Delay-Certified Readiness Barriers for Overactuated Multirotor Allocation Without Lipschitz Constants

Giuseppe Silano

cs.RONov 2, 2026

Delay-Certified Readiness Barriers for Overactuated Multirotor Allocation Without Lipschitz Constants

Authors: Giuseppe Silano

Organizations: Department of Power Generation Technologies and Materials, Ricerca sul Sistema Energetico (RSE), 20134 Milan, Italy · Multi-robot Systems (MRS) group, Department of Cybernetics, Czech Technical University, 12135 Prague, Czech Republic

Abstract

Overactuated multirotors can produce the same wrench with many rotor-speed combinations, some of which leave the vehicle unable to change its wrench quickly, e.g., to reject a gust. Readiness barriers keep this ability, the readiness, above a floor, but only in continuous time; with sampled commands and varying speed-controller delays, the available robustness bound covers less than one millisecond. We remove this limit by exploiting the structure of the problem: each rotor responds monotonically and in closed form to its own torque, so the speeds reachable under uncertain switching times lie in a cheaply computed box, and the lowest readiness over that box sits at a corner known in advance. This yields a Lipschitz-free test that a command keeps the readiness above its floor until the next sample, plus a fallback torque that keeps the vehicle on a certified plan. In hexarotor simulations with 2--40~ms delays and $\pm2$ ~ms jitter, the filter never violated the floor. At $10\pm2$ ~ms, it matched a delay-compensating predictor within the design envelope and cost 2--30% more tracking error beyond it, where the predictor alone violated the floor in 2 to 16 of 16 missions.

Figures & tables

Panel of Figure 1 — Figure 1: Certificate of one rotor at step $k$ (illustrative timing). (a) Commands switch at unknown instants in the gray intervals; $\tau_{i}^{\pm}$ take the extreme command. (b) The envelopes $v_{i}^{\pm}$ and slice boxes $\mathcal{B}_{k,r}$ enclose every admissible trajectory; after $T_{k}$ the hold torque drives both toward $v_{i}^{\star}$ . (c) $\psi_{i}$ is unimodal, so its minimum over a box side is at an endpoint.

Panel of Figure 2 — Figure 2: Nominal-delay sweep at jitter $\pm 2$ ms ( $\Delta d=4$ ms), $\alpha=5$ , synchronous switching, five jitter realizations per point; $c=0.75$ , (a) $\beta=1.5$ , $\bar{\ell}=-11.061$ , (b), (c) $\beta=2$ , $\bar{\ell}=-11.076$ . Pred-Lip-Loc was not run in this sweep. (a), (b): worst $\min_{t}h$ over the realizations (below zero: floor violated); (c): median RMS wrench error. Algorithm 1 stays above the floor at every delay, while the RB filter and SD-Lip fail at long delays; in (a), Algorithm 1 and Pred coincide.

	$\alpha=5$				$\alpha=20$
Filter	viol.	$h_{\min}$	$e_{w}$	act.	viol.	$h_{\min}$	$e_{w}$	act.
certifiable missions (34)
RB filter	0	$+0.014$	2.35 (3.05)	0	3	$\mathbf{-0.035}$	2.72 (3.36)	0
Pred	0	$+0.098$	1.00 (1.00)	0	0	$+0.013$	1.00 (1.00)	0
Pred-Lip	0	$+0.408$	7.70 (12.29)	0	0	$+0.135$	1.00 (1.46)	0
Pred-Lip-Loc	0	$+0.204$	1.21 (2.77)	0	0	$+0.058$	1.00 (1.00)	0

Table I : Monte Carlo missions at

10\pm 2

ms. Viol.: missions with

\min_{t}h<0

(bold);

h_{\min}

: worst

\min_{t}h

;

e_{w}

: median (90th percentile) over missions of the RMS wrench error relative to Pred, whose absolute median (sweet-spot collective

=2

) is 0.0023, 0.0022 (certifiable) and 0.0257, 0.0202 (readiness-priority) at

\alpha=5

, 20; act.: % of steps with active fallback (Algorithm 1) or infeasible barrier row (Lipschitz baselines). Algorithm 1 never violates and matches Pred on certifiable missions; beyond the envelope, Pred violates and the Lipschitz margins are safe but, except Pred-Lip-Loc at

\alpha=20

, costlier.

Filter	viol.	$h_{\min}$	$h^{\mathrm{true}}_{\min}$	$e_{w}$	act.	unc.
certifiable missions (34)
Pred	0	$+0.090$	$\mathbf{-0.018}$	1.00 (1.00)	0	–
Pred-Lip	0	$+0.399$	$+0.224$	3.61 (6.15)	0	–
Alg. 1	0	$+0.124$	$\mathbf{-0.004}$	1.00 (1.13)	1.8	6 (0.1)
Alg. 1-R	0	$+0.147$	$+0.026$	1.00 (1.27)	3.3	8 (0.1)
readiness-priority missions (16)

Table II : As Table I with

\pm 10\%

drag mismatch and

0.5\%

speed error,

\alpha=5

h^{\mathrm{true}}_{\min}

: with the plant drag; unc.: runs (% of steps) with a failed fresh hold check. Absolute

e_{w}

of Pred: 0.0062, 0.0266. Only Algorithm 1-R keeps the true-plant readiness above the floor.

Robust Control

Robust control designs feedback that maintains stability, safety, and performance despite disturbances, uncertainty, model errors, and changing conditions.

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Aug 17, 2026J/K move · Enter open · S save

Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation

Giuseppe Silano

Ricerca sul Sistema Energetico, Milan, Italy, and Czech Technical University, Prague, Czech Republic

Control Barrier Functions Quadrotor Control Robust Control

Open paper AskPDF arXiv

Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as

\ln(n/(n{-}m))

for symmetric designs. An explicit alignment ratio states when tracking can stay exact, otherwise the wrench error is bounded by

\mathcal{O}(ρ^{-1/2})

, and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision. Over

300

randomized missions, greedy maximization violates the certified floor in up to

51\%

of authority-scarce missions, while the proposed filter never leaves the certified set and, in the hardest moment reversal, commits a

79\times

smaller wrench error. The robust variant holds the floor on all

150

perturbed plants. A high-fidelity simulation with measured propeller and motor data shows that the floor holds under unmodeled aerodynamics, electrical limits, and delay, and where it stops applying.

Abstract

Robust Control

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