CBF-Based Control Allocation for Omnidirectional Tiltrotor Aerial Robots

Seobeom Lee; Hyondong Oh

cs.ROOct 15, 2026

CBF-Based Control Allocation for Omnidirectional Tiltrotor Aerial Robots

Authors: Seobeom Lee, Hyondong Oh

Organizations: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea

Abstract

Actively tilting aerial robots can generate six-dimensional wrenches, but slow servo response can make a desired wrench infeasible during reconfiguration. This paper develops a control barrier function (CBF) allocator that preserves wrench feasibility under bounded servo-configuration mismatch. An exact equivalent-wrench identity connects the thrust required at nominal and actual configurations. For a nonsingular six-channel allocation map, inverse allocation reduces robust wrench containment to twelve thrust margins tightened by an ellipsoidal reserve. Their complete derivatives yield a six-variable servo-rate quadratic program, followed by differential thrust allocation for tracking. A conditional forward-invariance result establishes actual-configuration feasibility under reserve coverage, feasible initialization, and admissible CBF inputs. A complementary MuJoCo study evaluates a measured-angle implementation against geometric, augmented differential, and normalized differential allocation in circular and cartwheel maneuvers, with and without disturbances. The proposed implementation achieves lower position error in all four recorded scenarios, with an attitude tradeoff in circular tracking. During the disturbed cartwheel, the desired wrench is feasible at all 1751 stored samples of continuous rotation; baseline violation rates range from 60.8% to 100%. These comparisons evaluate sampled feasibility; validation of the nominal-trajectory certificate requires nominal-state and reserve-coverage records.

Figures & tables

Method	Allocation mechanism	Constraint or feasibility property
GA [ 8 ]	Virtual-force inversion; thrust and tilt setpoint recovery	Selects an endpoint without constraining the wrench set along the servo transient.
DA [ 7 ]	Weighted inverse with secondary null-space motion	Matches a differential wrench-rate target; imposes no explicit thrust-margin constraint.
ADA [ 10 ]	Wrench-error feedback as the differential target	Uses actuator-state feedback for tracking; adds no wrench-containment constraint.
NDA [ 10 ]	Rate normalization, common scaling, and first-order setpoints	Enforces the modeled rate box; scaling may sacrifice exact wrench-rate tracking.
PDA [ 10 ]	Propulsion-dependent acceleration bounds	Incorporates speed-dependent power and acceleration limits; excluded from this benchmark.
Proposed CBF-based CA	Servo-rate QP ( 35 ) and differential thrust tracking	Preserves $w_{d}+\mathcal{E}_{w}\subseteq\mathcal{W}(\alpha_{n})$ ; Theorem 1 transfers its margins to the actual required thrust.

TABLE I: Allocation methods and the scope of their constraints

Panel of Figure 2 — Fig. 1: Proposed CBF-based CA. The servo QP controls feasibility through the nominal trajectory $\alpha_{n}$ ; the thrust QP uses actual actuator feedback for tracking. Solid arrows denote commands and dashed arrows measured or estimated feedback. The derivative $\dot{w}_{d}$ enters the barrier constraints, while $v_{w}$ is formed from ( 14 ).

Fig. 2: Two-dimensional illustration of the exact reduction. (a) The neighborhood

w_{d}+\mathcal{E}_{w}

lies inside

\mathcal{W}(\alpha_{n})

; the support point satisfies

c_{i}^{\top}\delta_{i}^{\star}=\rho_{i}

. (b) Projection onto channel

i

gives

[f_{n,i}-\rho_{i},f_{n,i}+\rho_{i}]

. The remaining gaps to the thrust limits are

B_{i}^{-}

and

B_{i}^{+}

Panel of Figure 4 — Fig. 3: Recorded MuJoCo scenes for the measured-angle implementation of the proposed CBF-based CA. Scenario labels specify world-frame external forces. Orange arrows point toward the body and indicate the positive half-cycle schematically; their directions reverse when $\sin(2\pi t)<0$ .

Case	Reference motion	World-frame force
S1	Circle: $r=1.5$ m, $T_{c}=3.0$ s	None
S2	Same circle	$[5,-3,4]^{\top}\sin(2\pi t)$ N
S3	Cartwheel: $90^{\circ}$ pitch, then $2.1$ rad/s body yaw	None
S4	Same cartwheel	$[6,0,0]^{\top}\sin(2\pi t)$ N

TABLE II: Recorded simulation scenarios

Quantity	Recorded value
Actuator groups	6 tilt joints, 12 propellers
Thrust-command limits	$0$ – $8$ N per propeller; $0$ – $16$ N per pair
Attitude gains	$K_{R}=\operatorname{diag}(10,10,6)$ ; $K_{\Omega}=\operatorname{diag}(2.8,2.8,1.8)$ ; integral gain zero
NRIC gain settings	$(k_{p},k_{d},k_{i})=(300,30,3)$
NRIC filter time constant	$0.10$ s
Run length / logging interval	$20$ s / $8$ ms (2500 samples)

TABLE III: Common settings preserved in the run records

Position RMSE $E_{p}$ (m)
Case	GA	ADA	NDA	Proposed CBF-based CA
S1	0.081	0.028	0.023	0.006
S2	30.474	0.057	0.054	0.026
S3	8.601	0.070	0.084	0.025
S4	16.024	1.045	0.786	0.028
Attitude RMSE $E_{R}$ ( ∘ )

TABLE IV: Tracking performance across the four scenarios

Fig. 4: Disturbed cartwheel (S4). (a) Original video frames at the displayed time $7.02$ s, including the measured-angle implementation of the proposed CBF-based CA. The legend identifies the native force-space objects; the red neighborhood is not a certificate of the prescribed $\mathcal{E}_{w}$ . (b) Full six-dimensional margin ( 48 ) over continuous rotation: nonnegative values indicate feasibility. The vertical dashed line marks the displayed frame time. All samples in this interval are plotted without smoothing on a symmetric-log scale.

Aerial Robotics

Aerial robotics studies the design, perception, control, and coordination of flying robots for navigation, inspection, transport, and physical interaction.

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Sep 18, 2026J/K move · Enter open · S save

Tilt as a Certified Resource: Preserving Motor Wrench-Rate Authority on Articulated Multirotors

Giuseppe Silano, Martin Saska

Department of Power Generation Technologies and Materials, Ricerca sul Sistema Energetico (RSE) S.p.A., 20134 Milan, Italy · Department of Cybernetics, Czech Technical University in Prague, 12135 Prague, Czech Republic

Quadrotor Control Robot Morphology-Control Co-Design

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Fully-actuated multirotor aerial vehicles must not only track nominal wrenches but retain the "readiness" to modulate them rapidly under disturbances. Classical effort-minimizing allocators ignore this dynamic limit, whereas maximizing readiness leads to topologically disconnected optimal sheets demanding physically impossible actuator rates. Enforcing a readiness safety floor on fixed-geometry symmetric platforms further encounters a zero-sum degeneracy: motor-speed redistribution cannot improve authority without conceding wrench tracking. This paper uses active morphology to break the degeneracy, treating servo tilt as a geometric resource supplying authority-recovery directions unavailable to static rotors. We construct a configuration-dependent, motor-only readiness certificate - the log-volume of the reachable wrench-rate set - that explicitly excludes servo capacity, preventing a "ghost capacity fallacy" in which the certificate would falsely credit slow mechanical kinematic limits instead of collapsing accurately at motor saturation. The certificate is enforced as a Control Barrier Function (CBF) within a Unified Physical-Command Quadratic Program acting on motor torques and servo setpoints. Closed-loop simulations of an articulated octorotor under severe gust disturbances show classical allocators diverging and uncertified articulated allocators violating the safety floor, while the proposed CBF filter bounds the system state and preserves vehicle authority.

Abstract

Aerial Robotics

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