In recent years, quadrotor unmanned aerial vehicles (UAVs) have gained widespread adoption in various fields such as aerial photography, surveying, and surveillance due to their agility and operational flexibility. However, a significant limitation persists: the limited endurance of quadrotor systems, primarily constrained by aerodynamic inefficiencies of propellers and the energy density of batteries. This restriction hampers mission efficiency, especially in applications requiring prolonged operation. To address this, we explore a novel approach leveraging the aerodynamic phenomenon known as the propeller wall effect, where a quadrotor perches on vertical or horizontal surfaces to drastically reduce power consumption. This paper presents the design of an aerodynamic perching mechanism, trajectory planning, and control strategies for aggressive perching maneuvers, validated through experimental prototypes.
The core innovation lies in a ducted aerodynamic perching mechanism that amplifies the wall effect, generating substantial negative pressure when the quadrotor approaches a surface. This allows the quadrotor to adhere to walls with minimal energy input. Our design optimizes duct geometry, including lip radius and wall clearance, to maximize suction force while maintaining flight performance. Numerical simulations and experimental tests confirm that the perching state reduces power consumption by up to 71% compared to hovering, significantly extending operational time. Furthermore, we develop a real-time trajectory planning method based on differential flatness and a geometric tracking controller to handle the aggressive maneuvers required for perching, ensuring precise control of position, velocity, and attitude during high-dynamics transitions.
The quadrotor dynamics are modeled using rotation matrices to avoid singularities associated with Euler angles. The equations of motion are expressed as:
$$ m\ddot{\mathbf{x}} = -mg\mathbf{e}_3 + f\mathbf{R}\mathbf{e}_3 $$
$$ \dot{\mathbf{R}} = \mathbf{R}\hat{\boldsymbol{\omega}} $$
$$ \mathbf{J}\dot{\boldsymbol{\omega}} = \mathbf{M} – \boldsymbol{\omega} \times \mathbf{J}\boldsymbol{\omega} $$
where \( m \) is the mass, \( \mathbf{x} \) is the position vector, \( \mathbf{R} \) is the rotation matrix from body to inertial frame, \( \boldsymbol{\omega} \) is the angular velocity, \( \mathbf{J} \) is the inertia matrix, \( f \) is the total thrust, and \( \mathbf{M} \) is the control moment. The hat operator \( \hat{\cdot} \) denotes the skew-symmetric matrix form. For a standard quadrotor, the force and moment inputs are related to individual rotor thrusts \( f_i \) by:
$$ \begin{bmatrix} f \\ \mathbf{M} \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 & 1 \\ 0 & -l & 0 & l \\ l & 0 & -l & 0 \\ -c & c & -c & c \end{bmatrix} \begin{bmatrix} f_1 \\ f_2 \\ f_3 \\ f_4 \end{bmatrix} $$
where \( l \) is the arm length and \( c \) is the torque coefficient. This model forms the basis for our control design.
For the aerodynamic perching mechanism, we designed a duct with an outward-flared lip to enhance the wall effect. The duct parameters were optimized through computational fluid dynamics (CFD) simulations, evaluating suction force under varying lip radii and wall clearances. The optimal design achieves a lip radius-to-duct height ratio of 0.27 and a wall clearance-to-duct height ratio of 0.114, balancing suction force and structural mass. Key parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Wall Clearance \( S \) (mm) | 4 |
| Lip Radius \( r \) (mm) | 9.5 |
| Maximum Duct Diameter \( D \) (mm) | 100 |
| Rotor Disk Height \( h \) (mm) | 19 |
| Rotor Disk Diameter \( d \) (mm) | 63 |
| Tip Clearance \( s \) (mm) | 1.5 |
| Duct Height \( H \) (mm) | 35 |
| \( d/H \) | 1.8 |
| \( r/H \) | 0.27 |
| \( h/H \) | 0.543 |
| \( S/H \) | 0.114 |
| Tip Clearance Ratio \( s/D \times 100\% \) | 1.5% |
The suction force \( F_s \) generated by the duct near a wall is modeled as a function of the pressure difference \( \Delta P \) and the effective area \( A_{\text{eff}} \):
$$ F_s = \Delta P \cdot A_{\text{eff}} $$
where \( \Delta P \) is derived from the Bernoulli principle and CFD results. Experimental measurements on a test rig using a six-axis force sensor validated the performance, showing that the ducted system increases thrust by approximately 11% compared to an isolated propeller at the same power input. For perching on vertical surfaces, the equilibrium condition requires the suction force to counteract gravity and friction:
$$ F_s \geq \frac{mg}{\mu} $$
where \( \mu \) is the friction coefficient. With \( \mu = 1 \), the minimum suction force equals the quadrotor weight.
Trajectory planning for aggressive perching is formulated as an optimization problem minimizing the snap (fourth derivative of position) to ensure smooth motions. The flat outputs are the position coordinates \( \sigma(t) = [x(t), y(t), z(t)]^\top \), parameterized as seventh-order polynomials:
$$ \sigma(t) = \sum_{i=0}^{7} c_i t^i $$
for each segment between waypoints. The cost function is:
$$ J = \int_{t_0}^{t_f} \left\| \frac{d^4 \sigma}{dt^4} \right\|^2 dt $$
subject to constraints including initial and terminal states, continuity between segments, and inequality constraints on derivatives. The terminal acceleration constraint incorporates the wall inclination angle \( \theta \):
$$ \ddot{\sigma}(t_f) = \frac{f}{m} \mathbf{R}_{\text{end}} \mathbf{e}_3 + g \mathbf{e}_3 $$
where \( \mathbf{R}_{\text{end}} \) is the desired rotation matrix at perch. This ensures the quadrotor approaches the wall with the correct orientation and force profile. The optimization is solved as a quadratic programming problem for real-time applicability.
For trajectory tracking, we employ a geometric controller that computes the desired thrust and moments based on position and attitude errors. The position error \( \mathbf{e}_x \) and velocity error \( \mathbf{e}_v \) are:
$$ \mathbf{e}_x = \mathbf{x} – \mathbf{x}_d, \quad \mathbf{e}_v = \mathbf{v} – \mathbf{v}_d $$
The control force \( \mathbf{F}_c \) is:
$$ \mathbf{F}_c = -k_x \mathbf{e}_x – k_v \mathbf{e}_v + mg\mathbf{e}_3 + m\ddot{\mathbf{x}}_d $$
where \( k_x \) and \( k_v \) are gain matrices. The thrust magnitude \( f \) and desired body z-axis \( \mathbf{b}_{3,c} \) are:
$$ f = \mathbf{F}_c^\top \mathbf{b}_{3,c}, \quad \mathbf{b}_{3,c} = -\frac{\mathbf{F}_c}{\|\mathbf{F}_c\|} $$
The desired rotation matrix \( \mathbf{R}_c \) is constructed from \( \mathbf{b}_{3,c} \) and a desired yaw angle. The attitude error \( \mathbf{e}_R \) and angular velocity error \( \mathbf{e}_\omega \) are:
$$ \mathbf{e}_R = \frac{1}{2} (\mathbf{R}_c^\top \mathbf{R} – \mathbf{R}^\top \mathbf{R}_c)^\vee, \quad \mathbf{e}_\omega = \boldsymbol{\omega} – \mathbf{R}^\top \mathbf{R}_c \boldsymbol{\omega}_d $$
The control moment \( \mathbf{M} \) is:
$$ \mathbf{M} = -k_R \mathbf{e}_R – k_\omega \mathbf{e}_\omega + \boldsymbol{\omega} \times \mathbf{J}\boldsymbol{\omega} – \mathbf{J} (\hat{\boldsymbol{\omega}} \mathbf{R}^\top \mathbf{R}_c \boldsymbol{\omega}_d – \mathbf{R}^\top \mathbf{R}_c \dot{\boldsymbol{\omega}}_d) $$
where \( k_R \) and \( k_\omega \) are gains. This controller ensures stable tracking even during aggressive maneuvers.
Experimental validation involved a custom quadrotor with a mass of 400 g and a frame size of 150 mm. The perching mechanism was attached to each rotor, and flights were conducted in an indoor environment with motion capture for state estimation. The quadrotor initiated perching from a hover position 1.43 m from a vertical wall, with a planned trajectory duration of 1 s. The terminal velocity was set to 3 m/s, and the acceleration constraint reflected the wall orientation. Figure 1 shows the quadrotor during hover and perching states.
Table 2 compares the power consumption and force efficiency between hovering and perching states for the ducted quadrotor. The data confirms a 71% reduction in power during perching, with force efficiency rising from 2 g/W to 7 g/W.
| State | Total Power (W) | Thrust per Rotor (N) | Force Efficiency (g/W) |
|---|---|---|---|
| Hovering | 184 | 1.03 | 2.0 |
| Perching | 52 | 1.03 | 7.0 |
Trajectory tracking results demonstrated minor errors in position and velocity, primarily due to unmodeled aerodynamic disturbances and localization inaccuracies. The quadrotor successfully perched on the vertical wall with a contact velocity of 3.14 m/s, and the attitude converged to the desired orientation post-contact. The root mean square errors for trajectory tracking are summarized in Table 3.
| Axis | Position Error (m) | Velocity Error (m/s) |
|---|---|---|
| x | 0.117 | 0.255 |
| y | 0.013 | 0.037 |
| z | 0.016 | 0.077 |
In conclusion, this work demonstrates a comprehensive approach to enabling quadrotor UAVs to perform aggressive perching on vertical surfaces using propeller wall effect. The optimized duct design enhances suction force with minimal weight penalty, while the trajectory planning and geometric control ensure reliable and stable maneuvers. Experimental results validate the significant energy savings and robustness of the method. Future work will focus on adapting the system to uneven surfaces and dynamic environments, further expanding the applicability of quadrotor perching in real-world scenarios.
The integration of aerodynamic principles with advanced control strategies highlights the potential for quadrotor technology to achieve prolonged missions through innovative perching capabilities. This research contributes to the evolving landscape of autonomous UAV operations, where energy efficiency and adaptability are paramount.