Preserving Full 6-DOF Actuation Under Abrupt Total Rotor Failures: Passive Fault-Tolerant Flight Control Using a Biaxial-Tilt Hexacopter

Abstract: Conventional multirotors suffer from a rapid collapse of attainable wrench space (AWS) under abrupt total rotor failures, rendering full 6-DOF recovery physically impossible. This paper addresses passive fault-tolerant flight of a biaxial-tilt overactuated hexacopter (BTO) under abrupt total rotor failures that are a priori unknown to the controller. The control design and analysis focus on representative abrupt rotor-failure cases for which the post-failure system remains fully actuated, while no explicit fault detection, isolation, or fault-mode switching is assumed. First, we extend the inscribed-sphere metric of the AWS by incorporating the transient-wrench-jump term, enabling quantitative feasibility assessment under up to three simultaneous rotor failures and benchmarking against uniaxial-tilt and coplanar hexacopters. Second, we develop two computationally efficient passive schemes without relying on fault detection or online optimization. One scheme operates at the controller layer by combining a high-order fully actuated (HOFA) controller with a linear extended state observer (LESO) for lumped-disturbance rejection. The other scheme operates at the allocator layer by using model-reference adaptive control allocation with momentum-based wrench estimation to compensate for control-allocation biases. Simulations and flight experiments validate stable hovering and 6-DOF trajectory tracking under single and multiple rotor failures. Further systematic comparisons confirm that the BTO provides larger recovery margins than uniaxial-tilt and coplanar designs. Additional onboard-sensor-only experiments, including indoor tracking under wind disturbance, outdoor tracking under extreme conditions, narrow-frame traversal, and contact-based aerial writing, further validate the robustness of the proposed framework in complex operational environments.

• The paper introduces a biaxial-tilt hexacopter and AWS-based analysis showing it preserves full 6-DOF actuation after representative single-, double-, and triple-rotor failures, while coplanar designs lose torque authority.
• The paper compares controller-layer and allocator-layer passive fault-tolerant control, finding that adaptive allocation improves BTO position and attitude RMSE by 25.45% and 37.79% over disturbance rejection under mild faults.
• The paper experimentally demonstrates autonomous fault-tolerant flight, including outdoor Figure-8 tracking, confined traversal, and aerial writing, achieving 0.009 m position RMSE and 0.89° attitude RMSE despite wind and escalating rotor failures.

Motivation and problem statement

Abrupt total rotor failures—caused by blade fracture, motor seizure, or impact—introduce large impulsive wrench disturbances and severe aerodynamic asymmetry that conventional coplanar multirotors cannot absorb. Because each rotor produces only unidirectional thrust, the attainable wrench space (AWS) collapses rapidly under such failures, making full 6-DOF recovery physically impossible for coplanar designs regardless of actuator redundancy. The paper argues that this bottleneck is structural rather than control-related, and addresses it with a biaxial-tilt overactuated hexacopter (BTO): six tilting-rotor actuator units (TAUs), each with two orthogonal servo axes, providing full 3-DOF thrust vectoring per rotor.

Two design constraints shape the contribution. First, the framework must run in real time on a resource-constrained STM32H7 flight controller, ruling out MPC-based or optimization-driven fault-tolerant control (FTC). Second, failures are assumed abrupt and a priori unknown: no explicit fault detection, isolation, or mode switching is used anywhere in the pipeline. The analysis and design are restricted to representative failure cases for which the post-failure system remains fully actuated.

Attainable wrench space analysis

The authors extend an inscribed-sphere metric for the AWS by incorporating transient wrench jumps at the instant of failure. The AWS is decomposed into an attainable force space (AFS) and attainable torque space (ATS), each characterized as a convex hull over sampled wrench vectors subject to tilt-angle and thrust constraints ($\alpha_{c/\max}=\pi$, $\lambda_{c/\max}=\pi/12$, thrust capped at $0.8\times 20$ N). The inscribed-sphere radii $r_F$ and $r_T$ quantify post-failure controllability margins for three configurations: the coplanar hexacopter (CCU), uniaxial-tilt hexacopter (UTO), and BTO.

The quantitative comparison is stark:

Fault condition	$r_F$ BTO [N]	$r_F$ UTO [N]	$r_T$ BTO [N·m]	$r_T$ UTO [N·m]	CCU
Fault-free	63.92	55.17	8.42	8.17	0.42 / 0
Single rotor	33.46	31.24	4.36	4.14	0
Two rotors ($\overline{\Lambda}_{1,2}$)	32.36	26.08	2.91	2.78	0
Three rotors ($\lambda_{c/\max}=\pi/12$0)	15.92	14.78	1.41	1.40	0

The CCU retains nonzero torque authority only in the fault-free case; both tilted configurations remain fully actuated up to three simultaneous failures except for the degenerate case $\lambda_{c/\max}=\pi/12$1, where all margins vanish. On average, UTO's $\lambda_{c/\max}=\pi/12$2 and $\lambda_{c/\max}=\pi/12$3 fall below BTO's by 18.39% and 24.33%, respectively—an explicit quantification of the benefit of biaxial over uniaxial tilting. The analysis also shows that asymmetric fault patterns degrade the AWS more severely than symmetric ones: the symmetric two-rotor failure $\lambda_{c/\max}=\pi/12$4 reduces BTO's $\lambda_{c/\max}=\pi/12$5 by 91.56% and $\lambda_{c/\max}=\pi/12$6 by 92.09%. This asymmetry motivates the fault-severity indicator $\lambda_{c/\max}=\pi/12$7 used later to characterize which faults lie within the recoverable envelope.

Controller-layer passive FTC (CL-PFTC)

CL-PFTC treats rotor failures as lumped disturbances at the controller level. A high-order fully actuated (HOFA) baseline controller achieves 6-DOF trajectory tracking on the error dynamics, assuming the input matrix $\lambda_{c/\max}=\pi/12$8 has full row rank—which requires the attitude quaternion error scalar $\lambda_{c/\max}=\pi/12$9, i.e., attitude errors bounded away from $0.8\times 20$0. A linear extended state observer (LESO) estimates the lumped disturbance $0.8\times 20$1, which combines inertial uncertainty, gravity/rotational model errors, and the discontinuous wrench jump $0.8\times 20$2 induced by the unknown fault matrix $0.8\times 20$3.

Stability is established via a Lyapunov argument showing uniform ultimate boundedness of the tracking error within a generalized ellipsoid whose size scales with the disturbance estimation error bound $0.8\times 20$4. The authors state plainly that this guarantee rests on two conditions that severe faults can violate: near-nominal attitude (large transients may push $0.8\times 20$5 toward zero) and attainability of commanded wrenches (the finite AWS makes some commands unreachable). Control allocation uses a weighted pseudo-inverse plus a closed-form algorithm that exploits diagonal force-difference invariance to enforce the outer-servo maximum tilt constraint without online optimization; the paper acknowledges that this allocator can only fully handle the tilt constraint under fault-free conditions, so the practical effective AWS is smaller than the analyzed one.

Allocator-layer passive FTC (AL-PFTC)

AL-PFTC relocates fault accommodation from disturbance rejection to allocation-bias compensation. Abrupt total rotor failures are reformulated as unknown biases in the control-allocation matrix, and a virtual control-allocation system—a closed-loop reference model driven by the aerodynamic wrench error $0.8\times 20$6—is introduced. The desired allocation matrix $0.8\times 20$7 satisfies $0.8\times 20$8; its existence is assumed precisely for the fully actuated fault cases identified in the AWS analysis.

Three components complete the design. An element-wise error bound on $0.8\times 20$9 is derived from the AWS, conservatively approximated by the maximum inscribed cube under the most severe considered failure $r_F$0, then simplified to a hypercube. External wrench estimation uses a low-pass-filtered accelerometer-based force estimate and a momentum-based torque observer, so that $r_F$1 is a first-order filtered version of the true external wrench. The adaptive law $r_F$2 yields, via a Lyapunov argument, exponential convergence of the virtual allocation error to a bounded set, ensuring boundedness of the actual wrench error under fault conditions.

Simulation results

Simscape Multibody simulations compare BTO and UTO under identical controllers. With CL-PFTC and a single rotor failure at increasing hover roll angles, position RMSE improves from 0.0154 m (Roll = 0°) to 0.0095 m (Roll = 90°) for the BTO, while the CCU loses stability outright. Across the fault-tolerance capability study, CL-PFTC maintains stability for both platforms under mild faults but fails for $r_F$3 (UTO) and $r_F$4 (both); the BTO reduces average position RMSE by 25.93% and attitude RMSE by 24.31% relative to the UTO.

AL-PFTC extends the stable envelope: the BTO remains stable under every tested condition including $r_F$5, while the UTO still fails under $r_F$6 and $r_F$7. Relative to CL-PFTC on the BTO, AL-PFTC cuts position RMSE by 25.45% and attitude RMSE by 37.79% under mild faults, and uniquely sustains trajectory tracking under $r_F$8 (albeit with degraded attitude accuracy, RMSE$r_F$9 = 6.85°). These results establish AL-PFTC as the stronger scheme in both accuracy and fault envelope.

Experimental validation

All experiments run fully autonomously on onboard sensing: FAST-LIVO2 LiDAR-inertial-visual odometry at 10 Hz on an NX Upboard, with the control layer at 200 Hz and allocation at 800 Hz on the STM32H7. The UTO comparison platform is obtained by mechanically locking the outer servos, ensuring identical physical parameters.

Hovering: with AL-PFTC, both platforms hold stable hovering under all nine tested fault combinations at Roll = 0°. At Roll = 45°, only BTO$r_T$0 remains stable across all conditions; UTO$r_T$1 fails several cases (e.g., single-rotor $r_T$2), and both CL-PFTC variants lose stability under multiple moderate-to-severe faults. This confirms both the superiority of the biaxial configuration under non-zero attitudes and the inadequacy of controller-layer-only compensation when the AWS collapses.

Trajectory tracking: indoor tracking of an 80 s trajectory exciting both position and attitude dynamics, with a fault sequence spanning single, double, and triple failures and ~5 m/s wind, yields RMSE$r_T$3 = 0.0154 m and RMSE$r_T$4 = 1.87° for BTO$r_T$5 versus instability for UTO$r_T$6. Degradation relative to the fault-free baseline is modest (+0.0058 m, +1.05°), with peak errors below 0.1 m and 10°. An outdoor Figure-8 flight at approximately −20 °C with 3.4–5.4 m/s wind and escalating faults up to $r_T$7 achieves RMSE$r_T$8 = 0.009 m and RMSE$r_T$9 = 0.89°.

Flight tasks: a narrow-frame traversal (frame 1.0 m × 0.4 m, tilted 20°, vehicle 0.76 m × 0.26 m) under mid-flight fault injection achieves RMSE$r_F$0 = 0.017 m with attitude error reconverging below its RMSE within 1.9 s. A contact-based aerial writing task on a vertical wall under single-rotor failure—with unmeasured, time-varying contact friction and wall-proximity aerodynamics—achieves RMSE$r_F$1 = 0.0037 m, Hausdorff distance 0.0711 m, and HD$r_F$2 = 0.0420 m, indicating centimeter-level average accuracy with bounded worst-case deviation dominated by fault-injection transients.

Limitations and open questions

Several restrictions are conceded explicitly. The entire framework applies only to fault cases preserving full actuation; the triple-failure case $r_F$3 destabilizes even the BTO in simulation, and $r_F$4 eliminates all wrench margin, so behavior outside the fully actuated envelope is untreated. The HOFA stability proof assumes $r_F$5 and attainable wrench commands, conditions that severe transients can violate; the paper notes that a more detailed analysis is needed for full guarantees. The adaptive-law error bound is conservative (inscribed-cube approximation of the AWS), and the hypercube simplification trades robustness against fault-tolerance performance through a tuning constant. The MATC-handling algorithm guarantees constraint satisfaction only under fault-free conditions. Finally, the aerial writing task uses a compliant sponge tool without force sensing, leaving contact-force regulation during interaction under faults as an open question, and the conclusion identifies real-time onboard perception for dynamic environments as future work.

Conclusion

This work couples a quantitative AWS-based feasibility analysis with two computationally lightweight passive FTC schemes for a biaxial-tilt hexacopter facing abrupt, undetected total rotor failures. The structural analysis shows the BTO dominates the uniaxial and coplanar alternatives in post-failure wrench margins, and the experimental campaign—spanning tilted hovering under triple failures, outdoor sub-zero flight, confined-space traversal, and contact-based writing—demonstrates that allocator-layer adaptive allocation (AL-PFTC) recovers full 6-DOF controllability where controller-layer disturbance rejection alone does not. The combination of reconfigurable actuation and passive, optimization-free FTC offers a validated path to retaining full-pose authority under failures that would be unrecoverable for conventional multirotors.