Bioinspired Soft Quadrotors Jointly Unlock Agility, Squeezability, and Collision Resilience

TL;DR

This work tackles the limitation of rigid quadrotor frames by introducing FlexiQuad, a bioinspired soft-frame quadrotor with functionally anisotropic stiffness and distributed energy storage. By combining a ring-shaped airframe with decentralised actuation, FlexiQuad preserves rigid-like agility while enabling substantial squeezability and collision resilience; its performance is validated across a broad design space using Euler elastica-based squeezing models, planar and 3D finite-element analyses, and experimental tests. Key findings include an optimal stiffness range $k$ in the ballpark of $0.006$–$0.77$ N/mm that yields simultaneous agility, squeezability, and resilience, plus practical demonstrations of squeezing through gaps as narrow as 70% of nominal width and frontal/glancing collision resilience up to 5 m/s with markedly reduced peak loads. The results offer a path to robust, interactive quadrotor operation in cluttered environments and motivate future co-optimization of morphology and control (body-brain design) for soft aerial robots with real-time shape sensing and adaptive control.

Abstract

Natural flyers use soft wings to seamlessly enable a wide range of flight behaviours, including agile manoeuvres, squeezing through narrow passageways, and withstanding collisions. In contrast, conventional quadrotor designs rely on rigid frames that support agile flight but inherently limit collision resilience and squeezability, thereby constraining flight capabilities in cluttered environments. Inspired by the anisotropic stiffness and distributed mass-energy structures observed in biological organisms, we introduce FlexiQuad, a soft-frame quadrotor design approach that limits this trade-off. We demonstrate a 405-gram FlexiQuad prototype, three orders of magnitude more compliant than conventional quadrotors, yet capable of acrobatic manoeuvres with peak speeds above 80 km/h and linear and angular accelerations exceeding 3 g and 300 rad/s$^2$, respectively. Analysis demonstrates it can replicate accelerations of rigid counterparts up to a thrust-to-weight ratio of 8. Simultaneously, FlexiQuad exhibits fourfold higher collision resilience, surviving frontal impacts at 5 m/s without damage and reducing destabilising forces in glancing collisions by a factor of 39. Its frame can fully compress, enabling flight through gaps as narrow as 70% of its nominal width. Our analysis identifies an optimal structural softness range, from 0.006 to 0.77 N/mm, comparable to that of natural flyers' wings, whereby agility, squeezability, and collision resilience are jointly achieved for FlexiQuad models from 20 to 3000 grams. FlexiQuad expands hovering drone capabilities in complex environments, enabling robust physical interactions without compromising flight performance.

Figures (12)

• Figure 1: FlexiQuad: a bioinspired class of soft quadrotors. a, Natural flyers’ wings combine rigid and soft materials, resulting in structures that are orders of magnitude more flexible than the frames of conventional quadrotors. Elastic moduli ranges extracted from experimental values in the literature for bird wing bones and primary feather keratin and medulla, resilin-rich tissues in insect wing folds and tendons appel2024resilin, and stiffer insect wings’ chitin-rich and sclerotised cuticlesvincent2004designcombes2003flexuralI. b, Incorporating soft materials into the existing quadrotor frame morphology results in limited out-of-plane rigidity, leading to excessive flexural deformations that ultimately reduce efficiency and agility. c, Perspective and top views of a FlexiQuad model in its nominal and fully deformed configurations, with indication of its radius ($R$), frame strips width ($w$), mass ($M$), stiffness ($k$), and actuation units (AUs). Its extreme in-plane flexibility allows it to be fully compressed by a fragile pencil lead. d, Despite its high in-plane compliance, FlexiQuad retains sufficient out-of-plane rigidity owing to its anisotropic stiffness and decentralisation of masses beneath the rotors.
• Figure 2: Squeezability. a, Applying a compression force ($F_C$) reduces FlexiQuad’s width by a diametric compression ($\delta_R$) in the transverse plane. b, Squeezability levels across varying FlexiQuad masses ($M$) and frame stiffnesses ($k$), analytically modelled by solving the planar Euler elastica. c, FlexiQuad model ($M$ = 0.405 kg, $k$ = 0.1 N/mm) subject to a 90% frontal squeeze under weights of mass $\sim1.9 M$. d, A single actuator driving a string-and-pulley system enables frame squeezing. Alternative string-routing configurations leading to distinct equilibrium morphologies with variable propeller overlap distances ($d$), relative to the propeller diameter ($D_p$). e, Squeezing is accompanied by a decrease in energy efficiency as propellers are drawn close together and relative overlap $d/D_p$ increases. f, Active squeezing enables flight through gaps 0.7 as narrow as the drone’s nominal width (254 mm).
• Figure 3: Collision resilience. a, During frontal collisions, FlexiQuad’s compliant frame preferentially deforms within its transverse plane. The control unit (CU) experiences a deceleration $a_{CU}$, and the impact plane exerts a reaction collision force $F_R$. b, Heatmaps of the collision resilience metric ($res$) across varying FlexiQuad masses ($M$) and frame stiffnesses ($k$) at impact velocities $v_0$ = 1, 3, and 5 m/s, computed via finite element analysis. c, Temporal profiles of deceleration, collision force, and frontal relative diametric compression ($\delta_R/2R$) for frames with increasing stiffness at a collision velocity of 3 m/s. d, Experimental recording of a frontal collision of a FlexiQuad model ($M$ = 0.405 kg, $k$ = 0.1 N/mm) at 3 m/s. e, Time-dependent velocity ($v_{CU}$) and acceleration ($a_{CU}$) profiles at the CU measured during the frontal collision with a motion capture system. f, Sequential snapshots of a squeeze-and-fly manoeuvre, showing momentum-driven passive squeeze through a narrow gap (180 mm), 70% as narrow as the model’s nominal width. g, Experimental temporal profiles of force and torque measured during a simulated glancing collision on the FlexiQuad model FQ1 ($M$ = 0.405 kg, $k$ = 0.1 N/mm) and on a rigid quadrotor with identical mass and avionics. Solid lines represent the mean, and shaded regions denote $\pm$1 standard deviation ($\sigma$; n = 6 and 8 trials for soft and rigid, respectively).
• Figure 4: Agility. a, Schematics of FlexiQuad’s body coordinate frame ($x$, $y$, $z$) and the corresponding roll ($\phi$), pitch ($\vartheta$), and yaw ($\psi$) angles. b, Linear, roll, and pitch agility results in FlexiQuad’s ($M$, $k$) design space, with indication of 0.405-kg FlexiQuad models FQ1 ($k$ = 0.1 N/mm) and FQ2 ($k$ = 0.01 N/mm). c,d, Simulation results of step linear acceleration command for 0.405-kg FQ1 (c) and FQ2 (d) at TWR = 4. e,f, Comparison of vertical centre-of-mass accelerations ($a_z$) and lateral actuator inter-axis distance ($dist/D_p$) – relative to propeller diameter $D_p$ – between FQ1 (e) and FQ2 (f) from simulation results in (c), (d). g, Simulation results of a step linear acceleration of an equivalent 0.405-kg model, FQctr, with concentrated battery mass (indicated in yellow) and $k$ = 0.1 N/mm. h, Comparison of vertical acceleration $a_z$ between FQ1 and FQctr from simulations in (c) and (g). j, Comparison of angular deviation from the vertical at the control unit ($\alpha_{CU}$) and at the actuation units ($\alpha_{AU}$, averaged across all units) between FQ1 and FQctr from simulations in (c) and (g). k,l, Snapshots and graphs of vertical acceleration ($a_z$) and velocity ($v_z$) measured during experimental maximum step vertical acceleration with throttle percentage indicated as % $thr$, using a FlexiQuad model ($M$ = 0.405 kg, $k$ = 0.1 N/mm, TWR = 4.15). m,n, Snapshots and graphs of roll acceleration ($\ddot \phi$, blue) and angle ($\phi$, red) measured during aggressive lateral dodging manoeuvre with percent reference roll torque command (% $\tau_\phi$, dashed black), using the FlexiQuad model FQ1 ($M$ = 0.405 kg, $k$ = 0.1 N/mm), TWR = 4.15.
• Figure 5: Stiffness and performance comparison. a, Comparison in the stiffness-mass plane between FlexiQuad, biological flyers, and rigid quadrotors. Colour-shaded regions indicate FlexiQuad’s parameter combinations guaranteeing complete squeezability ($sqt$ = 1, blue) and agility greater than 0.5 (yellow). Blue points indicate the upper bound of $k$ at different $M$ for squeezability = 1, yellow points the lower bound for agility $\geq$ 0.5 (corresponding to TWR = 4.5), red points the optimal $k$ for collision resilience at $v_0$ = 3 m/s. Grey shading indicates mass and stiffness parameter values found in commercially available rigid quadrotor frames. b, Performance comparison between 0.405-kg FlexiQuad models with varying stiffness: one that is too soft (FQ2, $k$ = 0.01 N/mm), one in the optimal stiffness range (FQ1, $k$ = 0.1 N/mm), and a full rigid one (FQ3, $k$ = 100 N/mm).