2.1. Actuation mechanism

• • Forelimb Actuation: To achieve wing kinematics that enable the wings to fold during the upstroke and extend during the downstroke, two types of actuators are employed: a morphing actuator and a flapping actuator. The morphing actuator operates through a crank-slider mechanism, where the slider is constrained to linear motion along a guide rail. A connecting rod extends from both sides of the slider, linking it to the proximal ends of the humerus via a Hooke hinge (see Figure 3(d)). This configuration restricts the range of wing folding and allows precise control of wing morphing via a servo motor. In parallel, the flapping actuation system utilizes a spatial crank-rocker mechanism. Here, the distal end of the rocker is hinged to the proximal end of the humeral connecting rod, facilitating symmetrical up-and-down movements of the left and right wings.

• • Hindlimb Actuation: From a kinematic perspective, bat ankles move ventrally during the downstroke and dorsally during the upstroke [Reference Cheney, Ton, Konow, Riskin, Breuer and Swartz26]. Inspired by this natural motion, two asynchronously active legs were designed to control the trailing edge of the membrane wing. As illustrated in Figure 3(d), each leg is connected to the body through an active revolute joint, enabling dorsoventral movements within a plane tilted relative to the parasagittal plane. Unlike biological bats, the robot’s legs do not perform mediolateral movements, as studies by Riskin et al. [Reference Riskin, Willis, Iriarte-Diaz, Hedrick, Kostandov, Chen, Laidlaw, Breuer and Swartz27] indicate that such movements are less significant in natural bat locomotion.

Figure 3.

Structure of the morphing wings: (a) The left side illustrates the wings in their fully extended state, while the right side shows the skeletons in a fully folded configuration. (b) Close-up view of the wrist joint, emphasizing passive digit deformation. (c) Rear view of the fully stretched wing skeleton, highlighting the three curved digits. (d) Close-up view of the actuation mechanism responsible for forelimb and hindlimb movement.

2.2. Wing structure and components

The bat-inspired robotic wing is divided into two segments: an inner and an outer section. The inner segment, referred to as the “arm wing,” consists of two primary hinged components, representing the humerus and radius (see Figure 3(b)). These components are actuated through a series of linkages that control the arm’s extension and flexion. This motion is governed by the linear distance between the shoulder and the proximal end of lever 1, indicated by red double arrows in Figure 3(a).

The outer section, called the “hand wing,” is supported by three digits that span its surface. These digits are specifically designed to curve downward, creating a positive airfoil curvature that enhances lift efficiency (see Figure 3(d)). All three digits connect proximally to the distal carpus. Additionally, digits 1 and 3 are, respectively, hinged to the radius and radial support rod via auxiliary linkages, as shown in Figure 3(b). This setup allows passive adjustments of the angles between digits during wing deformation, enhancing the folding ratio. For details on movement, see Section 3.2.

3.1. Kinematic analysis of the flapping mechanism

To ensure flight stability through symmetrical movement, a spatial crank-and-rocker mechanism is utilized to achieve the flapping motion of the wings. A schematic representation of the mechanism’s structure is shown in Figure 4. The parameters $a , b$ , and $c$ denote the lengths of the rocker, link, and crank, respectively. The two joints on the link are spherical joints. The initial structural parameters of the flapping mechanism are provided in Table I.

As a spatial four-bar mechanism, the movement planes of the crank and the rocker are orthogonal. Assuming that $\theta$ and $\varphi$ denote the angular positions of the crank and rocker, respectively. The position vector of point $B$ and $C$ can be expressed as:

(1) \begin{equation}{\boldsymbol{r}_{B}=\left[\begin{array}{l@{\quad}l@{\quad}l} -a\cos \theta & d & a\sin \theta \end{array}\right]^{T} } \end{equation}

(2) \begin{equation}{\boldsymbol{r}_{C}=\left[\begin{array}{l@{\quad}l@{\quad}l} -s & c\cos \varphi & c\sin \varphi +h \end{array}\right]^{T} } \end{equation}

Table I.

Structure parameters and initial conditions of the flapping mechanism (mm).

Figure 4.

Flapping mechanism: (a) Axonometric view, and (b) sketch of the RSSR space four-link mechanism.

To establish the relationship between the input angle $\theta$ and flapping angle $\varphi$ , the geometric constraint is given by:

(3) \begin{equation} \left\| \boldsymbol{r}_{C}-\boldsymbol{r}_{B}\right\| ^{2}=b^{2} \end{equation}

Here, $\| \cdot \|$ indicates the 2-norm or amplitude of the vector $\boldsymbol{r}_{C}-\boldsymbol{r}_{B}$ .

By substituting the vectors $\boldsymbol{r}_{B}$ and $\boldsymbol{r}_{C}$ into Eq. (3), we have:

(4) \begin{equation} \left(-s+a\cos \theta \right)^{2}+\left(c\cos \varphi -d\right)^{2}+\left(c\sin \varphi +h-a\sin \theta \right)^{2}=b^{2} \end{equation}

After simplifying, Eq. (4) becomes:

(5) \begin{equation} a^{2}+c^{2}+d^{2}+h^{2}+s^{2}-b^{2}-2ah\sin \theta -2as\cos \theta =-2c\left(h-a\sin \theta \right)\sin \varphi +2cd\cos \varphi \end{equation}

To solve for $\varphi$ , an auxiliary angle $x$ is introduced, expressed as:

(6) \begin{equation} k_{1}\sin x+k_{2}\cos x=\sqrt{{k_{1}}^{2}+{k_{2}}^{2}}\sin \left(x+\arctan \frac{k_{2}}{k_{1}}\right) \end{equation}

The angular displacement $\varphi$ of the link CD is then determined as:

(7) \begin{equation} \varphi =\arcsin \left(\frac{a^{2}+c^{2}+d^{2}+h^{2}+s^{2}-b^{2}-2ah\sin \theta -2as\cos \theta }{2c\sqrt{\left(h-a\sin \theta \right)^{2}+d^{2}}}\right)-\arctan \frac{d}{-h+a\sin \theta } \end{equation}

3.2. Kinematic analysis of the morphing mechanism

Since the morphing mechanisms of the left and right wings are identical, the kinematic analysis is conducted using the left wing as an example. The corresponding frames of the left wing are depicted in Figure 2, while the DOFs and morphological parameters are detailed in Figure 4. Gray variables represent each hinge joint, and black variables correspond to structural parameters. The coordinate frames are shown in green. Blue arrows indicate biologically relevant angles in the left forelimb that are not directly actuated, while red arrows represent directly actuated angles. The initial structural parameters of the morphing mechanism are listed in Table II.

Table II.

Structure parameters and initial conditions of the morphing mechanism (mm).

Table III.

Deavit-Hartenberg parameters.

For the four-bar linkage $PHED$ , the shoulder angle $(\angle PHE)$ , denoted as $\theta _{s}$ , and the elbow angle $(\angle HEG)$ , represented as $\theta _{e}$ , can be determined using the known displacement of the slider $l_{s}$ , as shown follows:

(8) \begin{equation}{\theta _{s}=\arccos \frac{l_{1}-l_{0}}{l_{DH}}+\arccos \left(\frac{{l_{2}}^{2}+l_{DH}^{2}-{l_{14}}^{2}}{2l_{2}l_{DH}}\right)\\[-10pt]\nonumber } \end{equation}

(9) \begin{equation}{\qquad\,\, \theta _{e}=\pi -\arccos \left(\frac{{l_{2}}^{2}+{l_{14}}^{2}-l_{DH}^{2}}{2l_{2}l_{14}}\right) } \end{equation}

where $l_{DH}$ is the length of link $DH$ , as $l_{DH}=\sqrt{(l_{1}-l_{0})^{2}+{l_{s}}^{2}}$ .

For the four-bar linkage $EGKI$ , the wrist angle $(\angle EGK)$ , denoted as $\theta _{w}$ is given by:

(10) \begin{equation} \theta _{w}=\arccos \left(\frac{l_{IG}^{2}+\left(l_{12}+l_{13}\right)^{2}-{l_{3}}^{2}}{2l_{IG}\left(l_{12}+l_{13}\right)}\right)+\arccos \left(\frac{l_{IG}^{2}+{l_{11}}^{2}-\left(l_{4}+l_{5}\right)^{2}}{2l_{11}l_{IG}}\right) \end{equation}

where $l_{IG}$ is the length of link $IG$ , as $l_{IG}=\sqrt{(l_{12}+l_{13})^{2}+{l_{3}}^{2}+2(l_{12}+l_{13})l_{3}\cos \theta _{e}}$ .

For the four-bar linkage $GMLF$ , the angle between the first phalanx and the second phalanx, denoted as $\alpha _{1}$ , is calculated as:

(11) \begin{equation} \alpha _{1}=\frac{2\pi }{3}-\arccos \left(\frac{{l_{9}}^{2}+l_{MF}^{2}-{l_{10}}^{2}}{2l_{9}l_{MF}}\right)+\arccos \left(\frac{\left(l_{6}+l_{11}\right)^{2}+l_{MF}^{2}-{l_{12}}^{2}}{2\left(l_{6}+l_{11}\right)l_{MF}}\right) \end{equation}

where $l_{MF}$ is the length of link $MF$ , as $l_{MF}=\sqrt{{l_{12}}^{2}+(l_{6}+l_{11})^{2}-2l_{12}(l_{6}+l_{11})\cos \theta _{w}}$ .

For the four-bar linkage $KMNJ$ , the angle between the second phalanx and the third phalanx, denoted as $\alpha _{2}$ , is determined by:

(12) \begin{equation} \alpha _{2}=\frac{5\pi }{6}-\arccos \left(\frac{{l_{7}}^{2}+l_{JM}^{2}-{l_{8}}^{2}}{2l_{7}l_{JM}}\right)-\arccos \left(\frac{{l_{6}}^{2}+l_{JM}^{2}-{l_{5}}^{2}}{2l_{6}l_{JM}}\right) \end{equation}

where $l_{JM}$ is the length of link $JM$ , as $l_{JM}=\sqrt{{l_{6}}^{2}+{l_{5}}^{2}+2l_{6}l_{5}\left(\frac{{l_{11}}^{2}+\left(l_{4}+l_{5}\right)^{2}-l_{IG}^{2}}{2l_{11}\left(l_{4}+l_{5}\right)}\right)}$ .

As shown in Figure 2, the shoulder frame $(\mathcal{F}_{s})$ , humerus frame $(\mathcal{F}_{h})$ , radius frame $(\mathcal{F}_{r})$ and wrist frame $(\mathcal{F}_{w})$ are established following the Denavit-Hartenberg (DH) convention. Based on the structural parameters, the DH parameters for the wing are derived and summarized in Table III.

A homogeneous transformation is utilized to convert kinematic parameters between coordinate systems, where $\textbf{H}_{a}^{b}$ denotes the transformation matrix that maps coordinates from $\mathcal{F}_{\textrm{b}}$ to $\mathcal{F}_{a}$ . According to the definition, $\textbf{H}_{s}^{b}$ is expressed as:

(13) \begin{equation} \textbf{H}_{s}^{b}=\textbf{R}_{z}\left(\frac{\pi }{2}\right)\textbf{R}_{y}\left(-\varphi \right)\textbf{T}_{x}\left(l_{1}\right) \end{equation}

Here, $\textbf{R}_{i}$ and $\textbf{T}_{i}$ ( $i=x,y,z$ ) represent the homogeneous rotational and translational matrices along the respective axes. $l_{1}$ is the distance between the origins of frames $\mathcal{F}_{b}$ and $\mathcal{F}_{s}$ . Similarly, the matrices $\textbf{H}_{h}^{s} , \textbf{H}_{r}^{h}$ , and $\textbf{H}_{w}^{r}$ are expressed as follows:

(14) \begin{equation} \begin{array}{l@{\quad}l} \textbf{H}_{h}^{s}=\textbf{R}_{z}\left(\pi -\theta _{s}\right), & \textbf{H}_{w}^{r}=\textbf{T}_{x}\left(l_{12}+l_{13}\right)\textbf{R}_{z}\left(\pi -\theta _{w}\right) \\[6pt] \textbf{H}_{r}^{h}=\textbf{T}_{x}\left(l_{2}\right)\textbf{R}_{z}\left(-\left(\pi -\theta _{e}\right)\right), & \textbf{H}_{d}^{w}=\textbf{T}_{x}\left(l_{6}+l_{11}\right)\textbf{R}_{z}\left(\dfrac{\pi }{6}\right) \end{array} \end{equation}

Further, the Cartesian coordinates of the seven revolute joints $O,A,\cdots ,F$ in $\mathcal{F}_{b}$ are given by:

(15) \begin{equation} \left\{\begin{array}{l} \textbf{P}_{P}=\textbf{Proj}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} 0 & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{H}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} 0 & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{E}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} l_{2} & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{I}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} \left(l_{2}+l_{3}\right) & 0 & 0 & 1 \end{array}\right]\\[4pt] \textbf{P}_{C}=\textbf{Proj}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} -r_{s} & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{D}=\textbf{Proj}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} -r_{s} & l_{0} & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{G}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} \left(l_{12}+l_{13}\right) & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{K}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \textbf{H}_{w}^{r}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} l_{11} & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{M}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \textbf{H}_{w}^{r}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} \left(l_{6}+l_{11}\right) & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{{D_{2}}}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \textbf{H}_{w}^{r}\cdot \textbf{H}_{d}^{w}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} d_{2} & 0 & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{{D_{1}}}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \textbf{H}_{w}^{r}\cdot \textbf{H}_{d}^{w}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} d_{1}{\cos }\alpha _{1} & -d_{1}{\sin }\alpha _{1} & 0 & 1 \end{array}\right]^{T}\\[4pt] \textbf{P}_{{D_{3}}}=\textbf{Proj}\cdot \textbf{H}_{s}^{b}\cdot \textbf{H}_{h}^{s}\cdot \textbf{H}_{r}^{h}\cdot \textbf{H}_{w}^{r}\cdot \textbf{H}_{d}^{w}\cdot \left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} \left(d_{3}+l_{7}\right){\cos }\alpha _{2} & \left(d_{3}+l_{7}\right){\sin }\alpha _{2} & 0 & 1 \end{array}\right]^{T} \end{array}\right. \end{equation}

where $\textbf{P}_{i}(i=O,A,\cdots F)$ represents the position vectors of $O,A,\cdots F$ , and the projection matrix $\textbf{Proj}$ is given as:

(16) \begin{equation} \textbf{Proj}=\left[\begin{array}{l@{\quad}l@{\quad}l@{\quad}l} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0 \end{array}\right] \end{equation}

3.3. Numerical simulation

The coordinated motion of wing flapping and folding is depicted in Figure 5. The simulated trajectories of the wingtip and wrist (see Figure 5(a)) closely resemble those observed in bats in previous studies. While the robot’s flapping amplitude is smaller than that of a biological bat, the synchronization of flapping and folding follows a comparable pattern. During the upstroke, the wing gradually unfolds, reaching full extension at its highest point. Conversely, during the downstroke, the wing folds completely at its lowest point in preparation for the next upstroke. This synchronization is achieved through two actuators driving the wings.

Figure 5.

Simulation results of the wing flapping kinematics of the bat robot. (a) Wingtip and wrist trajectories under the flapping-folding coupling mode. (b) The wing extends as the slider moves forward and folds as it moves backward.

Several key angular parameters govern wing movement, including the flapping angle, digit angles, and the angles at the shoulder, elbow, and wrist joints. These angles, calculated over two complete wingbeat cycles and depicted in Figure 6, exhibit the following characteristics: the flapping angle varies within an interval of $38.5^{\circ}$ , while the angles between the second and first phalanges, as well as between the third and second phalanges, range from $18.6^{\circ}$ and $59.4^{\circ}$ , respectively. Additionally, the intervals for the shoulder, elbow, and wrist angles are $9.7^{\circ} , 21.4^{\circ}$ , and $74.3^{\circ}$ , respectively.

Figure 6.

Biologically significant changes in joint angles during two wingbeat cycles.

4.1. Materials, fabrication, and assembly

The wing skeleton constitutes the primary structural framework of the robot, providing both load-bearing capacity and actuation transmission. Digits I–III and the slender linkages around the carpus joint were fabricated from 3K carbon–fiber composite plates (1.5–2 mm thickness) using CNC milling (JINGDIAO Carver S400), ensuring lightweight construction and high stiffness. The main load-bearing elements, including the humerus, radius, radius sup, and shoulder connectors, were likewise machined from carbon–fiber plates, with miniature bearings embedded at the joints to enhance wear resistance and structural strength. The leg linkages were constructed from 2 mm stainless-steel rods, with one end threaded and connected to U-type servomotor joints.

Ultra-thin silicone-based membranes (0.1 mm thick) were used to replicate the elastic properties of bat wings. The membrane was stretched over the wing frame and then secured with cyanoacrylate adhesive. The adhesive was applied to the forelimbs, digital bones, and hindlimbs of the frame. Once the adhesive dried, any excess was removed, leaving the silicone membrane to form the robot’s wings and tail.

Within the flapping mechanism, the crank and rocker were milled from aluminum alloy, while the stainless-steel connecting rods were threaded at both ends and coupled through spherical joints for flexibility. The motor pinion was precision-hobbed from brass, whereas the remaining reduction gears were injection-molded from engineering plastics (nylon/PA), with a gear accuracy grade of ISO 7.

The overall configuration of the robot is illustrated in Figure 7, and its key specifications are summarized in Table IV. The bat-inspired robot has a total mass of 620 g, a maximum wingspan of 1.4 m, and a folding ratio of 0.57. The mass distribution, presented in Figure 8, reveals that the structural and mechanical components constitute the largest share (36%), followed by the wings, which account for 21.7% of the total mass.

Figure 7.

Global state of the bat robot.

Figure 8.

Weight breakdown of the bat-inspired robot, with mass values given in grams.

Table IV.

Bat-inspired robot main specifications.

As shown in Figure 9, the robot is powered by a 3S 850 mAh Li-Po battery and utilizes a brushless DC motor (New Xida KV-3500) to drive the flapping mechanism. The folding mechanism is operated by a servo motor (KST DS315MG), while two additional servo motors (KST DS213MG) control the left and right legs, respectively. The flight controller, housed within the body frame, integrates an inertial measurement unit, a GPS module (SR1818M10D), a power management module (DM21-5W055), and a multi-threaded servo motor controller (PCA9685). Additional components consist of an RC receiver for control inputs, a Pyboard micro-controller, and a memory card for recording flight data, including attitude angles, angular velocity, and acceleration information.

Figure 9.

Avionics, sensors, and power transmission system integrated into the body frame.

4.2. Indoor bench testing

To measure the actual wingbeat kinematics, angular displacement sensors (AS5048A) were mounted at key wing joints, as shown in Figure 10. The AS5048A is a magnetic sensing device that determines rotation by detecting variations in the magnetic field generated by an external magnet, which are converted into electrical signals through an internal Hall-effect sensor array and digitally processed to obtain accurate angular measurements. Considering the bilateral symmetry of the wings, the sensors were installed only on the left wing, specifically at the shoulder, elbow, wrist, and digit joints, as well as at the flapping shaft connecting the crank and the frame.

Figure 10.

Bench testing setup of the bat-inspired robot: (a) front view of the flapping mechanism and (b) isometric view of the morphing mechanism.

Figure 11 shows the comparison of joint angle trajectories over two wingbeat cycles. Experimental results are plotted as solid red lines, while simulations are shown as blue dashed lines. The overall trends show good consistency, confirming that the theoretical model accurately captures the wingbeat kinematics. During each cycle, the wings extend in the downstroke and fold in the upstroke. The measured trajectories of the shoulder ( $\theta _{\textrm{e}}$ ), elbow ( $\theta _{\textrm{e}}$ ), and wrist ( $\theta _{\textrm{w}}$ ) angles closely match the simulated results, with experimental ranges of $8.9^{\circ} , 19.6^{\circ}$ , and $72.1^{\circ}$ , which deviate only slightly from the theoretical values of $9.7^{\circ} , 21.4^{\circ}$ , and $74.3^{\circ}$ . These small differences mainly arise from elastic deformation of carbon–fiber linkages and friction between silicone film layers during folding.

Figure 11.

Comparison of joint angle trajectories over two wingbeat cycles: (a) shoulder angle, (b) elbow angle, (c) wrist angle, and (d) flapping angle.

For the flapping angle, the experimental results exhibit a larger amplitude range of $41.2^{\circ}$ and a phase lag of about 0.1 s relative to the theoretical prediction, as shown in Figure 11(d). The enlarged amplitude primarily originates from the inertial and bending effects of the flexible carbon–fiber framework, which exacerbate wingbeat deformation. The observed phase lag is mainly attributed to the distributed inertia of the wings, which must overcome both gravitational and inertial resistance during the upstroke.

4.3. Outdoor tethered flight

The design and electronics systems are further validated through a series of outdoor manual flights. These tests were conducted in an open sports field. The wing flapping motion is displayed in Figure 12, showing various positions within a stroke. The results demonstrate that the robot successfully achieves coupled flapping and folding motions: the wings fold during the upstroke and unfold during the downstroke. Typical flight data, recorded on an SD card, is presented in Figures 13–16, with the data covering the time interval from 7 to 12 s.

Figure 12.

Composite image showcasing bat robot throughout a wingbeat cycle.

Figure 13.

Acceleration data change with time.

Figure 14.

Angular velocity data changes with time.

Figure 15.

Attitude data changes with time.

Figure 16.

Schematic diagram of the morphing mechanism: (a) The closed-loop MNKJ, (b) the closed-loop LMGF, and (c) the morphological parameters of bat robot.

Figures 13 and 14 illustrate the acceleration and angular velocity data, respectively. The x-axis represents the robot’s forward direction, while the z-axis points vertically upward along its back. The y-axis is determined according to the right-hand rule. The acceleration data in all three directions fluctuate within a certain range but remain relatively stable over time. The mean acceleration along the x-axis is 0.73 m/s², indicating that the propulsion system provides consistent thrust. The z-axis mean acceleration is 0.51 m/s², suggesting that the flight system facilitates smooth ascent.

The angular velocity across all three axes fluctuates around 0 rad/s, indicating stable flight performance. Figure 15 displays the recorded pitch, roll, and yaw angles. The data reveal that the aircraft successfully executed stable turns and level flight maneuvers. The attitude was initially recorded under the geodetic coordinate system and subsequently converted to a local coordinate system.