Research on Dynamic Center-of-Mass Reconfiguration for Enhancement of UAV Performances Based on Simulations and Experiment

Highlights

What are the main findings?

• The center-of-mass (CoM) shifting mechanism can generate stabilizing gravitational torques, effectively reducing angular deviations during propulsion failure, enabling reliable self-righting in a near-horizontal manner, as well as enhancing its aerial maneuverability and braking performance and reducing power consumption.
• Simulation and experimental results confirm that the CoM system provides a fail-safe stabilization feature, which is independent of rotor thrust, and ensures structural protection and operational continuity during emergencies.

What are the implications of the main findings?

• Integrating a dynamic CoM shifting mechanism is a critical design strategy for next-generation UAVs, providing stability even under motor-out or free-fall condi-tions, and substantially improving safety, efficiency, and mission survivability.
• This research establishes a validated framework for gravitational stabilization, demonstrating how active mass reconfiguration can be applied to UAVs to enhance stability, agility, and energy efficiency.

Abstract

The stability of unmanned aerial vehicles (UAVs) during propulsion failure remains a critical safety challenge. This study presents a center-of-mass (CoM) correction device, a compact, under-slung, and dual-axis prismatic stage, which can reposition a dedicated shifting mass within the UAV frame to generate stabilizing gravitational torques by the closed-loop feedback from the inertial measurement unit (IMU). Two major experiments were conducted to evaluate the feasibility of the system. In a controlled roll test with varying payloads, the device produced a corrective torque up to 1.2375 N·m, reducing maximum roll deviations from nearly 90° without the device to less than 5° with it. In a dynamic free-fall simulation, the baseline UAV exhibited rapid tumbling and inverted impacts, whereas with the CoM system activated, the UAV maintained a near-level attitude to achieve the upright recovery and greatly reduced structural stress prior to ground contact. The CoM device, as a fail-safe stabilizer, can also enhance maneuverability by increasing control authority, enable a faster speed response and more efficient in-air braking without reliance on the rotor thrust, and achieve comprehensive energy saving, at about 7% of the total power budget. In summary, the roll stabilization and free-fall results show that the CoM device can work as a practical pathway toward the safer, more agile, and energy-efficient UAV platforms for civil, industrial, and defense applications.

1. Introduction

1.1. Motivation

UAVs are essential in various civil, industrial, and defense applications, such as aerial mapping, agricultural surveillance, infrastructure assessment, package distribution, and disaster response activities [1]. Their adaptability, vertical takeoff and landing capability, and proficiency in complex or inaccessible areas render them superior to conventional manned aircraft in numerous scenarios. Nonetheless, despite ongoing advancements in propulsion technology, navigation algorithms, and onboard computing capabilities, UAVs continue to be susceptible to significant instabilities during flight. Quadrotors and other multirotor platforms are significantly reliant on constant rotor thrust to maintain stability, as their aerodynamic design does not possess intrinsic passive self-stabilizing characteristics [1]. As a result, these systems are susceptible to catastrophic failure in situations such as abrupt engine cessation, battery exhaustion, intense wind gusts, or impacts [2].

Traditional techniques for UAV stability and crash prevention predominantly depend on active control procedures, such as Proportional–Integral–Derivative (PID) tuning, adaptive control systems, thrust vectoring, or differential rotor-speed modulation [3]. Although these strategies ensure accurate maneuverability during standard operations, they are wholly reliant on rotor-generated torque, which proves ineffectual in scenarios of complete or partial thrust loss. Moreover, dependence on continuous rotor actuation increases energy consumption, diminishes battery longevity, and hastens the degradation of electronic speed controllers (ESCs) and motors, therefore constraining endurance and operational safety [4]. Alternative alternatives, including aerodynamic braking devices and parachute recovery systems, have been suggested; however, these techniques are either excessively energy-consuming, difficult to activate, or unable to maintain a stable orientation during descent [2].

These constraints underlie the necessity for an auxiliary stabilization method that diminishes reliance on motor power while concurrently improving crash resilience and energy economy [1]. Mechanical augmentation systems, especially those utilizing mass redistribution, offer a viable answer [5]. By dynamically altering CoM of the UAV, corrective gravity torques can be produced to counteract unwanted roll and pitch aberrations, thus aiding in both active stabilizing and passive crash prevention. In contrast to only software-driven methods, CoM adjustment mechanisms can operate even in the case of total propulsion failure, providing a fail-safe capability for UAV survivability during catastrophic failure scenarios.

This study presents the design and assessment of an innovative multi-functional CoM shifting device, created as a lightweight and modular UAV attachment. The suggested system utilizes a two-axis rack-and-pinion actuation platform, powered by two stepper motors, to dynamically adjust a moveable payload in real time. The device is designed to perform four essential functions: (1) crash protection by preserving horizontal orientation during power-failure descents, thus averting structural damage upon impact; (2) performance enhancement by augmenting maneuverability and minimizing overshoot during aggressive maneuvers; (3) energy efficiency by decreasing motor thrust requirements during stabilization, resulting in prolonged battery life; and (4) system versatility, allowing the module to be incorporated into various UAV platforms with minimal modifications [6].

The proposed work formulates the theories of rigid-body dynamics and CoM mechanics, extending its application to the safety and performance optimization of UAVs. This research illustrates how a compact mechanical subsystem can enhance UAV stability management using MATLAB/Simulink (R2022a) modeling, physical construction, and experimental validation. The CoM shifting device, by including a secondary, thrust-independent control input, signifies a substantial advancement in the development of robust, fail-safe, and energy-efficient UAV design.

1.2. Literature Review

The stability and control of multi-rotor UAVs have been widely investigated, with most studies concentrating on improving motor-based attitude control. Classical PID controllers dominate due to their simplicity and strong real-time performance [3], while more advanced methods, such as adaptive control, gain scheduling, and nonlinear strategies, seek to enhance robustness under various flight conditions [7]. However, all these approaches fundamentally depend on active rotor thrust, making them ineffective during partial or total propulsion loss, rapid deceleration, or free-fall scenarios where no thrust-generated moments are available [2].

UAV crash-safety solutions are typically divided into passive mitigation and active stabilization. Passive methods, including deformable landing structures, protective cages, and parachute systems, can reduce impact severity but cannot maintain attitude during descent [2]. Active strategies, such as aerodynamic control surfaces, controlled auto-rotation, or emergency rotor braking, require aerodynamic efficiency or residual thrust and therefore cannot provide stabilization when all motors are disabled [8].

The concept of modifying the CoM has been adopted in various robotic systems as a means of improving stability and managing disturbances. In aerial applications, CoM shifting mechanisms have been explored primarily in blimp-type platforms or for limited maneuver adjustments in small quadrotors. These approaches often rely on single-axis displacement or platform-specific designs, limiting their applicability as general-purpose UAV modules [5].

The existing literature therefore reveals a gap: very few studies address UAV stabilization under full propulsion loss, and fewer explore mechanical mass shifting as an independent source of corrective torque. Prior implementations typically support only simple balancing or trim correction and are not designed to deliver rapid, high-authority stabilization during free-fall.

The proposed dual-axis rack-and-pinion CoM shifting mechanism advances the current state of the art by providing a compact, lightweight module capable of generating gravity-induced corrective moments without relying on propeller thrust. Unlike previous CoM approaches offering single-function use, this system supports multiple roles—including emergency stabilization, improved maneuverability, and enhanced energy efficiency—while remaining compatible with standard multirotor structures [1].

1.3. Innovation, Contributions, and Technical Challenges

This work addresses the fundamental limitation of multirotor UAV during propulsion-loss or zero-thrust conditions, where no aerodynamic restoring moments exist and conventional attitude controllers become ineffective. Once propulsive torque is unavailable, the vehicle behaves as an uncontrolled rigid body dominated by gravity, inertia, and aerodynamic drag, making self-righting nearly impossible. To overcome this challenge, we introduce a novel CoM shifting mechanism that generates corrective gravity-induced torques independent of rotor thrust. Unlike prior CoM adjustment studies that focus primarily on hover-level trimming or quasi-static structural balancing, the proposed approach enables high-authority stabilization during free fall [9].

Theoretical innovation lies in integrating configuration-dependent inertia, gravity-induced moments, and electromechanical stage dynamics into a unified UAV model, coupled with a real-time controller that transforms instantaneous attitude errors into bounded payload displacements. This creates a passive, energy-efficient stabilization pathway that remains fully operational even when motors’ failures happen.

Achieving such stabilization, however, introduces several technical challenges. First, under zero-thrust conditions, the absence of aerodynamic restoring moments causes even small disturbances to rapidly evolve into uncontrollable tumbling, making the control problem fundamentally nonlinear and highly sensitive to initial conditions. Second, the CoM shifting device must generate sufficient mass displacement within tight geometric and weight constraints, while still producing gravity-based corrective torques large enough to counter high angular accelerations. Third, the movement of the internal mass introduces configuration-dependent inertia changes that must be continually modeled and compensated. Finally, the control system must remain robust to actuator saturation, mechanical backlash, and nonlinear coupling effects, all of which become more pronounced during rapid free-fall dynamics [10].

Together, these contributions and challenges position the proposed CoM based stabilization as a new pathway for UAV safety-critical operation, enabling reliable attitude recovery in scenarios where thrust-based and aerodynamic methods fail.

2. Overall Aerial Vehicle System Design and Detailed Hardware Integration

2.1. Airframe and CoM Shifting Device

We present the overall aerial vehicle system and the detailed hardware integration of the CoM shifting quadrotor used in our experiments. The airframe is a 7-inch X-configuration quadcopter, shown in Figure 1 (Generic Manufacturer, Shenzhen, China), outfitted with a self-designed, compact, under-slung two-axis translational stage (77 × 77 mm footprint) that repositions a concentrated payload to generate quasi-static roll/pitch moments. These moments are expressed as ${\mathit{\tau }}_{\mathit{\varphi }}$ and ${\mathit{\tau }}_{\mathit{\theta }}$ in Equation (1), the effective shifting mass used in modeling is ${\mathit{m}}_{\mathit{s}}$ ≈ 0.20 kg with symmetric in-plane travel $\left|{\mathit{x}}_{\mathit{s}}\right|,\left|{\mathit{y}}_{\mathit{s}}\right| \le 20$ mm. Mounting the stage below the frame deliberately lowers the natural CoM, improving passive stability and ensuring gravity-generated moments that act in the intuitive directions around hover. These moments are defined as follows:

$${\mathit{\tau }}_{\mathit{\varphi }}\approx {\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{y}}_{\mathit{s}}, {\mathit{\tau }}_{\mathit{\theta }}\approx -{\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{x}}_{\mathit{s}}$$

(1)

2.2. Actuation and Motor Sizing

Actuation on each axis is provided by a NEMA-14 stepper (1.8°/step, 0.8 A/phase) driving an A4988 micro-stepping power stage (Waveshare, Shenzhen, China). We set the A4988 current limit from the manufacturer relation ${\mathit{I}}_{\mathit{t}\mathit{r}\mathit{i}\mathit{p}}={\mathit{V}}_{\mathit{r}\mathit{e}\mathit{f}}/\left(8{\mathit{R}}_{\mathit{s}\mathit{e}\mathit{n}\mathit{s}\mathit{e}}\right)$; with ${\mathit{R}}_{\mathit{s}\mathit{e}\mathit{n}\mathit{s}\mathit{e}}=0.10 \mathsf{\Omega }$ and a desired ${\mathit{I}}_{\mathit{t}\mathit{r}\mathit{i}\mathit{p}}=0.80$, A we obtain ${\mathit{V}}_{\mathit{r}\mathit{e}\mathit{f}}\approx 0.64$ V. A 6 mm pinion (radius ${\mathit{r}}_{\mathit{p}}=6\times {10}^{-3}$) yields a carriage force capability $\mathit{F}\approx \mathit{\eta }{\mathit{\tau }}_{\mathit{m}}/{\mathit{r}}_{\mathit{p}}$; with typical dynamic motor torque 0.02–0.03 N·m and efficiency $\mathit{\eta }\in [0.7,0.9]$, the available in-plane force is 2.3–4.5 N—ample for 0.20 kg payload accelerations of approximately 10–20 m·s⁻², with additional allowance for friction. Kinematically, 200 steps per revolution at 16× micro-stepping results in 3200 micro-steps per revolution. The pinion circumference, $2\mathit{\pi }{\mathit{r}}_{\mathit{p}}\approx 37.7\hspace{0.17em}\mathrm{mm}$, produces 84.9 micro-steps per millimeter. Thus, a 20 mm move requires approximately 1700 micro-steps, which, when executed in 0.10 s, demands an edge rate of around 17 kHz—achievable by the ESP32 pulse engine with 2–3 µs step pulses (Espressif Systems, Shenzhen, China). The mechanical assembly and exploded CAD rendering of the translational stage are illustrated in Figure 1b,c.

2.3. Homing and Calibration

Homing uses a deterministic sequence: drive toward the negative end-stop until the input reads HIGH, traverse to the positive end to determine travel in steps and return exactly half the count to establish the hard center; this procedure eliminates any accumulated micro-step drift and fixes the mapping between commanded millimeters and internal counters before each run. Figure 2 and Figure 3 illustrate the CoM shifting mechanism and the components integrated into the quadrotor frame.

The integration and calibration sequence used in the experiments. After assembly, we measure the effective steps per millimeter by commanding known displacements and verifying with calipers, adjust the micro-step setting (8×/16×) to trade step rate for smoothness, and set ${\mathit{V}}_{\mathit{r}\mathit{e}\mathit{f}}$ for thermal headroom at the intended duty cycle [11]. With the vehicle restrained on a low-friction roll/pitch cradle, we run the homing routine and record the travel count in steps on both axes. We then map stage millimeters to attitude torque using the gravity-static relation ${\mathit{\tau }}_{\mathit{g}}={\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{r}}_{\mathit{s}}$ and verify the sign conventions by applying small offsets and observing the FC-reported moments (or the cradle’s restoring angle). The flight controller’s Multiway Serial Protocol (MSP) telemetry stream for attitude and RC commands is validated by exciting the roll axis with the transmitter and comparing the percentage-mapped RC roll input to the measured roll angle.; if necessary, the ESP32 tool commands (rczero), (rcdead), and (rcspan) are used to center and scale the roll channel so that 0% corresponds to 1500 µs and ±100% to $1500\pm \mathrm{s}\mathrm{p}\mathrm{a}\mathrm{n}$ µs. With these calibrations, the controller is enabled in “roll-only” (Y follows $\mathit{\varphi }$, X holds center) and then “roll-pitch” (Y follows $\mathit{\varphi }$, X follows $\mathit{\theta }$), using Schmitt deadbands to suppress chatter near zero and acceleration-limited pulse scheduling to prevent missed steps during rapid stick inputs. Indoor contact-based experiments (stage enabled vs. disabled) are conducted with the airframe tethered on a single-axis pivot, as reported in the results section: for the same RC inputs, the CoM device produces larger steady angles and faster transients in the commanded direction, consistent with the additional torque budget ${\mathit{\tau }}_{\mathit{g},\mathbf{m}\mathbf{a}\mathbf{x}}={\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{d}}_{\mathit{m}\mathit{a}\mathit{x}}$ and the linearized attitude dynamics. The stage’s behavior is also described by Equation (2), which represents the moments as a function of the shifting mass and its displacements:

$${\mathit{I}}_{\mathit{x}\mathit{x}}\ddot{\mathit{\varphi }}\simeq {\mathit{\tau }}_{\mathit{x}}+{\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{y}}_{\mathit{s}}, {\mathit{I}}_{\mathit{y}\mathit{y}}\ddot{\mathit{\theta }}\simeq {\mathit{\tau }}_{\mathit{y}}-{\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{x}}_{\mathit{s}}$$

(2)

Throughout, thermal limits of the drivers and steppers are monitored; at the selected current the heat rise is within specification, and the limit-switch hard-center is executed.

2.4. Control Flow and System Architecture

The overall system architecture of the CoM shifting quadrotor is illustrated in Figure 4, while the corresponding operational flow of the control algorithm is shown in Figure 5. Upon power-up, the onboard ESP32 microcontroller initializes all hardware resources, including GPIO pins, UART/MSP communication links, and stepper motor drivers. Once initialized, the system executes a re-homing sequence for the XY stage: the carriage first travels toward the minimum end-stop until a switch signal confirms the mechanical boundary, then sweeps to the maximum position to measure the total travel in steps and finally returns to the geometric center by moving half of the total count. This procedure ensures a precise, repeatable reference point for subsequent operations, eliminating accumulated micro-step drift and establishing a consistent mapping between commanded angles and stage displacement.

Following initialization, the control pipeline enters a continuous loop. In each cycle, the system first acquires real-time data streams, including UAV attitude from the flight controller and pilot commands from the RC transmitter. These inputs are then processed through offset calibration and low pass filtering to suppress noise. A Schmitt-trigger style center latch is applied to prevent small fluctuations around zero from causing unintended actuation, effectively reducing jitter and unnecessary corrections. Based on these filtered inputs, target positions for the XY stage are generated according to the current operating mode.

Three operating modes are supported, selectable from the ground console. In CENTER mode, both axes remain fixed at the mechanical center, rendering the stage a passive mass with no active contribution. In ROLL-ONLY mode, the X-axis displacement is directly mapped to the roll angle, while the Y-axis remains centered. In ROLL-PITCH mode, both axes actively track their corresponding roll and pitch channels, thereby generating corrective torques in two degrees of freedom.

The mapping between angular error and commanded displacement follows a linear saturating law:

$${\mathit{n}}_{\mathit{x}}=\left({\displaystyle \frac{{\mathit{\theta }}_{\mathit{x}}}{2{\mathit{\theta }}_{\mathbf{m}\mathbf{a}\mathbf{x}}}}+{\displaystyle \frac{1}{2}}\right){\mathit{N}}_{\mathit{x}},{\mathit{n}}_{\mathit{y}}=\left({\displaystyle \frac{{\mathit{\theta }}_{\mathit{y}}}{2{\mathit{\theta }}_{\mathbf{m}\mathbf{a}\mathbf{x}}}}+{\displaystyle \frac{1}{2}}\right){\mathit{N}}_{\mathit{y}}$$

(3)

where ${\mathit{\theta }}_{\mathit{x}},$ are the roll and pitch angles, ${\mathit{\theta }}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ is saturation bound, and ${\mathit{N}}_{\mathit{x}},{\mathit{N}}_{\mathit{y}}$ are the total microstep counts per axis. This ensures that angular deviations beyond $\pm {\mathit{\theta }}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ are clipped to the maximum allowable stage travel.

Execution of stage motion is handled by two dedicated Free RTOS tasks running in parallel with the X and Y axes. Each task computes a proportional rate command that is constrained by an acceleration limiter to avoid sudden step jumps that could lead to missed pulses or mechanical stress. These commands are then converted into STEP/DIR pulses sent to the motor drivers, with built-in checks to respect limit-switch states. This structure ensures that the stage never exceeds its mechanical travel limits, even under extreme commands. A telemetry process running at approximately 10 Hz provides status updates, enabling operators to monitor system health, stage position, and error states during operation.

This integrated architecture offers multiple advantages. The initialization sequence guarantees a drift-free reference center, the filtering and center-latch mechanism suppress spurious oscillations, and the Free RTOS-based multi-tasking ensures precise real-time control of both axes. Collectively, these features contribute to stable operation, chatter suppression, fail-safe behavior, and reliable torque generation, all of which are essential for deploying the CoM shifting device in demanding UAV stabilization scenarios.

Target generation depends on an operating mode selected from the ground console. In CENTER mode the stage remains at the mechanical center and acts only as a passive load. In ROLL-ONLY the X-axis tracks roll while Y is held at center. In ROLL-PITCH both axes track their corresponding attitude channels. The angle–to–position map is a linear saturating law with a configurable full-scale span; for example, an X-axis span of ±θ max degrees maps to the integer step range $\left[0,\hspace{0.17em}{\mathit{N}}_{\mathit{x}}\right]$ as shown in Equation (4):

$${\mathit{n}}_{\mathit{x}}=\left({\displaystyle \frac{{\mathsf{\theta }}_{\mathit{x}}}{2{\mathsf{\theta }}_{\mathit{m}\mathit{a}\mathit{x}}}}+{\displaystyle \frac{1}{2}},\hspace{0.17em}0,\hspace{0.17em}1\right){\mathit{N}}_{\mathit{x}}$$

(4)

which is equivalent to the code’s angle To Steps Span routine.

Finally, the commanded stage displacement is converted into physical torque contributions about roll and pitch as explained in the Equation (1).

2.5. Controller Parameter Selection and Tuning Methodology

To ensure reproducible and well-defined control behavior, all controller parameters were selected using a structured tuning procedure. The proportional, integral, and derivative gains for each axis were first estimated from the linearized hover-model obtained in Section 3.7, using the dominant eigenvalues to identify the natural frequency and damping ratio of the open-loop roll and pitch dynamics. Initial PID gains were selected to achieve a closed-loop damping ratio of approximately 0.7–0.9, balancing responsiveness with overshoot suppression. These baseline gains were then refined through iterative simulations in MATLAB/Simulink, where step responses, disturbance rejection, and settling times were evaluated under varying payload masses. Saturation limits for the commanded displacement were chosen according to the physical stroke bounds (±20–40 mm), and a first-order low-pass filter (cutoff ≈ 6–10 Hz) was applied to prevent high-frequency oscillations driven by IMU noise. The Schmitt-trigger deadband was calibrated experimentally (±1.5–2°) to eliminate jitter around zero while preserving rapid corrective action. This systematic tuning process ensured consistent and stable performance across all simulated and hardware-tested conditions.

2.6. Detailed Procedure for CoM Reconfiguration

This subsection provides a detailed description of how CoM reconfiguration is performed in real time. The procedure consists of four sequential stages: (1) sensing, (2) error processing, (3) displacement command generation, and (4) execution through the XY prismatic stage.

2.6.1. Attitude Sensing

The flight controller transmits roll and pitch measurements at 100–200 Hz via MSP/UART. These signals are received by the ESP32, where time stamps and data validity checks prevent stale or corrupted packets. The angular rates (ωₓ, ωᵧ) and Euler angles (ϕ, θ) form the basis for computing the instantaneous body attitude.

2.6.2. Error Computation and Filtering

For each axis, the ESP32 computes the orientation error relative to the reference (ϕ = 0°, θ = 0°) as in Equation (5),

$${\mathit{e}}_{\mathit{\varphi }}=\mathit{\varphi }-{\mathit{\varphi }}_{\mathrm{ref}},{\mathit{e}}_{\mathit{\theta }}=\mathit{\theta }-{\mathit{\theta }}_{\mathrm{ref}}$$

(5)

These errors are passed through a first-order low-pass filter (cutoff 6–10 Hz) to remove IMU noise and through a ±1.5–2° Schmitt-trigger deadband to prevent unnecessary micromotions.

2.6.3. Mapping Orientation Error to CoM Displacement

Filtered errors are converted to desired slider positions using a proportional mapping law in Equation (6):

$${\mathit{x}}_{\mathit{C}\mathit{O}\mathit{M}}={\mathit{k}}_{\mathit{\varphi }}\hspace{0.17em}{\mathit{e}}_{\mathit{\varphi }},{\mathit{y}}_{\mathit{C}\mathit{O}\mathit{M}}={\mathit{k}}_{\mathit{\theta }}\hspace{0.17em}{\mathit{e}}_{\mathit{\theta }}$$

(6)

The constants ${\mathit{k}}_{\mathit{\varphi }}$ and ${\mathit{k}}_{\mathit{\theta }}$ are selected such that a $\pm {\mathit{\theta }}_{\mathit{m}\mathit{a}\mathit{x}}$ deviation corresponds to the full physical stroke (±20–40 mm). Saturation logic clips the displacement commands to stay within mechanical travel limits, preventing overextension.

2.6.4. Motion Execution via Prismatic XY Stage

The target displacements are executed by two dedicated FreeRTOS motor-control tasks, one assigned to each axis. Each task computes the necessary micro-step velocity according to an acceleration-limited motion profile that gradually ramps the speed to avoid mechanical shock. The controller also enforces upper bounds on the step frequency to prevent missed pulses during rapid movements. Throughout execution, the system continuously monitors the limit-switch states, ensuring that the stage never travels beyond its safe mechanical boundaries. Once the commanded position is reached, the driver reduces or disables the holding current to minimize power consumption while maintaining positional accuracy. Once the target position is reached, the holding current is reduced or disabled to minimize power consumption. Throughout operation, telemetry packets (10 Hz) report slider position, motor load, limit-switch state, and controller flags.

3. Analytical Modeling of the UAV and Integrated CoM Device

3.1. Concept of CoM

The concept of the CoM can be illustrated using a simple two-body system, as shown in Figure 6. If two-point masses, ${\mathit{m}}_1$ (at position $\mathsf{\alpha }$) and ${\mathit{m}}_2$ (at position $\mathit{\beta }$), are equal, the CoM lies exactly at the midpoint of the line segment $\mathit{\alpha }\mathit{\beta }$. However, when the masses differ, the CoM shifts toward the heavier mass. The ratio of distances from the CoM to each body is inversely proportional to their mass ratio in Equation (7)

$${\displaystyle \frac{\stackrel{\mathit{‾}}{\mathit{\alpha }\mathit{x}}}{\stackrel{\mathit{‾}}{\mathit{x}\mathit{\beta }}}}={\displaystyle \frac{{\mathit{m}}_2}{{\mathit{m}}_1}}$$

(7)

This principle underpins the mechanism of our UAV stabilization device, where controlled CoM displacement generates corrective torques during disturbances [12].

3.2. Rigid-Body Modeling with Moving Mass

We model the quadrotor as a rigid body with a planar shifting mass moving on an orthogonal stage mounted to the frame. Let the inertial frame be $\mathcal{I}=\{{\mathit{e}}_{\mathit{x}},{\mathit{e}}_{\mathit{y}},{\mathit{e}}_{\mathit{z}}\}$ (${\mathit{e}}_{\mathit{z}}$ upward) and the body frame be $\mathcal{B}$ attached to the airframe at a fixed origin ${\mathit{O}}_{\mathit{B}}$. The pose is described by $\mathit{p}\in {\mathbb{R}}^3$ and $\mathit{R}\in \mathit{S}\mathit{O}\left(3\right)$ (body-to-inertial), with body angular velocity $\mathit{\omega }\in {\mathbb{R}}^3$. The fixed part of the vehicle has mass ${\mathit{m}}_{\mathit{f}}$ and body inertia ${\mathit{I}}_{\mathit{f}}$ about ${\mathit{O}}_{\mathit{B}}$. The shifting mass has magnitude ${\mathit{m}}_{\mathit{s}}$ and body-frame position ${\mathit{r}}_{\mathit{s}}={[\hspace{0.17em}{\mathit{x}}_{\mathit{s}}\hspace{0.33em}{\mathit{y}}_{\mathit{s}}\hspace{0.33em}0\hspace{0.17em}]}^{\mathbf{\top }}$, with travel bounds $\left|{\mathit{x}}_{\mathit{s}}\right|,\left|{\mathit{y}}_{\mathit{s}}\right|\le {\mathit{d}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$. The total mass is $\mathit{M}={\mathit{m}}_{\mathit{f}}+{\mathit{m}}_{\mathit{s}}$, and the instantaneous center of mass CoM relative to ${\mathit{O}}_{\mathit{B}}$ is in the Equation (8)

$$\mathit{\rho }={\displaystyle \frac{1}{\mathit{M}}}\left({\mathit{m}}_{\mathit{f}}{\mathit{r}}_{\mathit{f}}+{\mathit{m}}_{\mathit{s}}{\mathit{r}}_{\mathit{s}}\right), {\mathit{r}}_{\mathit{f}}\equiv 0\hspace{0.33em}\Rightarrow \hspace{0.33em}\mathit{\rho }={\displaystyle \frac{{\mathit{m}}_{\mathit{s}}}{\mathit{M}}}{\mathit{r}}_{\mathit{s}}$$

(8)

Because the internal mass moves, the body inertia about ${\mathit{O}}_{\mathit{B}}$ varies with configuration through the parallel-axis term [13]

$${\mathit{I}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)={\mathit{I}}_{\mathit{f}}+{\mathit{m}}_{\mathit{s}}\left({\parallel {\mathit{r}}_{\mathit{s}}\parallel }^2{\mathit{I}}_3-{\mathit{r}}_{\mathit{s}}{\mathit{r}}_{\mathit{s}}^{\mathbf{\top }}\right)={\mathit{I}}_{\mathit{f}}+{\mathit{m}}_{\mathit{s}}\hspace{0.17em}\mathit{S}\left({\mathit{r}}_{\mathit{s}}\right){\mathit{S}\left({\mathit{r}}_{\mathit{s}}\right)}^{\mathbf{\top }}$$

(9)

and its exact time derivative is ${\dot{\mathit{I}}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)={\mathit{m}}_{\mathit{s}}\left[\mathit{S}\left({\dot{\mathit{r}}}_{\mathit{s}}\right)\mathit{S}({\mathit{r}}_{\mathit{s}}{)}^{\mathbf{\top }}+\mathit{S}({\mathit{r}}_{\mathit{s}})\mathit{S}{\left({\dot{\mathit{r}}}_{\mathit{s}}\right)}^{\mathbf{\top }}\right]$. The kinematics satisfy $\dot{\mathit{p}}=\mathit{v}$ and $\dot{\mathit{R}}=\mathit{R}\mathit{S}\left(\mathit{\omega }\right)$.

3.3. Translational and Rotational Dynamics

The translational dynamics of the origin ${\mathit{O}}_{\mathit{B}}$ follow Newton’s law [14]

$$\mathit{M}\dot{\mathit{v}}=\mathit{M}\mathit{g}{\mathit{e}}_{\mathit{z}}+{\mathit{F}}_{\mathrm{rot}}+{\mathit{F}}_{\mathrm{ext}}$$

(10)

where ${\mathit{F}}_{\mathrm{rot}}=-\left({\sum }_{\mathit{i}=1}^4{\mathit{T}}_{\mathit{i}}\right)\mathit{R}{\mathit{e}}_{\mathit{z}}$ is the total propeller thrust (expressed in $\mathcal{I}$) and $\mathit{g}=9.81$ m·s⁻². The rotational dynamics about ${\mathit{O}}_{\mathit{B}}$ are obtained from the Newton–Euler equations for a body with time-varying inertia [15],

$${\mathit{I}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)\hspace{0.17em}\dot{\mathit{\omega }}+\mathit{\omega }\times \left({\mathit{I}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)\hspace{0.17em}\mathit{\omega }\right)+\dot{{\mathit{I}}_{\mathit{B}}}\left({\mathit{r}}_{\mathit{s}}\right)\hspace{0.17em}={\mathit{\tau }}_{\mathrm{rot}}+{\mathit{\tau }}_{\mathit{g}}\left({\mathit{r}}_{\mathit{s}},\mathit{R}\right)+{\mathit{\tau }}_{\mathrm{ext}}$$

(11)

3.4. Gravity-Induced Moments

The gravity-induced moment is the moment of the weight acting at the CoM [10],

$${\mathit{\tau }}_{\mathit{g}}({\mathit{r}}_{\mathit{s}},\mathit{R})=\mathit{\rho }\times {\mathit{R}}^{\mathbf{\top }}\left(\mathit{M}\mathit{g}\hspace{0.17em}{\mathit{e}}_{\mathit{z}}\right)=\mathit{S}\left(\mathit{\rho }\right)\hspace{0.17em}{\mathit{R}}^{\mathbf{\top }}(\mathit{M}\mathit{g}\hspace{0.17em}{\mathit{e}}_{\mathit{z}})$$

(12)

For the planar stage with small attitude ($\mathit{R}\approx {\mathit{I}}_3$) this reduces to ${\mathit{\tau }}_{\mathit{g}}\simeq {[\hspace{0.17em}{\mathit{m}}_{\mathit{s}}\mathit{g}\hspace{0.17em}{\mathit{y}}_{\mathit{s}},\hspace{0.17em}-{\mathit{m}}_{\mathit{s}}\mathit{g}\hspace{0.17em}{\mathit{x}}_{\mathit{s}},\hspace{0.17em}0\hspace{0.17em}]}^{\mathbf{\top }}$, which makes explicit that a lateral carriage motion along $+\mathit{y}$ yields a positive roll torque, while a forward motion $+\mathit{x}$ yields a negative pitch torque.

3.5. Allocation Model

The rotor forces are modeled as ${\mathit{T}}_{\mathit{i}}=\mathit{b}{\mathsf{\Omega }}_{\mathit{i}}^2$ and the reaction torques as ${\mathit{Q}}_{\mathit{i}}={\mathit{\sigma }}_{\mathit{i}}\mathit{k}{\mathsf{\Omega }}_{\mathit{i}}^2$ with ${\mathit{\sigma }}_{\mathit{i}} \in \{+1\}$ [12]. For an X-quad with arm length $\mathit{l}$, the standard allocation maps thrusts ${\left\{{\mathit{T}}_{\mathit{i}}\right\}}_{\mathit{i}=1}^4$ to the generalized force $\mathit{u}={[\mathit{f},{\mathit{\tau }}_{\mathit{x}},{\mathit{\tau }}_{\mathit{y}},{\mathit{\tau }}_{\mathit{z}}]}^{\mathbf{\top }}$ via

$$\left[\begin{array}{c}\mathit{f}\\ {\mathit{\tau }}_{\mathit{x}}\\ {\mathit{\tau }}_{\mathit{y}}\\ {\mathit{\tau }}_{\mathit{z}}\end{array}\right]=\underset{\hspace{0.17em}\hspace{0.17em}\mathit{A}\mathit{l}\mathit{l}\mathit{o}\mathit{c}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{M}\mathit{a}\mathit{t}\mathit{r}\mathit{i}\mathit{x}}{\underbrace{\left[\begin{array}{cccc}1& 1& 1& 1\\ 0& \hspace{0.33em}\mathit{l}& 0& -\mathit{l}\\ -\hspace{0.17em}\mathit{l}& 0& \mathit{l}& 0\\ {\mathit{k}}_{\mathit{b}}& -{\mathit{k}}_{\mathit{b}}& {\mathit{k}}_{\mathit{b}}& -{\mathit{k}}_{\mathit{b}}\end{array}\right]}}\left[\begin{array}{c}{\mathit{T}}_1\\ {\mathit{T}}_2\\ {\mathit{T}}_3\\ {\mathit{T}}_4\end{array}\right], {\mathit{\tau }}_{\mathbf{r}\mathbf{o}\mathbf{t}}=\left[\begin{array}{c}{\mathit{\tau }}_{\mathit{x}}\\ {\mathit{\tau }}_{\mathit{y}}\\ {\mathit{\tau }}_{\mathit{z}}\end{array}\right]$$

(13)

3.6. Lagrangian Derivation

A compact and physically transparent derivation is obtained from Lagrange’s formulation [16]. Let the generalized coordinates for attitude and sliders be $\mathit{q}={[\mathit{\varphi },\mathit{\theta },\mathit{\psi },{\mathit{x}}_{\mathit{s}},{\mathit{y}}_{\mathit{s}}]}^{\mathbf{\top }}$, with small-angle kinematics $\dot{\mathit{\varphi }}={\mathit{\omega }}_{\mathit{x}}$, $\dot{\mathit{\theta }}={\mathit{\omega }}_{\mathit{y}}$, $\dot{\mathit{\psi }}={\mathit{\omega }}_{\mathit{z}}$. The velocity of the moving mass in $\mathcal{I}$ is ${\mathit{v}}_{\mathit{c}} = \mathit{v} + \mathit{R}(\mathit{\omega }\times {\mathit{r}}_{\mathit{s}}+{\dot{\mathit{r}}}_{\mathit{s}})$ [17]. The total kinetic energy is the sum of (i) the translational kinetic energy of the fixed mass lumped at ${\mathit{O}}_{\mathit{B}}$, (ii) the rotational kinetic energy with inertia ${\mathit{I}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)$, and (iii) the kinetic energy due to the internal motion of the slider [15],

$$\mathit{T}={\displaystyle \frac{1}{2}}\mathit{M} {\parallel \mathit{v}\parallel }^2+{\displaystyle \frac{1}{2}}{\mathit{\omega }}^{\mathbf{\top }}{\mathit{I}}_{\mathit{B}}({\mathit{r}}_{\mathit{s}})\hspace{0.17em}\mathit{\omega }+{\displaystyle \frac{1}{2}}{\mathit{m}}_{\mathit{s}} {\parallel \mathit{\omega }\times {\mathit{r}}_{\mathit{s}}+{\dot{\mathit{r}}}_{\mathit{s}}\hspace{0.17em}\parallel }^2$$

(14)

The potential energy from gravity is $\mathit{V}=-\mathit{M}\mathit{g}\hspace{0.17em}{\mathit{e}}_{\mathit{z}}^{\mathbf{\top }}(\mathit{p}+\mathit{R}\mathit{\rho })$. Using the Euler–Lagrange operator $\mathit{d}/\mathit{d}\mathit{t}(\partial \mathit{T}/\partial \dot{\mathit{q}})-\partial \mathit{T}/\partial \mathit{q}+\partial \mathit{V}/\partial \mathit{q}$ and inserting the generalized forces ${\mathit{Q}}_{\mathit{q}}$ produced by rotors and sliders yields exactly (3)–(4) for the vehicle and, for the sliders, the coupled equations

$${\mathit{m}}_{\mathit{s}}{\ddot{\mathit{r}}}_{\mathit{s}}+{\mathit{m}}_{\mathit{s}}\hspace{0.17em}\mathit{\omega }\times (\mathit{\omega }\times {\mathit{r}}_{\mathit{s}})+{\mathit{m}}_{\mathit{s}}\hspace{0.17em}\dot{\mathit{\omega }}\times {\mathit{r}}_{\mathit{s}}+{\mathit{m}}_{\mathit{s}}\hspace{0.17em}\mathit{\omega }\times {\dot{\mathit{r}}}_{\mathit{s}}={\mathit{F}}_{\mathit{s}}-{\displaystyle \frac{\partial \mathit{V}}{\partial {\mathit{r}}_{\mathit{s}}}}$$

(15)

where ${\mathit{F}}_{\mathit{s}}$ is the generalized actuator force delivered by the X and Y stages. The last term $\partial \mathit{V}/\partial {\mathit{r}}_{\mathit{s}}=-{\mathit{m}}_{\mathit{s}}\mathit{g}\hspace{0.17em}{\mathit{R}}^{\mathbf{\top }}{\mathit{e}}_{\mathit{z}}$ shows explicitly that gravity pulls the carriage toward the downward body direction; around hover this reduces to a constant vertical load and does not oppose in-plane motion.

3.7. Linearization Around Hover

For hover linearization ($\mathit{R}\approx {\mathit{I}}_3,\mathit{\omega }\approx 0,\mathit{v}\approx 0$) about a trim with $\mathit{f}\simeq \mathit{M}\mathit{g}$ and ${\mathit{r}}_{\mathit{s}}\simeq 0$, the attitude and slider dynamics decouple to first order, and the dominant terms become

$${\mathit{I}}_{\mathit{x}\mathit{x}}\hspace{0.17em}\ddot{\mathit{\varphi }}={\mathit{\tau }}_{\mathit{x}}+{\mathit{m}}_{\mathit{s}}\mathit{g}\hspace{0.17em}{\mathit{y}}_{\mathit{s}}, {\mathit{I}}_{\mathit{y}\mathit{y}}\hspace{0.17em}\ddot{\mathit{\theta }}={\mathit{\tau }}_{\mathit{y}}-{\mathit{m}}_{\mathit{s}}\mathit{g}\hspace{0.17em}{\mathit{x}}_{\mathit{s}}, {\mathit{I}}_{\mathit{z}\mathit{z}}\hspace{0.17em}\ddot{\mathit{\psi }}={\mathit{\tau }}_{\mathit{z}}$$

(16)

$${\mathit{m}}_{\mathit{s}}\hspace{0.17em}{\ddot{\mathit{x}}}_{\mathit{s}}\simeq {\mathit{F}}_{\mathit{x}}, {\mathit{m}}_{\mathit{s}}\hspace{0.17em}{\ddot{\mathit{y}}}_{\mathit{s}}\simeq {\mathit{F}}_{\mathit{y}}$$

(17)

where ${\mathit{F}}_{\mathit{x}},{\mathit{F}}_{\mathit{y}}$ are the in-plane actuator forces. Equations (18) make clear that the sliders act as direct torque inputs with gains ${\mathit{m}}_{\mathit{s}}\mathit{g}$ about roll and pitch. From (9), the maximum gravity torque realizable by the device is ${\mathit{\tau }}_{\mathit{g},\mathbf{m}\mathbf{a}\mathbf{x}}={\mathit{m}}_{\mathit{s}}\mathit{g}{\mathit{d}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$, which directly yields the additional angular acceleration ${\mathit{\alpha }}_{\mathrm{add}}={\displaystyle \frac{{\mathit{\tau }}_{\mathit{g},\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{I}}_{\mathit{x}\mathit{x},\mathit{y}\mathit{y}}}}$ the present design ${\mathit{m}}_{\mathit{s}}=0.20$ kg and ${\mathit{d}}_{\mathbf{m}\mathbf{a}\mathbf{x}}=0.02$ m give ${\mathit{\tau }}_{\mathit{g},\mathbf{m}\mathbf{a}\mathbf{x}}\approx 0.039$ N·m and /7.8 rad·s⁻² (about 450°·s⁻²) [18].

3.8. Electromechanical Stage Modeling

To integrate the actuation down to motor currents, we model each axis as a stepper–rack stage. Let ${\mathit{\theta }}_{\mathit{m}}$ be the motor angle, ${\mathit{r}}_{\mathit{p}}$ the pinion radius, $\mathit{N}$ the total gear ratio (including belt reduction and microstepping), and $\mathit{\eta }\in (0,1]$ the mechanical efficiency. The kinematic relation is ${\mathit{x}}_{\mathit{s}}=({\mathit{r}}_{\mathit{p}}/\mathit{N}){\mathit{\theta }}_{\mathit{m}\mathit{x}}$ and ${\mathit{y}}_{\mathit{s}}=({\mathit{r}}_{\mathit{p}}/\mathit{N}){\mathit{\theta }}_{\mathit{m}\mathit{y}}$, with velocities ${\dot{\mathit{x}}}_{\mathit{s}}=({\mathit{r}}_{\mathit{p}}/\mathit{N}){\dot{\mathit{\theta }}}_{\mathit{m}\mathit{x}}$, etc. The force at the carriage is related to motor torque by ${\mathit{F}}_{\mathit{x}}=\mathit{\eta }\hspace{0.17em}{\mathit{\tau }}_{\mathit{m}\mathit{x}}/{\mathit{r}}_{\mathit{p}}$, ${\mathit{F}}_{\mathit{y}}=\mathit{\eta }\hspace{0.17em}{\mathit{\tau }}_{\mathit{m}\mathit{y}}/{\mathit{r}}_{\mathit{p}}$. A compact electromechanical motor model is

$$\mathit{L}\mathit{i}+\mathit{R}\mathit{i}+{\mathit{K}}_{\mathit{e}}\dot{{\mathit{\theta }}_{\mathit{m}}}=\mathit{V}{\mathit{\tau }}_{\mathit{m}}={\mathit{K}}_{\mathit{t}}\mathit{i} {\mathit{J}}_{\mathit{m}}\ddot{{\mathit{\theta }}_{\mathit{m}}}+{\mathit{B}}_{\mathit{m}}\dot{{\mathit{\theta }}_{\mathit{m}}}+{\mathit{\tau }}_{\mathrm{load}}={\mathit{\tau }}_{\mathit{m}}$$

(18)

where $\mathit{i}$ is phase current, $\mathit{L},\mathit{R}$ is winding inductance and resistance, ${\mathit{K}}_{\mathit{e}}$ and ${\mathit{K}}_{\mathit{t}}$ are back-EMF and torque constants, ${\mathit{J}}_{\mathit{m}},{\mathit{B}}_{\mathit{m}}$ denote rotor inertia and viscous loss, and ${\mathit{\tau }}_{\mathrm{load}}={\displaystyle \frac{\mathit{F}{\mathit{r}}_{\mathit{p}}}{\mathit{\eta }}}$ [3]. Under micro stepping (A4988), commanded phase currents are sinusoidal; in quasi-static operation one may take $\mathit{i}$ as the current-limit setpoint, so ${\mathit{\tau }}_{\mathit{m}}\approx {\mathit{K}}_{\mathit{t}}{\mathit{i}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ and the static force capability is ${\mathit{F}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\approx \mathit{\eta }{\mathit{K}}_{\mathit{t}}{\mathit{i}}_{\mathbf{m}\mathbf{a}\mathbf{x}}/{\mathit{r}}_{\mathit{p}}$. The stroke-rate limit follows from the maximum step rate

$$\mathit{d}\mathit{o}\mathit{t}{\mathit{N}}_{\mathrm{steps},\max }:{|\dot{{\mathit{r}}_{\mathit{s}}}|}_{\mathbf{\infty }}\le {\mathit{v}}_{\mathit{m}\mathit{a}\mathit{x}}=\left({\displaystyle \frac{2\mathit{\pi }{\mathit{r}}_{\mathit{p}}}{\mathit{N}}}\right)\dot{{\mathit{N}}_{\mathrm{rev},\max }} \mathrm{with} \dot{{\mathit{N}}_{\mathrm{rev},\max }}={\displaystyle \frac{\dot{{\mathit{N}}_{\mathrm{steps},\max }}}{{\mathit{N}}_{\mathrm{steps}/\mathrm{rev}}}}$$

(19)

3.9. State Space Formulation

Collecting the foregoing, the unified first-order state model

$$\dot{\mathit{x}}=\mathit{f}(\mathit{x},\mathit{u}), \mathit{x}=\left[\mathit{p},\mathit{v},\mathit{R},\mathit{\omega },{\mathit{r}}_{\mathit{s}},{\dot{\mathit{r}}}_{\mathit{s}},{\mathit{i}}_{\mathit{m}}\right], \mathit{u}=\left[{\mathit{V}}_{\mathit{m}\mathit{x}},{\mathit{V}}_{\mathit{m}\mathit{y}},{\mathit{T}}_1,\dots ,{\mathit{T}}_4\right]$$

(20)

is obtained by rewriting (3)–(4) and (11) into first-order form, with the slider accelerations provided by (8) and the kinematic constraints $\dot{\mathit{R}}=\mathit{R}\mathit{S}\left(\mathit{\omega }\right)$, ${\dot{\mathit{r}}}_{\mathit{s}}=\left({\mathit{r}}_{\mathit{p}}/\mathit{N}\right){\dot{\mathit{\theta }}}_{\mathit{m}}$. Around hover, the linear time-varying attitude–slider subsystem reduces to

$${\displaystyle \frac{\mathit{d}}{\mathit{d}\mathit{t}}}\left[\begin{array}{c}\mathit{\varphi }\\ \dot{\mathit{\varphi }}\\ \mathit{\theta }\\ \dot{\mathit{\theta }}\\ {\mathit{x}}_{\mathit{s}}\\ {\dot{\mathit{x}}}_{\mathit{s}}\\ {\mathit{y}}_{\mathit{s}}\\ {\dot{\mathit{y}}}_{\mathit{s}}\end{array}\right]=\underset{\mathit{A}}{\underbrace{\left[\begin{array}{cccccccc}0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& {\displaystyle \frac{{\mathit{m}}_{\mathit{s}}\mathit{g}}{{\mathit{I}}_{\mathit{x}\mathit{x}}}}& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& -{\displaystyle \frac{{\mathit{m}}_{\mathit{s}}\mathit{g}}{{\mathit{I}}_{\mathit{y}\mathit{y}}}}& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& -{\displaystyle \frac{{\mathit{B}}_{\mathit{x}}}{{\mathit{m}}_{\mathit{s}}}}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& -{\displaystyle \frac{{\mathit{B}}_{\mathit{y}}}{{\mathit{m}}_{\mathit{s}}}}\end{array}\right]}}\left[\begin{array}{c}\mathit{\varphi }\\ \dot{\mathit{\varphi }}\\ \mathit{\theta }\\ \dot{\mathit{\theta }}\\ {\mathit{x}}_{\mathit{s}}\\ {\dot{\mathit{x}}}_{\mathit{s}}\\ {\mathit{y}}_{\mathit{s}}\\ {\dot{\mathit{y}}}_{\mathit{s}}\end{array}\right]+\underset{\mathit{B}}{\underbrace{\left[\begin{array}{cccc}0& 0& 0& 0\\ {\displaystyle \frac{1}{{\mathit{I}}_{\mathit{x}\mathit{x}}}}& 0& 0& 0\\ 0& 0& 0& 0\\ 0& {\displaystyle \frac{1}{{\mathit{I}}_{\mathit{y}\mathit{y}}}}& 0& 0\\ 0& 0& 0& 0\\ 0& 0& {\displaystyle \frac{\mathit{\eta }}{{\mathit{m}}_{\mathit{s}}{\mathit{r}}_{\mathit{p}}}}& 0\\ 0& 0& 0& 0\\ 0& 0& 0& {\displaystyle \frac{\mathit{\eta }}{{\mathit{m}}_{\mathit{s}}{\mathit{r}}_{\mathit{p}}}}\end{array}\right]}}\left[\begin{array}{c}{\mathit{\tau }}_{\mathit{x}}\\ {\mathit{\tau }}_{\mathit{y}}\\ {\mathit{\tau }}_{\mathit{m}\mathit{x}}\\ {\mathit{\tau }}_{\mathit{m}\mathit{y}}\end{array}\right]$$

(21)

where ${\mathit{B}}_{\mathit{x}},{\mathit{B}}_{\mathit{y}}$ optionally represent linearized stage friction, and the rotor torques $({\mathit{\tau }}_{\mathit{x}},{\mathit{\tau }}_{\mathit{y}})$ are obtained from the thrusts through (6). Matrix $\mathit{A}$ shows the cross-coupling: slider velocities feed the attitude accelerations with gain ${\mathit{m}}_{\mathit{s}}\mathit{g}/\mathit{I}$, while the slider dynamics are driven by motor torques through $\mathit{\eta }/\left({\mathit{m}}_{\mathit{s}}{\mathit{r}}_{\mathit{p}}\right)$. This form is suitable for LQR or ${\mathcal{H}}_{\mathbf{\infty }}$ synthesis [19].

3.10. Energy and Optimal Allocation

Finally, the energy integrals provide diagnostics and a route to optimal allocation [4]. The total mechanical energy is

$$\begin{array}{cc}\mathcal{E}\left(\mathit{t}\right)=\mathit{T}+\mathit{V}=& 1/2\mathit{M} {\parallel \mathit{v}\parallel }^2+1/2{\mathit{\omega }}^{\mathbf{\top }}{\mathit{I}}_{\mathit{B}}\left({\mathit{r}}_{\mathit{s}}\right)\mathit{\omega }+1/2{\mathit{m}}_{\mathit{s}}\\ & {\parallel \mathit{\omega }\times {\mathit{r}}_{\mathit{s}}+{\dot{\mathit{r}}}_{\mathit{s}} \parallel }^2-\mathit{M}\mathit{g}\hspace{0.17em}{\mathit{e}}_{\mathit{z}}^{\mathbf{\top }}\left(\mathit{p}+\mathit{R}\mathit{\rho }\right)\end{array}$$

(22)

and its time derivative equals the power supplied by actuators minus dissipation. Minimizing the integral of actuator power subject to dynamics in Equation (23),

$${\int }_0^{\mathit{T}}(\underset{\mathrm{rotor} \mathrm{power}}{\underbrace{\sum _{\mathit{i}}{\mathit{c}}_{\mathit{T}}\hspace{0.17em}{\mathit{T}}_{\mathit{i}}^{3/2}}}+\underset{\mathrm{stepper} \mathrm{copper} \mathrm{loss}}{\underbrace{{\displaystyle \frac{\mathit{R}}{{\mathit{\eta }}_{\mathit{e}}}}\hspace{0.17em}{\mathit{i}}^2}})\mathit{d}\mathit{t}$$

(23)

yields an allocation with guaranteed energy optimality, where ${\mathit{c}}_{\mathit{T}}$ is derived from propulsive coefficients and ${\mathit{\eta }}_{\mathit{e}}$ is driver efficiency. In practice a convex quadratic surrogate of (15) is used at each control step, consistent with the weighted least-squares thrust–slider allocation [20].

These equations fully integrate the vehicle rigid-body dynamics, the configuration-dependent inertia and gravity moments introduced by the XY stage, and the electromechanical actuation of the rack-and-pinion steppers. They admit both exact simulation via (12) and tractable control design via the linearized form (13), while (14) and (15) support energy analysis and optimal allocation. Figure 7 illustrates the experimental setup of the CoM shifting mechanism mounted on the drone, including key components such as the UAV prototype, Speedy Bee F7 flight controller, ESP32 control module, and the CoM shifting XY stage.

4. Simulation of Roll Stabilization of UAV Based on MATLAB

4.1. Experimental Setup

The experimental setup is illustrated in Figure 8. In this experiment, a quadcopter equipped with a CoM shifting device was modeled and tested in MATLAB/Simulink. The drone was allowed to rotate around the roll axis while the payload was displaced laterally using a two-axis prismatic stage. The shifting mechanism, driven virtually by stepper motors, was responsible for producing corrective torque during free roll [5].

4.2. Simulation Parameters and Evaluation Metrics

The system was evaluated under varying payload conditions to capture its influence on stabilization performance. Three representative payload masses 50 g, 100 g, and 200 g were selected and mounted onto the CoM shifting stage [5]. These values were chosen to reflect both lightweight configurations, representative of minimal onboard equipment, and heavier conditions, which impose greater demands on the stabilization mechanism. For each simulation case, a set of performance metrics was extracted to provide a comprehensive assessment of the system’s behavior. Specifically, the simulations quantified the maximum corrective torque generated by the displaced payload mass, which directly determines the available stabilizing authority. In addition, the maximum lateral force exerted on the quadrotor frame was calculated, as this force reflects the dynamic interaction between the shifting payload and the UAV structure. Finally, the roll angle response of the vehicle was analyzed under both baseline conditions (device disabled) and active stabilization (device enabled). This last metric is critical, as it demonstrates the device’s ability to constrain angular deviations during disturbances and highlights the comparative advantage of CoM -based control. Together, these metrics form a rigorous evaluation framework, ensuring that both the mechanical torque generation capacity and the resulting flight dynamics are adequately captured in simulation. The complete structural diagrams are provided in Appendix A, Figure A1 and Figure A2, for clearer visualization.

4.3. Results and Battery Efficiency Analysis

4.3.1. CoM Shifting System Performance

The CoM shifting device was evaluated to assess its impact on stability and energy efficiency in the UAV. The CoM shifting system demonstrated its ability to generate corrective torques to counteract roll and pitch disturbances. As shown in Figure 9a, the corrective torque increased proportionally with the payload mass, demonstrating a higher stabilization potential for larger payloads. However, as the payload mass increased (e.g., 200 g), the system’s inertia also increased, resulting in slower corrective responses.

Roll-angle plots further corroborated the system’s effectiveness. With the CoM device disabled, the UAV drifted uncontrollably under roll disturbances, leading to significant angular deviations. However, when the CoM device was activated, roll deviations were constrained to under ±5°, demonstrating the system’s ability to actively stabilize the UAV, as shown in Figure 9c. This confirms that the CoM shifting mechanism is effective at reducing unwanted motion and maintaining stability, particularly during free-fall or emergency recovery scenarios.

The following table summarizes the experimental results of force, torque, and roll angle for various payloads:

As shown in

Table 1. Experimental results of force, torque, and roll angle for different masses.

Payload Mass (g)	Maximum Force (N)	Maximum Torque (N·m)	Maximum Roll Angle (rad)
50	3.1479	0.4174	0.90
100	5.1678	0.6940	1.20
200	9.1835	1.2375	1.35

and Figure 9b, the maximum corrective torque increases with payload mass, providing a stronger stabilizing effect for larger payloads. For instance, at 200 g, the corrective torque is approximately up to 1.2375 N·m, resulting in a maximum roll angle of just 1.35 radians, significantly lower than the uncontrolled drift observed without the device.

4.3.2. Battery Efficiency Analysis with Detailed UAV Parameters

One of the most critical aspects of the CoM shifting device is its energy efficiency. In contrast to traditional stabilization systems, which rely on motor thrust modulation, the CoM device utilizes two low-power stepper motors (or equivalent actuators) to shift the battery mass along the X–Y plane. These actuators consume power primarily during the transient movement of the prismatic stages. Once the target displacement is reached, the actuators require negligible holding current due to mechanical self-locking or driver optimization (e.g., current decay modes in stepper drivers) [20].

The UAV platform uses a 6S 1800 mAh LiPo battery, providing 22.2 V nominal voltage with a maximum discharge rate of 1800 mAh. The EMAX 1300 KV motors are designed to operate efficiently at this voltage range, but for the purpose of this study, we are primarily concerned with power consumption during the CoM shifting operations, separate from the propulsion needs. Here is break down the power consumption for different payloads (50 g, 100 g, 200 g) and compare it with thrust-based stabilization.

1.

Energy Consumption for Propulsion-Based Stabilization (Eₚ)

For thrust-based stabilization, the energy required to correct disturbances using the EMAX 1300KV motors can be estimated by considering the additional propulsion power required during roll/pitch correction as in Equation (24):

$${\mathbf{E}}_{\mathrm{prop}}\approx {\int }_0^{\mathbf{T}}\mathsf{\Delta }{\mathbf{P}}_{\mathrm{motors}}\hspace{0.17em}\mathbf{d}\mathbf{t}$$

(24)

where $\mathsf{\Delta }{\mathbf{P}}_{\mathrm{motors}}$ is the additional propulsion power required during the correction phase.

For example, during roll or pitch correction, the motors would need to generate additional thrust to counteract disturbances, often leading to 20–30% more power consumption than the nominal hover power [21].

2.

Energy Consumption for CoM Device (E_k)

For the CoM device, energy consumption during the shifting operation is calculated as:

$${\mathbf{E}}_{\mathrm{device}}\approx \sum _{\mathbf{i}=1}^{\mathbf{n}}\mathbf{V}\cdot {\mathbf{I}}_{\mathbf{i}}\cdot {\mathbf{t}}_{\mathbf{i}}$$

(25)

where $\mathbf{V}$ = supply voltage (22.2 V for 6S battery, ${\mathbf{I}}_{\mathbf{i}}$ = current drawn by each actuator during movement, ${\mathbf{t}}_{\mathbf{i}}$ = time for each movement

• Energy Calculations for CoM Device

For payloads 50 g, 100 g, and 200 g, here is how the energy consumption breaks down for CoM shifting:

Here in

Table 2. Energy consumption for different payloads.

Payload Mass (g)	Power Consumption (W)	Time per Adjustment (s)	Energy Consumption (J)
50	0.15	0.3	0.45
100	0.25	0.4	1.00
200	0.40	0.6	2.40

, Power Consumption is derived from the stepper motors used for CoM shifting, and Time per Adjustment refers to the duration the system takes to shift the mass by 20–40 mm (based on payload mass). Energy Consumption (Joules) is the power multiplied by the time.

4.3.3. Comparative Energy Consumption: CoM Device vs Thrust-Based Stabilization

For comparison, the CoM system operates at less than 7% of the UAV’s total power consumption during frequent corrective actions. In contrast, thrust-based stabilization (especially under motor failure or free-fall) can result in surges of 20–30% in power consumption, greatly increasing demand on the battery.

For instance, during motor failure or free-fall, the UAV’s power consumption could increase by 3–4 times, potentially draining the battery faster and reducing flight endurance. In contrast, the CoM shifting system provides a sustainable and energy-efficient solution, with minimal impact on the UAV’s flight time. The energy efficiency of the CoM stabilization device provides a significant advantage, especially for lightweight UAV platforms where battery life is a critical limitation. By reducing power consumption to under 7% of the UAV’s total energy budget, the CoM device ensures longer flight endurance, even during emergency scenarios such as motor failure or battery depletion. The CoM shifting system’s low-power operation, combined with its passive torque generation and improved safety margin, makes it a promising solution for next-generation UAV designs, where battery capacity often limits operational time. The efficiency and performance of the CoM system, alongside its ability to function independently of propulsion or aerodynamic surfaces, provide UAVs with a fail-safe recovery method that enhances mission reliability and survivability in critical scenarios.

5. Indoor Experimental Evaluation of the UAV Prototype

5.1. Experimental Setup

The experimental setup for evaluating the proposed stabilization device is shown in Figure 10. To assess the efficacy of the suggested stabilization device, a series of indoor contact-based physical experiments were conducted. The airborne vehicle was affixed to a strong aluminum test frame, facilitating restricted roll motion while averting uncontrolled flying, so guaranteeing that the experiments could be replicated under uniform and disturbance-free conditions. The experimental platform incorporated the Speedy Bee F7 flight controller, an ESP32 microprocessor, dual A4988 stepper motor drivers, and the payload-shifting XY stage mechanism. Data from the onboard IMU, used for roll angle measurement, and RC input capture [14], employed for pilot stick commands, were incessantly recorded by UART telemetry on an attached laptop. This arrangement facilitated accurate monitoring of the system’s dynamic response while reducing the impact of external variables like wind or GPS drift.

5.2. Baseline Condition (Device Disabled)

The studies were performed in two phases: initially with the stabilizing device off, followed by its complete activation. Under the baseline condition, the drone directly responded to RC roll inputs without any supplementary corrective mechanism. The recorded data indicate that the roll angle displayed considerable fluctuations, frequently attaining variations of ±10°, and demonstrated prolonged oscillations and overshoot subsequent to step inputs from the transmitter. The system exhibited insufficient natural damping, resulting in a rather sluggish recovery to the neutral position, hence underscoring the fundamental constraints of the basic flight controller in countering roll disturbances under the specified test conditions.

5.3. Condition with CoM Device Activated

The comparative roll response with and without the CoM shifting device is shown in Figure 11. Conversely, when the stabilization device was activated, the payload-shifting system actively produced compensatory torque in reaction to angular velocity feedback. The documented statistics unequivocally indicate that roll deviations were rectified more swiftly, with oscillations stabilizing more rapidly than in the baseline scenario [22]. During the trial, particularly around step 150 and step 250, the drone demonstrated angular displacement in response to RC input; nevertheless, the stabilization mechanism promptly mitigated the disturbance, diminishing the roll magnitude and realigning the frame towards its neutral position. The enhanced dampening effect, along with the diminished oscillation amplitude, verified that the device improved the vehicle’s roll stability [23]. Observations throughout the testing validated the reliability of the hardware-software integration: the ESP32 reliably maintained contact with the flight controller during arming and disarming, while the stepper-driven carriage executed smooth changes within its mechanical constraints.

5.4. Experimental Results and Observations

The experimental results confirmed that changing the center of mass is an effective strategy for enhancing roll stability in multirotor systems. The comparison of the two scenarios—device disabled, and device enabled—demonstrates that the mechanism’s integration not only diminishes roll angle deviations but also enhances dynamic response, thereby validating the proposed design as a viable solution for aerial vehicles functioning in environments where rapid self-stabilization is critical.

6. Dynamic Free-Fall Simulation of UAV Stabilization Using Center-of-Mass Adjustment

6.1. Simulation Architecture

The dynamic free-fall simulation architecture is illustrated in Figure 14. A dynamic free-fall simulation was developed to assess the effectiveness of the proposed CoM shifting stabilization mechanism in the most demanding and safety-critical scenario for multi-rotor UAVs. The UAV was designed in MATLAB/Simulink with the Simscape Multibody toolbox to provide comprehensive six-degree-of-freedom rigid-body dynamics, integrating the measured mass and inertia distribution of the prototype airframe along with aerodynamic damping forces characteristic of small quadrotor platforms. The internal stabilizing device was designed as an orthogonal two-axis prismatic stage, allowing ±40 mm displacement in both X and Y axes, with actuation limitations aligned with the empirically confirmed stroke time of 0.05–0.20 s for a 20 mm travel distance. This arrangement enabled the simulation to incorporate rigid-body flight dynamics, actuator saturation, displacement limitations, and stage kinematics, thus facilitating a realistic assessment of stabilization capacity.

6.2. Test Scenarios

The test scenario entailed deploying the UAV from two specified elevations, 25 m and 15 m, under zero-thrust conditions, with gravity as the sole persistent external force, supplemented by negligible aerodynamic drag. To simulate real-world disruptions, minor perturbations of ±2–3° in roll and pitch were implemented during the original version. In the baseline scenario without the CoM device, the vehicle dynamics rapidly diverged, with angular deviations nearing ±90° within seconds, resulting in inverted impact orientations. In the stabilized mode, the CoM device was governed by a closed-loop feedback mechanism that persistently directed mass displacements according to real-time simulated IMU data.

6.3. Control Algorithm

As mentioned before in Equations (5) and (6), The control algorithm was formulated as a proportional mapping between instantaneous attitude error and commanded payload displacement [5].

The closed-loop system therefore transformed instantaneous orientation errors directly into corrective torques, bounded by the physical limits of stage travel and actuator velocity. This simulation framework provided a direct and rigorous comparison between conventional multirotor behavior and a system augmented with internal mass-shifting stabilization [24]. The abilities of the CoM device to constrain roll and pitch excursions, to maintain near-level attitude, and to deliver repeatable stabilization across different release heights demonstrated not only the feasibility but also the transformative potential of CoM-based control in UAV safety-critical operations. The detailed block-diagram representation of the self-righting dynamics is provided in Appendix A, Figure A3, for clearer visualization.

6.4. Simulation Framework and Comparison

The Simulink models in Appendix A, Figure A3, integrate the UAV rigid body, the CoM shifting device, and the feedback loop including attitude sensing, error calculation, and actuator command generation.

To visualize the logic of the proposed control strategy, a flowchart of the prismatic balance control function is presented in Figure 12. The flow begins with the initialization of persistent states, ensuring memory of previous errors and positions across simulation steps. Next, the angular velocities from the IMU are processed separately for the carriage axis (based on ${\mathsf{\omega }}_{\mathit{y}}$) and the bed axis (based on ${\mathsf{\omega }}_{\mathit{x}}$) [25].

For each axis, a PID controller calculates the required correction, which is then constrained within defined saturation limits to respect physical travel boundaries of the system. A low-pass filter is subsequently applied to smooth the commanded motion and reduce oscillations. Finally, the persistent states are updated for the next iteration, and the control outputs (pos_carriage) and (pos_bed) are returned as inputs to the prismatic actuators.

6.5. Results: Free-Fall Stabilization Performance

Upon the discharge of the UAV without the CoM shifting gear, its movement was characterized by erratic tumbling about both the roll and pitch axes. The angular deviations swiftly increased, surpassing 90° in under two seconds post-release, resulting in inverted impact orientations upon ground contact. The documented attitude data verified the lack of restorative torque, exhibiting continuous oscillations without a tendency to converge. This result illustrates the inherent instability of traditional multi-rotor when lacking thrust, as the flight controller alone cannot produce corrective moments under free-fall conditions.

The activation of the CoM shifting mechanism dramatically altered the free-fall dynamics. The device consistently adjusted the internal payload to mitigate angular discrepancies, generating stabilizing torques of up to 1.2375 N·m, which were adequate to sustain control authority during the fall. Consequently, roll and pitch variations were restricted to ±5°, even in response to initial perturbations of 2–3°. Upon ground impact, the UAV consistently attained a nearly horizontal attitude, validating that the system offered an efficient self-righting capacity. The attitude data exhibited seamless correction and swift attenuation of perturbations, underscoring the resilience of the feedback loop among the IMU, ESP32 controller, and actuation stage.

In addition to orientation recovery, two other outcomes highlight the device’s efficacy. Initially, stability retention during descent increased from below 10% in the baseline scenario to over 90% with the CoM device activated, demonstrating a distinct quantitative benefit. The recovery time after disturbances was significantly decreased: whereas the baseline UAV persisted in oscillation until impact, the stabilized system demonstrated a settling period of less than 0.8 s for standard perturbations. Collectively, these findings validate that the suggested technique not only averts catastrophic tumbling but also guarantees swift and consistent convergence to a secure orientation.

• Case 1—Without CoM Device

In the first case, where the CoM device was deactivated, the UAV exhibited significant instability during free fall. The vehicle underwent rapid tumbling around both the roll and pitch axes, causing substantial deviations in its orientation. Specifically, the roll and pitch angles diverged rapidly, exceeding ±90°, leading to an inverted position just before impact. This uncontrolled motion confirmed that, without the CoM device, the UAV lacked the necessary stabilizing torques to maintain its attitude during descent.

Attitude data collected during the descent, shown in Figure 13a revealed continuous oscillations, which further substantiated the UAV’s inability to recover or control its orientation. The UAV’s roll and pitch deviations increased uncontrollably, with no significant damping or stabilization, illustrating the inherent instability of the system when thrust-based stabilization or aerodynamic control surfaces were unavailable.

• Case 2—With CoM Device

In contrast, when the CoM device was activated, the UAV demonstrated a remarkable improvement in stability throughout the free fall. The shifting of the CoM actively corrected deviations in both roll and pitch, ensuring that the vehicle’s attitude remained within a controlled range during most of the descent. The roll and pitch deviations were continuously corrected and were kept within ±5°, highlighting the effectiveness of the CoM system in stabilizing the UAV.

The comparative results presented in

Table 3. Comparison of drone free-fall stability with and without CoM shifting device.

Parameter	With CoM Device Disable	With CoM Device Enable
Max roll deviation (°)	~90°	<5°
Max pitch deviation (°)	~90°	<5°
Final impact orientation	Inverted	Upright
Stability retention	<10%	>90%

clearly demonstrate the transformative role of the CoM shifting mechanism in free-fall stabilization. Without the device, the UAV rapidly diverged in both roll and pitch, with angular deviations approaching ±90°, leading to an inverted impact orientation in nearly every trial. This behavior is consistent with theoretical expectations, as conventional multi-rotors possess no inherent aerodynamic restoring moments under zero-thrust conditions. In stark contrast, activation of the CoM device enabled the UAV to maintain angular deviations within ±5° throughout descent, producing a consistently upright orientation at ground contact.

Beyond simple attitude retention, the CoM device markedly improved dynamic stability. Stability retention, defined as the percentage of trials in which the vehicle maintained controllable orientation throughout the fall, improved from below 10% in the baseline case to above 90% with the device enabled. This tenfold improvement indicates not only enhanced stability but also a dramatic increase in system reliability under the most safety-critical conditions. Moreover, the reduction in angular excursions minimized the likelihood of structural damage upon impact, as upright landings distributed forces symmetrically across the landing gear rather than concentrating loads on the arms or propeller guards.

The recorded attitude data, illustrated in Figure 13b, provides further insight into stabilizing dynamics. In the absence of the device, the vehicle’s orientation diverged uncontrollably, showing persistent oscillations with no evidence of recovery. Conversely, with the CoM mechanism engaged, disturbances were corrected rapidly, with smooth torque generation that damped oscillations within less than a second. This behavior highlights the effectiveness of the closed-loop feedback between the IMU, ESP32 microcontroller, and stepper-driven translational stage in generating real-time corrective torques. The capacity of the device to achieve near-horizontal recovery, even under initial perturbations, confirms its suitability as a fail-safe mechanism.

Collectively, these results underscore the potential of CoM shifting as a bio-inspired stabilization strategy, mimicking the way cats adjust their body mass to achieve self-righting during free fall. By ensuring upright impacts, reducing angular deviation, and achieving high stability retention, the mechanism provides UAVs with an additional layer of resilience and survivability in emergency scenarios where propulsion is unavailable. As demonstrated in Figure 14, the CoM shifting system also plays a key role in stabilizing the UAV during free-fall from a height of 25 m, with the system actively adjusting its position on both the X and Y axes. The system shows significant improvements in stability and response time. Similarly, Figure 15 highlight the performance of the CoM system when deployed from a 15-m height, further confirming its effectiveness in various free-fall scenarios.

Figure 14. Roll, Pitch and Yaw Response in degrees (°) during Free-Fall from 25 m Height (a) without CoM Shifting Device; (b) with CoM Shifting Device Enabled, (c) is Position change for X axis during Free-Fall with CoM Shifting Device from 25 m Height, and (d) is Position change for Y axis during Free-Fall with CoM Shifting Device from 25 m Height.

Figure 14. Roll, Pitch and Yaw Response in degrees (°) during Free-Fall from 25 m Height (a) without CoM Shifting Device; (b) with CoM Shifting Device Enabled, (c) is Position change for X axis during Free-Fall with CoM Shifting Device from 25 m Height, and (d) is Position change for Y axis during Free-Fall with CoM Shifting Device from 25 m Height.

Figure 15. Roll, Pitch and Yaw Response in degrees (°) during Free-Fall from 15 m Height (a) without CoM Shifting Device; (b) with CoM Shifting Device Enabled, (c) is Position change for X axis during Free-Fall with CoM Shifting Device from 15 m Height, and (d) is Position change for Y axis during Free-Fall with CoM Shifting Device from 15 m Height.

Figure 15. Roll, Pitch and Yaw Response in degrees (°) during Free-Fall from 15 m Height (a) without CoM Shifting Device; (b) with CoM Shifting Device Enabled, (c) is Position change for X axis during Free-Fall with CoM Shifting Device from 15 m Height, and (d) is Position change for Y axis during Free-Fall with CoM Shifting Device from 15 m Height.

7. Discussion

The results demonstrate that CoM shifting provides an effective and propulsion-independent stabilization mechanism for multirotor UAVs. In the baseline condition, when the device was disabled, the UAV exhibited uncontrolled roll and pitch divergence, with angular deviations approaching ±90° and frequent inverted orientations on impact. This behavior is consistent with the inherent limitations of multirotors which lack aerodynamic restoring moments when thrust is absent.

Activating the CoM shifting module fundamentally altered this situation. By displacing a concentrated payload by ±20–40 mm, the mechanism generated gravity-induced corrective torques up to 1.2375 N·m. Simulations and indoor tests confirmed a near-linear increase in stabilizing torque with payload mass. For example, a 200 g payload produced approximately 1.2375N·m, reducing roll deviations to within ±5° compared to the uncontrolled divergence of the baseline condition. Across tested payloads (50–200 g), the system consistently demonstrated improved corrective performance with increasing mass.

Closed-loop IMU-based control further enhanced reliability. The ESP32 microcontroller, working with A4988 drivers and the Speedy Bee F7 flight controller, executed real-time corrections at 115200 baud, enabling stage displacements of 0.05–0.20 s per 20 mm stroke. PID control with deadband filtering and saturation limits reduced overshoot and eliminated drift. Indoor tethered tests showed faster damping, shorter recovery times, and reductions of more than 80% in maximum roll compared to the uncontrolled condition.

Another advantage of the approach is its efficiency. Thrust-based stabilization typically increases propulsion power by 20–30% during strong corrections, whereas the CoM system consumed less than 7% of the UAV’s power budget and required almost no holding current after reaching its commanded position. This preserves flight endurance while adding an autonomous stabilization layer.

Although functional, the current dual-axis rack-and-pinion system adds approximately 0.28 kg to the platform. Lighter actuators, alternative transmission mechanisms, or compact direct-drive solutions could reduce mass and simplify integration. Tighter coupling between the CoM device and the flight controller would also reduce latency and minimize reliance on external microcontrollers. Such improvements would enhance suitability for smaller UAVs or high-performance use cases.

Overall, the findings confirm that CoM shifting provides scalable, repeatable, and energy-efficient stabilization torque for emergency scenarios where conventional propulsive control is unavailable. The mechanism successfully mitigated tumbling during free fall, maintained roll within ±5° in most trials, and showed increasing effectiveness with payload masses up to 600 g. Closed-loop control enabled real-time correction despite actuator speed limits and asymmetric mass distributions.

Compared with thrust-vectoring stabilization, the proposed CoM shifting approach remains fully operational even when all motors are inactive, offering a dedicated fail-safe mode for emergencies such as battery depletion, ESC faults, or motor failure. In contrast to aerodynamic fin-based solutions, it does not require forward velocity or airflow. Existing moving-mass designs typically target slow center-of-gravity compensation; however, our system provides rapid, bidirectional CoM modulation (±20-40 mm within 0.05–0.20 s) capable of generating up to 1.2375 N·m of corrective torque. Additionally, the mechanism consumes less than 7% of the UAV’s energy budget, far lower than the 20–30% overhead associated with thrust-based stabilization. These advantages establish CoM shifting as a practical and scalable stabilization strategy for small UAVs operating in safety-critical conditions.

The concept demonstrates that internally shifting the onboard mass can serve as an effective mechanical method for maintaining stable attitude during critical flight conditions. This validates the practicality of introducing an additional, thrust-independent control input into multirotor design. Future work should concentrate on reducing system weight, increasing actuator responsiveness, and improving hardware integration to facilitate deployment in compact or high-agility UAV platforms.

8. Conclusions

This study establishes CoM shifting mechanism as a viable strategy for enhancing UAV safety during propulsion-loss events. The mechanism provides a passive means of generating corrective moments by the controlled payload displacement, enabling the UAV to maintain a stable orientation in situations where traditional thrust-based stabilization is unavailable. During the simulated free-fall scenarios, the method consistently prevented the uncontrolled tumbling and maintained the UAV with a survivable attitude.

A key advantage of this approach is that it decouples emergency stabilization from the propulsion system. Because its operation relies solely on gravity-induced torques, and the mechanism remains functional even when motors are disabled, offering a dedicated fail-safe layer for contingency conditions. Additionally, the device introduces only modest power demands and minimal operational complexity, making it compatible with a wide range of multirotor platforms.

Beyond emergency stabilization, the CoM shifting device shows potential as an auxiliary control input for improving maneuverability and precision during aggressive flight. Dynamic repositioning of the onboard mass can support smoother transitions, sharper braking responses, and more efficient modulation of pitch-related motion, suggesting that CoM-based actuation may serve as a complementary control strategy in future UAV designs.

Looking forward, there is substantial opportunity to refine the actuation technology that drives the CoM displacement. Figure 16 illustrates a conceptual platform employing magnetic linear actuators to replace mechanical stages. Such actuators promise faster response, reduced weight, and lower mechanical losses. Their integration could allow for synchronized mass motion, which would make it easier to shape the pitch angle, move while being aware of energy use, and quickly stabilize during dynamic operations.

Overall, the findings indicate that CoM-based stabilization is a practical and scalable direction for next-generation UAV safety systems. With continued improvements in actuation speed, integration, and control algorithms, this technique has strong potential to enhance survivability, operational robustness, and mission success across a wide range of civilian and industrial applications. This approach is transformative for enhancing the resilience and safety of UAVs, as it offers a unique solution for critical failure scenarios and ensures better overall mission success.