⚡ electrical engineering

Simulation evaluation of the takeoff threshold of an ArduPilot Gazebo quadrotor and conditions for physical implementation

This study quantitatively determines the takeoff throttle threshold of an ArduPilot Gazebo quadrotor simulation to be between commands 1485 and 1486 for a 1.98 kg model, establishing a baseline for future physical implementation and calibration.

Original authors: Toshihiko TAKAYA

Published 2026-10-27

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CC BY 4.0

Original authors: Toshihiko TAKAYA

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Before a drone can lift off the ground, it must first overcome the invisible weight of gravity. For engineers building these flying machines, the moment of liftoff is a critical threshold: a specific point where the force pushing the vehicle upward finally becomes stronger than the force pulling it down. In the real world, finding this exact point is difficult because wind, battery health, and tiny mechanical differences can change the answer every time. To solve this, researchers often turn to computer simulations. These are not just simple cartoons; they are complex virtual environments where software acts as the drone's brain, and physics engines act as the air and gravity. By testing thousands of tiny adjustments in this safe, repeatable digital space, scientists can pinpoint the exact moment a machine is ready to fly before they ever build a physical prototype. This approach allows them to separate the true behavior of the design from the noise of the real world.

In a recent study, a researcher used this method to find the precise takeoff threshold for a specific type of drone using a popular open-source flight system. The work involved creating a virtual version of a quadrotor, a drone with four rotors, inside a sophisticated simulation environment. The researcher did not build a physical drone for this experiment. Instead, they ran the drone's flight control software on a computer, connecting it to a virtual world that mimics real physics. The goal was simple yet precise: to determine the exact radio control command that causes the drone to leave the ground. In the simulation, the researcher slowly increased the throttle command, which is the signal telling the motors to spin faster. They tested a series of specific numbers, moving from lower values that kept the drone on the ground to higher values that made it rise.

The results revealed a very narrow window where the drone's behavior changed. At a command value of 1485, the drone remained firmly on the ground. No matter how long the command was held, the virtual drone did not rise even a fraction of a meter. However, the moment the command was increased to the very next whole number, 1486, the drone lifted off. In two separate trials at this level, both yielded an altitude increase of 0.090 meters. This tiny but consistent rise marked the boundary between staying grounded and flying. As the researcher increased the command further to 1487, 1488, and up to 1500, the drone climbed higher and faster. The transition was sharp; there was no gradual wobble or hesitation between the two numbers. The drone either stayed down or went up, with the switch happening between the integer commands of 1485 and 1486.

The study also looked at the physical characteristics of the virtual drone to see how it might translate to a real machine. The computer model included a camera gimbal and specific parts, and when all the weights of these components were added together, the total mass came to 1.98 kilograms. This number serves as a starting point for engineers who might want to build a real version of this drone. The researcher compared this weight to a commercially available motor and propeller setup, finding that such a system would have enough power to lift the drone, though the simulation itself did not measure actual physical thrust. The study emphasized that the numbers found here are specific to this computer setup. The values for the throttle command and motor output are not calibrated to real-world force, meaning they cannot be directly copied to a physical drone without further testing.

This work provides a clear baseline for future experiments. It proves that computer simulations can identify the exact point where a drone begins to fly, provided the conditions are controlled and the data is analyzed carefully. The researcher noted that while the results are consistent within the simulation, they are not yet a guarantee for a physical vehicle. To bridge that gap, future work will involve testing the drone on multiple computers to see if the results hold up under different loads, and eventually building a real drone to calibrate the simulation against physical reality. For now, the study stands as a precise map of a digital boundary, showing exactly where a virtual machine decides to leave the ground.

Technical Summary: Simulation Evaluation of the Takeoff Threshold of an ArduPilot Gazebo Quadrotor and Conditions for Physical Implementation

Problem Statement
Physical flight testing of quadrotors is inherently subject to variability caused by vehicle condition, battery state, and external disturbances. While prior research has utilized onboard sensors and flight-control software for attitude estimation and control, there is a need for a reproducible simulation environment to isolate and compare minute input differences immediately preceding takeoff. This study addresses the challenge of quantitatively identifying the specific radio-control (RC) throttle command threshold at which a simulated quadrotor transitions from a grounded state to sustained upward motion, establishing a baseline for subsequent physical implementation.

Methodology
The research employed a Software-In-The-Loop (SITL) architecture coupling ArduPilot Copter software with the Gazebo physics simulator. The simulation ran on an Intel MacBook Pro (macOS 14.8.7) with Gazebo operating in server/headless mode, communicating via a JSON control interface. The vehicle model was a "Quad X" configuration using the iris_with_gimbal model, operating in STABILIZE flight mode.

The study systematically varied RC throttle commands across integer values: 1450, 1475, 1485, 1486, 1487, 1488, 1490, and 1500. Data analysis focused on MAVLink telemetry logs, specifically extracting RC_CHANNELS, GLOBAL_POSITION_INT, VFR_HUD, and SERVO_OUTPUT_RAW messages. For each command, a 7-second analysis window was defined based on host log-recording timestamps (from 1 to 8 seconds after a new command was observed).

Key metrics calculated included:

Altitude Increase ( $\Delta h$ ): The difference between the final and initial relative altitude values within the window.
Mean Climb Rate: The arithmetic mean of VFR_HUD.climb values, distinct from $\Delta h$ divided by time.
Mean Motor Output: The average of non-zero servo outputs for the four motors.

Takeoff was classified based on a numerical rule: a "Takeoff" state was assigned if the mean altitude increase for a command group was positive; otherwise, it was "No takeoff." The study utilized SHA-256 integrity checks to ensure data consistency and reproducibility.

Key Results
The simulation identified a distinct transition boundary between integer commands 1485 and 1486:

No Takeoff (RC 1485): At command 1485, no altitude increase was observed ( $\Delta h = 0.000$ m), and the mean climb rate was negligible ($0.00006$ m/s).
Takeoff (RC 1486): At command 1486, two separate trials both yielded an altitude increase of $0.090$ m. The mean climb rate was $0.02709 \pm 0.00064$ m/s.
Progression: Higher commands (1487–1500) resulted in progressively larger altitude increases and climb rates, reaching $1.710$ m and $0.540$ m/s respectively at RC 1500.

The mean motor output increased smoothly across the tested range (from 1560.77 at RC 1485 to 1561.55 at RC 1486), indicating that the transition was not caused by a discontinuity in motor output but rather represented the physical threshold where thrust overcame gravity and ground contact.

Model Mass and Physical Implementation Conditions
The study calculated the total inertial mass of the simulated iris_with_gimbal model by summing the masses defined in the Simulation Description Format (SDF) files:

Base link: 1.50 kg
IMU link: 0.15 kg
Four rotors: 0.10 kg (0.025 kg each)
Gimbal assembly: 0.23 kg
Total Simulated Mass: 1.98 kg

This value serves as a nominal design reference for a physical prototype. The study compared this mass against a commercial propulsion system (T-MOTOR AIR2216II-KV920 with T1045 propeller), noting that the theoretical hover requirement of approximately 495 gf per motor falls within the manufacturer's reported thrust range, suggesting a thrust-to-weight ratio of approximately 2.7 at maximum static thrust.

Significance and Claims
The paper establishes a reproducible baseline for evaluating takeoff thresholds in a controlled simulation environment. Its primary contributions are:

Quantitative Boundary Identification: It precisely brackets the takeoff transition between RC commands 1485 and 1486 under specific simulation conditions.
Design Reference: It provides a calculated mass (1.98 kg) and motor-speed scale for an initial physical prototype design.
Methodological Framework: It documents a rigorous data analysis procedure, including specific time-window definitions and integrity checks, to facilitate distributed simulation and future physical validation.

The author explicitly states that the observed boundary is specific to the current simulation configuration and that command values are not calibrated to physical thrust in Newtons. Consequently, the results are presented as a foundation for repeated threshold evaluation, distributed simulation across multiple computers, and subsequent physical thrust calibration, rather than as a definitive physical flight guarantee. Future work is proposed to address thermal load in distributed computing and to perform physical thrust calibration and low-altitude flight tests to bridge the gap between simulation and reality.

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