), even if the battery is subjected to non-constant discharge rates. Our approach is validated with real-world experiments on a test bench as well as with flights at speeds up to 65 km/h in one of the world's largest motion-capture systems. We also present an accurate pen-and-paper algorithm to estimate the range, endurance and optimal speed of multicopters to help future researchers build drones with maximal range and endurance, ensuring that future multirotor vehicles are even more versatile.

Figures (6)

• Figure 1: The approach presented in this work can be used to calculate accurate range, endurance, and optimal speed estimates for general multicopters. Depending on the accuracy requirements, either a state-of-the-art blade-element-momentum aerodynamics simulation can be combined with an accurate motor and battery model, or alternatively a simple, yet precise pen-and-paper algorithm can be employed to calculate the performance estimates. For the latter, the only information required is the mass, battery type, propeller size, and average surface area of the multicopter.
• Figure 2: Efficiency of six different motor-propeller combinations plotted over the entire operating range of each motor. The lines represent the fitted motor model (\ref{['eq:eta']}). Solid lines (circle marks) represent a motor-propeller combination recommended by the manufacturer, whereas the dashed lines (star marks) show mismatched pairings.
• Figure 3: Thevenin equivalent circuit for the one-time-constant (OTC) battery model. The load does not need to be static but could, for example, be a multirotor aerial vehicle.
• Figure 4: The left plot shows discharge curves for a typical 4S 1.8Ah battery. A higher power demand leads to lower voltages as well as a much shorter flight time. The right plot shows how well different models predict the Peukert effect: higher discharge rates lead to a reduction in effective capacity. The proposed model ("Ours") is compared with the original Peukert model ("Peuk.") and the state-of-the-art generalized Peukert model ("Gen. Peuk."). It can be seen that, albeit being a voltage model, the proposed model fits the measurements well.
• Figure 5: The plots show a comparison between real-world experiments and pure simulation results. On the left, the vehicle's power consumption on a circular trajectory is plotted as a function of the flight speed. The right plot shows the energy consumption per distance covered as a function of the flight speed. Simulation and experiment match very well, validating the accuracy of the multicopter simulator and motor model.