2.1 Baseline quadrotor configuration

The baseline quadrotor used in this study is a Hexsoon EDU-450, which is a commercially available hobby-scale quadrotor. It has a gross weight of 1.61 kg, four motors with a reported 880 ${K_V}$ rating and Master Airscrew 10 $ \times $ 4.5 rotors. There is a 5 ${}^{\circ}$ dihedral angle built into the root of each boom. The planform of the hubs is square with a 44.5 cm hub-to-hub diagonal distance.

Geometric measurements of the baseline quadrotor were taken and mass properties were identified using a series of swing tests. These parameters are presented in Table 1. The reference location for the positions given is relative to the geometric centre of the four rotor hubs using the north-east-down body-fixed convention relative to the vehicle’s orientation in hover (z is positive down). There was assumed to be a negligible CG shift with the wings mounted, as the vertical location of the quarter chord of the wing was mounted in line with the baseline quadrotor CG. The wing reference positions are reported relative to their quarter chords.

Table 1. Properties of the tested aircraft. Reference position is the geometric centre of the four hubs

^*Positions are relative with respect to geometric center of rotor hubs. Wing locations denote position of quarterchord.

2.2 Quadrotor biplane tailsitter configuration

For the quadrotor biplane tailsitter configuration, the baseline quadrotor vehicle is modified by attaching two wings to the outer edges of the four landing gear [Reference Torno, Armstrong, Munsell, Galindo and Juhasz9], as shown in Fig. 1. The wings have a NACA0012 aerofoil and are cut from a polystyrene foam sheet using a hot-wire foam cutter. The wing mount is constructed to counteract the dihedral angle imposed by the booms, such that the chordlines of the wings are parallel and vertically oriented. The thickness of the mount and mounting location imposes a 3.7 cm longitudinal offset between the centre of the rotor hubs and the chordline of the wings, with the wings being further outboard. The additional wings modify the mass properties of the vehicle, which are also reported in Table 1.

2.3 Motor cant

Custom wedge-shaped 3D printed motor mounts were designed to introduce cant rotations about each boom of 5 ${}^{\circ}$ and 10 ${}^{\circ}$ . The motor cant angle is implemented such that the rotor thrust adds with the reaction torque of the motor when resolved at the vehicle centre of gravity. Figure 2 shows how this angle introduces a coupling of thrust in the same direction as the reaction torque generated by the rotor.

Figure 2. Diagram of cant angles coupling the reaction torque with the yaw axis component of rotor thrust about the CG.

The front-right and rear-left rotors rotate counter-clockwise, which produces a clockwise reaction torque. If the front-right motor is rotated about the boom to point 5 ${}^{\circ}$ towards the rear-right of the aircraft, the portion of the thrust in the vehicle x-y plane will add to its reaction torque when resolved at the centre of gravity, and therefore increase the sensitivity of vehicle torque in the yaw axis to a commanded change in directional input. Similarly, the front-left, rear-left and rear-right motors are canted towards the rear-left, front-left and front-right of the aircraft, respectively.

3.1 Motor/rotor subsystem

To better isolate motor dynamics and their impacts on the aircraft response, particularly in the yaw axis, an individual rotor/motor pair was mounted on the test stand shown in Fig. 3 to facilitate system identification of the motor and electrical dynamics. The motor used was a T-Motor Air2216 880 KV motor.

Figure 3. Experimental test stand equipment.

In order to identify high-frequency dynamics, a significantly high sampling rate was necessary. TytoRobotics’ commercially available Flight Stand 15 Pro was selected to provide a sampling rate of 1 kHz with a load cell precision in thrust and torque of $ \pm $ 0.5%. An optical RPM sensor counts the number of instances the reflective marker passes in front of it, returning RPM with a reported precision of $ \pm $ 1 RPM. Time signals from the RPM sensor were synced with that of the flight stand and were recorded together.

A frequency sweep of the ESC command, a pulse width modulated (PWM) signal, was performed, with electrical measurements taken of the ESC input voltage and current, as well as rotor thrust, torque and speed. The rotor was first given a 1,500 PWM input signal to represent the nominal trimmed motor operating point. From here, the input frequencies ranged from 0.3 to 35 rad/sec were added to the trimmed signal, maintaining the total PWM value between 1000 and 2000 PWM. The parametric model identification of the coupled motor and rotor dynamics is shown in Fig. 4 [Reference Malpica and Withrow-Maser14].

Figure 4. Block diagram of motor/armature dynamics.

The motor/electrical equations form a pair of coupled differential equations, one governing a first-order representation of the dynamics of the motor electrical circuit (Equation (1)), and the other governing the torque equilibrium of the system (Equation(2)).

(1) \begin{align}{L_a}\dot i = - {R_a}i - {K_e}{\Omega} + V\end{align}

(2) \begin{align}I\dot{\Omega} = {K_T}i - {Q_A} - B{\Omega}\end{align}

The circuit equation contains the equivalent inductance ${L_a}$ , equivalent resistance ${R_a}$ and the back-EMF. The circuit is driven by the applied voltage scaled by the PWM signal and drives the motor through the torque constant, ${K_T}$ . The torque equation contains the total applied torque by the motor ${Q_T}$ , the aerodynamic torque from the rotor ${Q_A}$ , the total inertia of the rotor and motor drives $I$ , and friction $B$ . In the system identification process, the aerodynamic torque ${Q_A}$ is assumed to vary solely with rotor speed, ${\Omega}$ . Once linearised, this parameter, $\partial {Q_A}/\partial {\Omega }$ , sums with the internal motor friction. In state-space form, the equations are:

(3) \begin{equation}\left[ {\begin{array}{l@{\quad}l}{{L_a}} & {}0\\0 & {}I\end{array}} \right]\left[ {\begin{array}{c}{\dot i}\\ \dot{\Omega}\end{array}} \right] = \left[ {\begin{array}{l@{\quad}c}{ - {R_a}} & {}{ - {K_e}}\\{{K_T}} & {}{ - \left( {B + \partial {Q_A}/\partial {\Omega}} \right)}\end{array}} \right]\left[ {\begin{array}{c}i\\{\Omega}\end{array}} \right] + \left[ {\begin{array}{c}1\\0\end{array}} \right]\left[ {\begin{array}{c}V\end{array}} \right]\end{equation}

Torque and thrust were measured in a load cell below the rotor mount. Therefore, the torque measured is the total torque generated by the motor, not just aerodynamic torque, and includes the inertial and friction elements as well, ${Q_T} = {K_T}i = {Q_A} + I\dot{\Omega} + B{\Omega}$ . Since the total torque can be obtained from either the current (forcing input) or the rotor speed (forced response), both sets of equations are used in the output equations to improve the parameter identification. The linearised output equations are therefore:

(4) \begin{equation}\left[ {\begin{array}{c}{\Omega}\\i\\{{Q_T}}\\{{Q_T}}\\T\end{array}} \right] = \left[ {\begin{array}{l@{\quad}c}0 {}&1\\1 {}&0\\{{K_T}} {}&0\\0 {}&{B + \partial {Q_A}/\partial {\Omega}}\\0 {}&{\partial T/\partial {\Omega}}\end{array}} \right]\left[ {\begin{array}{c}i\\{\Omega}\end{array}} \right] + \left[ {\begin{array}{l@{\quad}l}0 {}&0\\0 {}&0\\0 {}&0\\0 {}& I\\0 {}&0\end{array}} \right]\left[ {\begin{array}{c}{\dot i}\\\dot{\Omega}\end{array}} \right]\end{equation}

CIFER [Reference Tischler and Remple10] was used to identify the parameters of the equations of motion (Equation (3)). Initially, all the parameters were left free to identify based solely on the test stand sweep data, and the resulting model is compared to test data in Figs. 5–8 with label test stand ${K_e}$ . The first column of parameters in Table 2 shows the identified parameters based on this identification approach. The model resulted in an average mismatch cost between data and model of ${J_{ave}} = 7.8$ , meaning a nearly perfect model was obtained to match the flight test data (average costs of ${J_{ave}} \lt 50$ are considered excellent model fits [Reference Tischler and Remple10]). Often in system identification, time delays are retained to account for computation or processing delays. No such delays were accounted for since all the signals were directly recorded at high sample rates.

Figure 5. Motor electrical current response to voltage-scaled ESC input. Data taken from a rotor thrust stand.

Figure 6. Rotor speed response to voltage-scaled ESC input. Data taken from a rotor thrust stand experiment.

Figure 7. Rotor output torque response to voltage-scaled ESC input. Data taken from a rotor thrust stand experiment.

Table 2. Identified motor constants based on no-load measurement and comprehensive identification

^aHeld constant based on motor subsystem identification.

^bAs reported on t-motor website. $K_{T}=K_{e}=1/K_{v}$

Figure 8. Rotor output thrust response to voltage-scaled ESC input. Data taken from a rotor thrust stand experiment.

A common practice for identifying the motor constants ${K_e}$ and ${K_T}$ is to perform a no-load test, measuring RPM as a function of input voltage with no rotor mounted to the motor. In this test, ${K_e} = \frac{{d{\Omega}}}{{dV}}$ and ${K_T} = {K_e}$ for consistent SI units of radians/volt-second, and Newton-meters/ampere. This process yielded a value of ${K_T} = 0.011$ . This is equivalent to a ${K_V} = \frac{1}{{{K_T}}}$ rating of 868, which is close to the reported 880 ${K_V}$ on the motor casing. A second identification, fixing ${K_T} = {K_e}$ to these parameters was also done, and this column is labeled no load ${K_e}$ in Table 2 and subsequent plots. The resulting mismatch cost increased to ${J_{avg}} = 36$ , still giving an overall excellent model. Note that the identified values of ${K_e}$ and ${K_T}$ from the initial test stand ${K_e}$ model were $7.39 \times {10^{ - 3}}$ and 0.014, respectively, which are equivalent to ${K_V}$ ratings of 1,340 and 680, respectively.

A compressed scale is used on the magnitude plot to highlight the slight differences between the two models in Figs. 5 and 7. Figure 5 shows the motor current to voltage input. The input voltage is scaled by the commanded PWM signal value to be between zero and the supply voltage. The current dynamics include a zero and two poles. Since the current drives the torque through the torque constant ${K_T}$ , Fig. 7 is a scaled version of Fig. 5. The torque drives the yaw response of the quadrotor without cant. The motor torque response in transfer function form is:

(5) \begin{align}\frac{{{Q_T}}}{V} = \frac{{K( {s + {\omega _{lead}}})}}{{( {s + {\omega _{mot}}})( {s + {\omega _{elec}}})}}\end{align}

Here, the gain $K$ represents the overall gain in the torque response, the zero dynamics are

\begin{align*} s + {\omega _{lead}} = s + \frac{{B + \partial {Q_A}/\partial {\Omega}}}{I} \end{align*}

and the quadratic roots are

\begin{align*} \left( {s + {\omega _{mot}}} \right)\left( {s + {\omega _{elec}}} \right) = \left( {s + \frac{{{R_a}}}{{{L_a}}}} \right)\left( {s + \frac{{B + \partial {Q_A}/\partial {\Omega}}}{I}} \right) + \frac{{{K_e}}}{{{L_a}}}\frac{{{K_T}}}{I} \end{align*}

The differences in magnitude between Figs. 5 and 7 are a result of the different values of ${K_T}$ from the two identification processes used. The two poles in the responses are associated with the mechanical motor system overcoming inertia and drag, and the electrical system overcoming inductance and back-EMF, as given in Equation (3).

The thrust response in Fig. 8 is similarly a scaled version of the motor speed response in Fig. 6, since motor thrust is dependent only on rotor speed to generate higher dynamic pressure and lift along the blades. The thrust response has the same poles as the torque response but doesn’t contain the zero:

(6) \begin{align}\frac{T}{V} = \frac{K}{{\left( {s + {\omega _{mot}}} \right)\left( {s + {\omega _{elec}}} \right)}}\end{align}

Here $K$ represents a gain that is a function of identified motor constants. The test stand ${K_e}$ results give a ${\omega _{mot}} = 11.1$ rad/sec and a ${\omega _{elec}} = 72.5$ rad/sec. The no load ${K_e}$ results give a ${\omega _{mot}} = 18.4$ rad/sec and a ${\omega _{elec}} = 32.9$ rad/sec. In both cases, the pole associated with the electrical inductance is at a higher frequency than was tested using the sweep and therefore was omitted from the subsequent identification of the aircraft dynamics. Both models predict a torque response zero at ${\omega _{lead}} = 5.0$ rad/sec. The subsequent identification results only retain the lead term and a single pole associated with the motor mechanical system response. Even though the no load ${K_e}$ model has a higher mismatch cost, it was used in the final set of comparison results of the different aircraft since the ${K_e}$ value matched closely to the specified value of the motor.

3.2 Hovering baseline quadrotor

To properly quantify the impacts of the wings and rotor cant, a baseline quadcopter identification was first undertaken. Figures 9–12 show the dynamics of the primary on-axis response for the longitudinal, lateral, heave and yaw axes, respectively. A state-space model was fit to the flight test-based frequency responses, and the resulting model is also shown. The models all represent the bare-airframe dynamics and are obtained from closed-loop data. This can be achieved when turbulence and other disturbances to the feedback look are minimised, so care was taken to perform flight tests only on calm days.

Figure 9. Lateral dynamics response of a hovering quadrotor taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

Figure 10. Longitudinal dynamics response of a hovering quadrotor taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

Figure 11. Yaw dynamics response of a hovering quadrotor taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

Figure 12. Heave response of a hovering quadrotor taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

The dominant dynamics of the baseline quadrotor agree qualitatively with trends observed in prior work [Reference Cheung11, Reference Ivler, Rowe, Martin, Lopez and Tischler12]. Both motor models were used to demonstrate the similarity between the responses. The no load ${K_e}$ responses have better fits at high frequency, particularly in the phase responses. This is due to the higher motor frequency.

The flight tests were broken into two records to facilitate data collection and piloting; each individual sweep was over two minutes in length, and multiple iterations were performed for each sweep. The lower frequency sweep flight tests ranged from 0.3 to 3 rad/sec, and the higher frequency sweeps ranged from 1.2 rad/sec to 30 rad/sec. The frequency responses generally show high coherence, above ${\gamma ^2} \gt 0.6$ , indicating quality test data. Drops in coherence are only present in the lateral (Fig. 9) and longitudinal axes (Fig. 10) around $\omega = 3$ rad/sec, where the unstable phugoid dynamics are in both axes. This trend has been observed in past tests [Reference Cheung11, Reference Ivler, Rowe, Martin, Lopez and Tischler12] as well.

The parameters of the state-space models were generally well identified. The average model mismatch costs in the roll and pitch responses were between ${J_{ave}} = 50$ and ${J_{ave}} = 100$ , indicating that acceptable models were found. In heave and yaw, the mismatch costs were generally below ${J_{ave}} = 50$ , indicating excellent identification results. Individual parameter values were also well identified, with Cramer-Rao bounds below $CR\left( {\rm{\% }} \right) \lt 20\% $ and Insensitivities below $I\left( {\rm{\% }} \right) \lt 10\% $ as per guidelines [Reference Tischler and Remple10].

The state-space models used in the identification are given below. The motor frequency was fixed at the identified value of ${\omega _{mot}} = 18.4$ rad/sec for all responses, based on the no load ${K_e}$ motor identification results, and the motor dynamics are represented by motor state $\tau $ .

3.2.1 Pitch and roll dynamics

The pitch axis equations of motion are:

(7) \begin{equation}\left[ {\begin{array}{c}{\dot u}\\{\dot \theta }\\{\dot q}\\{\dot \tau }\end{array}} \right] = \left[ {\begin{array}{l@{\quad}c@{\quad}c@{\quad}c}{{X_u}} {}&{ - g} {}&0 {}&0\\0 {}&0 {}&1 {}&0\\{{M_u}} {}&0 {}&{{M_q}} {}&{{M_{{\delta _{lon}}}}}\\0 {}&0 {}&0 {}&{ - {\omega _{mot}}}\end{array}} \right]\left[ {\begin{array}{c}u\\\theta \\q\\\tau \end{array}} \right] + \left[ {\begin{array}{c}0\\0\\0\\{{\omega _{mot}}}\end{array}} \right]{\delta _{lon}}\end{equation}

For the quadrotor configuration, the pitch damping derivative was not identified, ${M_q} = 0$ , though it is retained since it impacts the pitch dynamics of the tailsitter configuration significantly. Note that the input ${\delta _{lon}}$ drives the motor response, which then drives the pitch moment control derivative ${M_{{\delta _{lon}}}}$ . This formulation places the control derivative in the matrix of stability derivatives, but allows the model to retain the motor lag dynamics (Equation (6)), which is needed when thrust is used to drive the response in an axis. Figure 10 shows that both models capture the flight test response. The differences in motor modeling appear as a slight phase variation between 3 and 30 rad/sec. Individual parameter values will be compared later with the winged aircraft in Table 3.

Table 3. Identified longitudinal stability and control derivatives of each configuration

^*Held constant based on motor subsystem identification.

⁺Fixed at zero to remove parameter insensitivity to model ID result

The roll axis equations have the same form as the pitch axis equations, with lateral state substituted as appropriate. The roll response in Fig. 9 for the quadcopter configuration is nearly identical to the pitch response due to the symmetry of the vehicle.

3.2.2 Yaw dynamics

The yaw equations of motion are (following the notation from Ivler [Reference Ivler, Rowe, Martin, Lopez and Tischler12]):

(8) \begin{equation}\left[ {\begin{array}{c}{\dot \psi }\\{\dot r}\\{\dot \tau }\end{array}} \right] = \left[ {\begin{array}{l@{\quad}c@{\quad}c}0 {}&1 {}&0\\0 {}&{{N_r}} {}&{{N_{{\delta _{dir}}}}}\\0 {}&0 {}&{ - {\omega _{mot}}}\end{array}} \right]\left[ {\begin{array}{c}\psi \\r\\\tau \end{array}} \right] + \left[ {\begin{array}{c}0\\{N{{\rm{'}}_{{\delta _{dir}}}}}\\{{\omega _{mot}}}\end{array}} \right]{\delta _{dir}}\end{equation}

Here a control derivative for yaw is placed in the control derivative matrix, as well as the stability derivative matrix. This formulation gives the motor response a pole/zero dynamics that was shown in Equation (5) and shown in Fig. 7. In transfer function form, the yaw response is:

(9) \begin{align}\frac{r}{{{\delta _{dir}}}} = \frac{{N^{'}_{{\delta _{dir}}}}}{{s - {N_r}}}\frac{{s + {\omega _{lead}}}}{{s + {\omega _{mot}}}}\end{align}

where:

(10) \begin{align}{\omega _{lead}} = {\omega _{mot}}\left( {1 + \frac{{{N_{{\delta _{dir}}}}}}{{N{^{'}_{{\delta _{dir}}}}}}} \right)\end{align}

Since the lead frequency was also identified during the motor identification in Equation (5), this equation constrains the two yaw control derivatives $N{{\rm{'}}_{{\delta _{dir}}}}$ and ${N_{{\delta _{dir}}}}$ . Solving for ${N_{{\delta _{dir}}}}$ :

(11) \begin{align}{N_{{\delta _{dir}}}} = \left( {\frac{{{\omega _{lead}}}}{{{\omega _{mot}}}} - 1} \right)N{{\rm{'}}_{{\delta _{dir}}}}\end{align}

For the baseline uncanted quad, which uses pure torque to generate moments, the motor test stand identification resulted in ${\omega _{lead}}/{\omega _{mot}} = 5/18.4 = 0.2717$ , meaning ${N_{{\delta _{dir}}}} = - 0.728N{{\rm{'}}_{{\delta _{dir}}}}$ . This leaves only two unknowns in the yaw identification process, ${N_r}$ , and $N{{\rm{'}}_{{\delta _{dir}}}}$ .

3.2.3 Heave dynamics

Finally, the heave equations are:

(12) \begin{align}\left[ {\begin{array}{c}{\dot w}\\{\dot \tau }\end{array}} \right] = \left[ {\begin{array}{l@{\quad}c}{{Z_w}} {}&{{Z_{{\delta _{col}}}}}\\0 {}&{ - {\omega _{mot}}}\end{array}} \right]\left[ {\begin{array}{c}w\\\tau \end{array}} \right] + \left[ {\begin{array}{c}0\\{{\omega _{mot}}}\end{array}} \right]{\delta _{col}}\end{align}

As with the previous responses, the motor dynamics are held fixed, and only the heave damping ${Z_w}$ and control derivative ${Z_{{\delta _{col}}}}$ are identified.

3.3 Hovering quadrotor biplane tailsitter

Figures 13–16 show the primary on-axis identification results for the baseline tailsitter configuration as pictured in Fig. 1. This configuration was nearly uncontrollable due to poor yaw controlability and an inability of the baseline control system to reject yaw disturbances. However, frequency sweeps were still flown, and a good system identification result was obtained with low model fit mismatch costs.

Figure 13. Lateral dynamics response of a hovering tailsitter taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

Figure 14. Longitudinal dynamics response of a hovering tailsitter taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

Figure 15. Yaw dynamics response of a hovering tailsitter taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

As with the baseline quad, both motor models are included to highlight the similarity between the responses. The no load ${K_e}$ model shows better alignment in phase for all four axes.

3.3.1 Pitch dynamics

The inclusion of the wing changes the pitch axis system identification in that the pitch damping term ${M_q}$ needed to be included, whereas the pitch dynamics for the baseline quadrotor were insensitive to its inclusion. The stability derivatives for the pitch response comparisons are given in Table 3. The tailsitter exhibits nearly a ten-fold increase in drag, derivative ${X_u}$ , due to the large wings acting like flat plates when forward speed is perturbed. Pitch stability ${M_u}$ becomes negative, with the wing generating a nose-down moment to forward speed perturbations. As expected, the control derivative ${M_{{\delta _{lon}}}}$ remains relatively unchanged. The small decrease may be due to the interactional effects of the wings or the slightly increased pitch inertia resulting from the addition of the foam wings.

The difference in the stability derivatives results in different rigid body modes. The modes are visualised in the Bode plots of Figs. 10 and 14, and their differences are quantified in Table 4. The wing stabilises the Phugoid dynamics, but destabilises the first-order pitch mode.

Table 4. Comparisons of longitudinal modes for two configurations

^* $[{\zeta ;{\omega _n}}]$ is nomenclature for a second order mode, given in terms of damping ratio and natural frequency

⁺(a)is nomenclature for a first order pole ${s+a}$ .

Figure 16. Heave response of a hovering tailsitter taken from flight test. Models include motor derivatives using either the identified or no-load ${{\rm{K}}_{\rm{e}}}$ values.

3.4 Canted motor results and aircraft comparisons

To investigate the dynamic impact of rotor cant angle, the baseline quadrotor and tailsitter were modified by exchanging the motor mounts with one of two different wedge-shaped mounts. The three blue lines in Figs. 17–20 contain the on-axis response in the four primary control axes. The red lines show the same responses but for the tailsitter. The identified models for motor cants of 0 ${}^{\circ}$ , 5 ${}^{\circ}$ and 10 ${}^{\circ}$ are shown with different line styles. The 5 ${}^{\circ}$ motor cant was not flown in the tailsitter configuration. The identified model parameters are given in Table 5.

Figure 17. Lateral dynamics response comparisons of identified fit models for the quadrotor and tailsitter configurations with cant angles of 0°, 5° and 10°.

Table 5. Transfer function representations of the yaw response to of each configuration

^&Held constant based on motor subsystem identification.

Figure 18. Longitudinal dynamics response comparisons of identified fit models for the quadrotor and tailsitter configurations with cant angles of 0°, 5° and 10°.

Figure 19. Yaw dynamics response comparisons of identified fit models for the quadrotor and tailsitter configurations with cant angles of 0°, 5° and 10°.

Table 6. Transfer function elements of the yaw response to directional inputs ( ${\rm{r}}/{{\rm{\delta }}_{{\rm{dir}}}}$ ) of each configuration

Figure 20. Heave response comparisons of identified fit models for the quadrotor and tailsitter configurations with cant angles of 0°, 5° and 10°.

From the figures it is clear that the impact of cant on the on-axis roll, pitch and heave dynamics are negligible, and any observed differences fall within the precision of the model. Further, in the roll and heave responses (shown in Figs. 17 and 20, respectively), all of the configurations are nearly identical, so neither cant nor the wing changes the response significantly in those axes. The differences in the pitch axis can be entirely attributed to the presence of the wing, with no sensitivity to cant angles.