Task-Driven Closed-Loop Design Optimization of Passively Morphing Quadrotors for Contact-Mediated Narrow Gap Traversal

Etor Arza; Luca Girardi; Gabriel Maquignaz; Javier Paez; Stefan Leutenegger; Stefano Mintchev; Kostas Alexis

cs.RONov 6, 2026

Task-Driven Closed-Loop Design Optimization of Passively Morphing Quadrotors for Contact-Mediated Narrow Gap Traversal

Authors: Etor Arza, Luca Girardi, Gabriel Maquignaz, Javier Paez, Stefan Leutenegger, Stefano Mintchev, Kostas Alexis

Organizations: Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. · Mobile Robotics Lab, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland. · Agricultural Robotics, University of Bonn, Bonn, Germany.

Abstract

Aerial robots operating in cluttered environments may encounter openings narrower than their nominal width. Existing passively morphing drones reduce their width upon traversal, but they typically involve human-made designs, which can struggle to find the right balance among folding ratio, flight efficiency, and control tracking performance. We introduce a closed-loop design method that jointly optimizes quadrotor geometry and the torque-deflection response of two passively folding arms driven by the success rate in simulation for contact-mediated gap traversal. An optimization algorithm samples candidate designs that are evaluated in a contact-based simulation of the traversal task, where the task success rate is used as a feedback signal to sample progressively better designs over time. The resulting prototype passively reduces its width from 31.3 to 14.1 cm and traverses a 15 cm wide opening at a 2 m/s reference speed. It also tolerates gap approach-angle errors of up to 30 degrees and folds through a 40 cm long confined passage. Compared to a rigid twin, the soft configuration adds only 2 mm of position RMSE and less than 1% electrical power during contact-free flight. These results show that task-driven closed-loop design optimization can produce passively morphing airframes that are compact under contact, tolerant to approach error, and effectively rigid during nominal flight.

Figures & tables

Fig. 1: Task-driven closed-loop design optimization of passively morphing quadrotors for contact-mediated narrow-gap traversal. (a) Physical prototype in extended and folded configurations, with width reduced from $31.3$ to $14.1$ cm. (b) Airframe capabilities: contact-induced arm folding enables traversal through a long tube and narrow openings, including angled approaches. (c) Airframe geometry and passive joint responses are jointly optimized using simulated gap-traversal success rate, with repairs for control authority and joint realizability, followed by fabrication and real-world validation.

Panel of Figure 2 — Fig. 2: (a) Requested (dashed) and repaired (solid) ERC restoring-torque response parameterized by $(a,b,c,d)$ . (b) Geometry parameters on the optimized airframe.

Variables	Parameter	Symbols	Range	Optimized
$g_{1},g_{2}$	Front/Back arm length	$\ell_{\mathrm{F}},\ell_{\mathrm{B}}$	$[5,15]$ cm	$\phantom{-}8.51\phantom{-}/\phantom{-}8.99$
$g_{3},g_{4}$	Left/Right arm length	$\ell_{\mathrm{L}},\ell_{\mathrm{R}}$	$[5,15]$ cm	$\phantom{-}8.89\phantom{-}/\phantom{-}8.98$
$g_{5},g_{6}$	Front/Back propeller roll	$\phi_{\mathrm{F}},\phi_{\mathrm{B}}$	$[-45,45]^{\circ}$	$\phantom{-}0.42\phantom{-}/\phantom{-}0.44$
$g_{7},g_{8}$	Front/Back propeller pitch	$\vartheta_{\mathrm{F}},\vartheta_{\mathrm{B}}$	$[-45,45]^{\circ}$	$\phantom{-}16.57\phantom{-}/\phantom{-}17.21$
$g_{9},g_{10}$	Front/Back propeller yaw	$\psi_{\mathrm{F}},\psi_{\mathrm{B}}$	$[-45,45]^{\circ}$	$\phantom{-}0.00\phantom{-}/\phantom{-}0.00$
$g_{11},g_{12}$	Joint axis roll	$\phi_{\mathrm{j,L}},\phi_{\mathrm{j,R}}$	$[-30,30]^{\circ}$	$-24.15\phantom{-}/\phantom{-}30.00$

TABLE I: Geometry parameter ranges and optimized values.

Fig. 3: Repeated evaluation of four designs with

400

trials per gap width. Left: success probability. Right: mean maximum tilt during the first 0.2 seconds after traversal among successful trials where success exceeds

30\%

	Flight	Recovery
$\bm{e}_{p}$	$(0.05{,}30{,}10)$	$(2{,}2{,}10)$
$\bm{e}_{v}$	$(0.30{,}4{,}15)$	$(3{,}3{,}5)$
$\bm{e}_{R}$	$(4{,}2{,}2)$	$(4{,}2{,}2)$
$\bm{e}_{\omega}$	$(1{,}1{,}0.5)$	$(1{,}0.5{,}0.5)$
$\bm{u}$	$0.12$	$0.12$
$\Delta\bm{u}$	$35$	$80$

Table 5

Panel of Figure 6 — Fig. 4: Simulation optimization results. (a) Candidate success rates (gray), best-so-far curve (black), and BO–CMA-ES transition (dotted) over the $800$ evaluations. Optimized airframe (b) maximally folded and (c) overlaid with its extended configuration in top view; folding reduces its width from $31.3$ to $14.1$ cm ( $55\%$ ). (d) Requested and repaired left/right ERC restoring-torque responses; positive $\theta$ is the folding direction and negative $\theta$ is blocked.

Fig. 5: Success probability for the best designs optimized over the full and reduced design spaces.

Panel of Figure 8 — Fig. 6: Best designs from four optimization runs with different seeds. Top: render of folded airframes. Below: geometry parameters and restoring torque. Colored lines show the parameters of the best found airframe for each seed (color matches render above), while gray lines show all evaluated airframes.

Fig. 7: Traversal of a $15\times 20$ cm opening. Top: video frames of the crossing. Bottom: logged gap-relative position, velocity, tilt, and rotor speeds. Dotted vertical lines mark the frame instants.

Fig. 8: Traversal of a $40$ cm-long, $22.5$ cm-diameter tube. Top: video frames of the traversal. Bottom: entrance-relative position, velocity, tilt, and rotor speeds. The origin is at the tube entrance center where $x=y=z=0$ . Dotted vertical lines mark the frame instants, and shading marks the interval in which the vehicle is inside the tube.

Approach angle	$0^{\circ}$	$10^{\circ}$	$20^{\circ}$	$30^{\circ}$	$35^{\circ}$
Arm dislocation	0	0	0	1	3
Loss of control	0	0	0	0	0
Altitude loss	0	0	0	0	1
Max. altitude loss [m]	$0.50$	$0.50$	$0.51$	$0.49$	$0.96$

TABLE III: Failures over

20

consecutive traversals per approach angle.

Fig. 9: Traversal of a $20$ cm opening at approach angles of $0$ – $35^{\circ}$ . Top: high-speed camera frames. Bottom: top view of the trajectory and boxplots over $20$ traversals per angle of the peak angular velocity and of the altitude loss $\Delta z$ on successful traversals.

Fig. 10: Nominal-flight cost of the passive joints on a

2.4

m-diameter circular trajectory at

1.5

m/s. Left: position error for soft-arm and rigid-arm flights and Morphy [ 9 ] . Right: battery voltage during the six

250

s comparison windows, where line color identifies the arm configuration and line style identifies the battery pack.

Fig. 11: Left: maximum angular velocity norm. Right: maximum tilt. Both are measured over the first

0.2

s after crossing the gap plane at a

20

cm opening.

Aerial Robotics

Aerial robotics studies the design, perception, control, and coordination of flying robots for navigation, inspection, transport, and physical interaction.

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The size of a narrow gap traversable by a fixed-wing drone is limited by its wingspan. Inspired by birds, here, we enable the traversal of a gap of sub-wingspan width and height using a morphing-wing drone capable of temporarily sweeping in its wings mid-flight. This maneuver poses control challenges due to sudden lift loss during gap-passage at low flight speeds and the need for precisely timed wing-sweep actuation ahead of the gap. To address these challenges, we first develop an aerodynamic model for general wing-sweep morphing drone flight including low flight speeds and post-stall angles of attack. We integrate longitudinal drone dynamics into an optimal reference trajectory generation and Nonlinear Model Predictive Control framework with runtime adaptive costs and constraints. Validated on a 130 g wing-sweep-morphing drone, our method achieves an average altitude error of 5 cm during narrow-gap passage at forward speeds between 5 and 7 m/s, whilst enforcing fully swept wings near the gap across variable threshold distances. Trajectory analysis shows that the drone can compensate for lift loss during gap-passage by accelerating and pitching upwards ahead of the gap to an extent that differs between reference trajectory optimization objectives. We show that our strategy also allows for accurate gap passage on hardware whilst maintaining a constant forward flight speed reference and near-constant altitude.

Abstract

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