Real-Time Bounded Catenary Solver for UAV Tether Modeling
Real-Time Bounded Catenary Solver for UAV Tether Modeling
This paper introduces a real-time bounded catenary solver for non-stationary tethered multirotor UAVs. By reformulating the inner solver to reduce the problem to a single transcendental equation with proven convergence properties, the authors achieve a mean solve time of 4.0 microseconds and a worst-case of 4.6 microseconds, representing a 68-fold speedup over previous optimized implementations while maintaining high accuracy (relative deviation of 8.7e-9). The method is validated on embedded platforms, including a Lua implementation running directly on ArduPilot flight controllers with a mean solve time of 0.74 ms.
Source: arXiv Robotics — research abstracts · Read original article ↗
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What the source reports
Publisher-reported claims, with original evidence. These results have not been independently verified by RoboSignal.
Reported numbers
mean solve time (previous method)
0.51
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arXiv:2609.18482v2 Announce Type: replace Abstract: For non-stationary tethered multirotor UAVs in real-world conditions, simulating the forces imposed on the drone by the aerodynamic drag of the tether becomes crucial, with online use cases placing a hard bound on the maximum solve time. In previous work, a quasi-analytical catenary tether model reached a mean solve time of 0.51 ms using a general-purpose root finde
Open source S2mean iteration count (proposed solver)
2.24
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o-regime initial guess which approximates the true root within 3.4 % and reduces the mean iteration count by 69.2 % to 2.24 compared to the textbook initialization. Building on the hybrid root-finding method rtsafe (Newton-Raphson with bisection fallback giving bounded iteration counts), we implement a specialized variant that exploits the problem structure to omit unnecessary checks while retaining correctness, whic
Open source S4mean solve time (Lua implementation)
0.74
View original evidence
carries over unchanged. We further demonstrate its suitability for embedded, resource-constrained platforms with a Lua implementation running directly in ArduPilot on a drone's flight controller, where it stays well inside the scheduling budget with a mean solve time of 0.74 ms.
Open source S6solve time (proposed solver average)
4
View original evidence
h gives up to 1.37 times speedup. With the proposed solver the full tether model achieves a nearly constant solve time of 4.0 us on average and 4.6 us at worst, a 68 times speedup over an optimized re-implementation of the previous method, while agreeing with it to a relative deviation of 8.7e-9. Because the reformulation leaves the underlying physical model untouched, the experimental validation of the previous work
Open source S5solve time (proposed solver worst-case)
4.6
View original evidence
h gives up to 1.37 times speedup. With the proposed solver the full tether model achieves a nearly constant solve time of 4.0 us on average and 4.6 us at worst, a 68 times speedup over an optimized re-implementation of the previous method, while agreeing with it to a relative deviation of 8.7e-9. Because the reformulation leaves the underlying physical model untouched, the experimental validation of the previous work
Open source S5
- paper: not_reported
Source excerpts and review record
Automatically extracted; no manual editorial approval recorded.
arXiv:2609.18482v2 Announce Type: replace Abstract: For non-stationary tethered multirotor UAVs in real-world conditions, simulating the forces imposed on the drone by the aerodynamic drag of the tether becomes crucial, with online use cases placing a hard bound on the maximum solve time. In previous work, a quasi-analytical catenary tether model reached a mean solve time of 0.51 ms using a general-purpose root finde
Open source S2
o-regime initial guess which approximates the true root within 3.4 % and reduces the mean iteration count by 69.2 % to 2.24 compared to the textbook initialization. Building on the hybrid root-finding method rtsafe (Newton-Raphson with bisection fallback giving bounded iteration counts), we implement a specialized variant that exploits the problem structure to omit unnecessary checks while retaining correctness, whic
Open source S4
carries over unchanged. We further demonstrate its suitability for embedded, resource-constrained platforms with a Lua implementation running directly in ArduPilot on a drone's flight controller, where it stays well inside the scheduling budget with a mean solve time of 0.74 ms.
Open source S6
h gives up to 1.37 times speedup. With the proposed solver the full tether model achieves a nearly constant solve time of 4.0 us on average and 4.6 us at worst, a 68 times speedup over an optimized re-implementation of the previous method, while agreeing with it to a relative deviation of 8.7e-9. Because the reformulation leaves the underlying physical model untouched, the experimental validation of the previous work
Open source S5
Source：arXiv Robotics — research abstracts · arxiv.org