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

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.

• The paper introduces FlexiQuad, a bioinspired soft quadrotor that combines distributed mass and anisotropic flexibility to jointly achieve agility, squeezability, and collision resilience.
• The methodology integrates analytical modeling, finite element simulations, and experimental validation to demonstrate performance within biological stiffness regimes.
• The work paves the way for morphology-aware control and applications in confined, challenging environments like disaster zones and infrastructure inspections.

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

Introduction and Design Principles

This paper introduces FlexiQuad, a bioinspired quadrotor class that leverages functional stiffness anisotropy and distributed energy mass, revealing a design space that overcomes traditional trade-offs between agility, collision resilience, and morphing capability in aerial robots. Drawing from the structural principles of bird and insect wings—the combination of compliant and stiff regions with decentralised energy storage—the FlexiQuad airframe employs thin-walled, ring-shaped, soft composite strips and situates all actuation and energy hardware along its periphery. This morpho-functional arrangement delivers compliance for squeezability and resilience, while maintaining out-of-plane rigidity for high-performance flight.

Figure 1: FlexiQuad uses an anisotropic glass-fibre frame, decentralising heavy components and mimicking the flexible-yet-stiff architecture of biological flyers’ wings.

Squeezability Mechanism and Trade-Offs

By design, FlexiQuad features substantial in-plane compliance, enabling acute diametric compression, termed "squeezability." The airframe achieves full compression ($sqt=1$) across a wide range of masses and optimal frame stiffness ($0.006 \leq k \leq 0.77$ N/mm), matching biological flyers. Rigorous analytical modeling and finite element validation reveals the required compression force scales strongly with both frame stiffness and mass. The active squeezing mechanism utilises a single servo driving a string-and-pulley system, with multiple routing configurations enabling morphological adaptation for gap traversal or grasping.

Experimental results show stable flight through gaps only $0.7\times$ the drone’s nominal width, with an energy efficiency decline commensurate with propeller overlap ($d/D_p$), but manageable via non-diagonal routing. The airframe's softness also enables passive compression in direct collisions, facilitating high-speed passage through tight apertures.

Figure 2: FlexiQuad frame undergoes controlled and passive compressions, with analytical scaling laws predicting required forces and energy loss versus squeeze geometry.

Collision Resilience: Absorption and Recovery

FlexiQuad’s collision resilience stems from its elastic deformation and mass distribution. Through FEA and comprehensive drop tests, the frame demonstrates an order-of-magnitude extension of impact time and fourfold reduction in peak acceleration at sensitive electronics relative to rigid quadrotors. The decentralised payload prevents damaging stress concentrations, and the anisotropic frame ensures that impact forces are distributed and dissipated efficiently.

Peak decelerations in frontal collisions are limited to $<25 \mathrm{~g}$ at $3 \mathrm{~m/s}$, and glancing impacts transmit up to $39\times$ lower loads, mitigating instabilities and reducing the probability of mission failure due to immediate mechanical damage or loss of control authority. Passive compliance actively dampens destabilising moments, an emergent form of mechanical intelligence producing robust post-collision control behavior.

Figure 3: FE simulation and experimental validation illustrate multi-phase impact absorption, with drastic reduction in acceleration and force peaks for FlexiQuad.

Agility and Flight Performance

Despite a three-order magnitude decrease in airframe stiffness, FlexiQuad achieves high thrust-to-weight ratio ($\mathrm{TWR} \ge 4.5$) and matches the linear and angular accelerations of rigid counterparts—exceeding $3 \mathrm{~g}$ and $300 \mathrm{~rad/s^2}$, respectively, with vertical and horizontal speeds surpassing $80 \mathrm{~km/h}$. The bioinspired combination of frame anisotropy and decentralised mass suppresses unwanted flexural oscillations and preserves control bandwidth.

Critical to maintaining agility, energy storage and propulsion units are distributed axially under each rotor, which avoids large, frame-distorting moments. Comparative experiments and simulation with centralised battery configurations demonstrate an $8-13\times$ increase in oscillatory disturbances and overlap with maneuver bandwidth, underlying the necessity for bioinspired distributed mass for agile control in soft robots.

Figure 4: FlexiQuad maintains agile maneuvers in broad ($M$, $k$) configuration space, with experimental evidence for high acceleration, roll rates, and suppression of unwanted oscillations.

Design Space and Performance Regimes

The exhaustive parametric sweep—validated both analytically and numerically—delineates optimal stiffness and mass subspaces where squeezability, resilience, and agility are simultaneously achievable. This regime overlaps with values measured in bird and insect wings, and is well separated from conventional quadrotors. Outside this interval, stiff designs lose collision resilience and squeezability, while excessively soft configurations suffer inter-propeller contact and agility loss.

Figure 5: FlexiQuad’s stiffness-mass subspace for joint optimization, contrasted with biological and rigid machines, shows design trade-offs and optimal regions.

Experimental Realization and Validation

The prototype FlexiQuad employs glass-fibre composite strips, modular 3D-printed actuation units, and parallelised battery sets. Servomotor-driven active squeezing, motion-capture validation of dynamic maneuvers, and collision drop tests corroborate simulation and analytical predictions. The FE models used for impact and maneuver studies are validated to within $1-3$ standard deviations of measurement (see Figures 10, 12), supporting the applicability of these models for future design and scaling analyses.

Figure 6: Modular construction, decentralised energy components, and integrated active squeeze hardware in the FlexiQuad prototype.

Figure 7: Bench-top constrained acceleration tests validate FE models under high-throttle and gravity conditions against full-scale measurements.

Implications and Future Directions

FlexiQuad demonstrates that radically softer aerial robots need not sacrifice agility. The convergence of morphing ability, collision resilience, and maneuverability by exploiting bioinspired anisotropy and distributed mass substantially expands the operational envelope for autonomous drones in cluttered, dynamic environments. These results establish a fundamental design transition point—where control, sensing, and morphology must be co-optimised for robust autonomy. Achieving real-time morphology-aware control, integrating proprioceptive sensors for frame deformation, and leveraging bio-inspired evolutionary algorithms for "body-brain" optimization are identified as vital future targets.

From an application standpoint, soft quadrotors like FlexiQuad offer direct benefits for infrastructure inspection, autonomous search in confined or disaster-zone settings, and interactive tasks demanding both agility and mechanical resilience—outperforming conventional rigid drones in these contexts.

Conclusion

This work presents a comprehensive framework for the design, modeling, and validation of bioinspired soft quadrotors capable of agile flight, acute morphing for size reduction, and enhanced collision resilience, all within a stiffness regime matching that of biological flyers. The integration of functional anisotropy and distributed mass enables breaking conventional trade-offs and sets the ground for the emergence of morphology-adaptive aerial robotics. The systematic validation across modeling, simulation, and experiment provides a robust foundation for further advances in soft aerial machines and for embedding mechanical intelligence within autonomous mobile robots.