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Exploiting UAV Attitude for Covert Communications: Dynamics-Consistent Trajectory-Attitude Co-Design

Jinpeng Xu, Lin Zhou, Xin Xie, Mengyuan Zhang, Jingjing Wang

arXiv:2610.01307v1cs.ITmath.IT

TL;DR

Point-mass trajectory designs overlook how UAV maneuvers affect antenna orientation, leaving the attitude-dependent channels unmodeled. The paper co-designs trajectory and attitude for rotary-wing UAV covert communication and extends the approach to bounded attitude-control errors. Simulations report higher covert rates than point-mass designs, while the robust designs trade some performance for error protection.

  • Problem

    Point-mass UAV trajectory designs neglect the coupling between maneuvers, attitude, and antenna orientation, which can overestimate covert communication performance.

    Source: §I · p. 1

  • Method

    The paper models acceleration-induced attitude and its effect on directional channel gains, then develops MM-based trajectory-attitude optimization and a robust extension for bounded attitude errors.

    Source: A. Dynamics-Consistent Attitude Model · p. 4, §VII · p. 12

  • Results

    Algorithm 1 achieves the highest average covert rate, while the robust design sacrifices some performance for attitude-control error protection and the point-mass design converges faster but reaches a lower rate.

    Source: §VI · p. 11

  • Takeaways & Limitations

    The proposed co-design can exploit acceleration-induced attitude to enhance Bob’s link while limiting power received at Willie, and robust designs still outperform the Point-mass Actual-Attitude benchmark.

    Source: §VI · p. 12

    The study assumes perfect CSI, despite considering bounded attitude-control errors.

    Source: §VII · p. 13

Abstract

from arXiv · show

Existing trajectory designs for covert communications with uncrewed aerial vehicles (UAVs) typically rely on point-mass kinematics, which overlook the inherent coupling between flight maneuvers and antenna orientation. Motivated by recent studies linking UAV acceleration to attitude, we investigate dynamics-consistent trajectory and attitude co-design for rotary-wing UAV covert communications. We consider a UAV equipped with a directional antenna transmitting confidential information to a legitimate ground receiver in the presence of a warden. The acceleration-induced reduced attitude of the UAV is explicitly modeled together with its impact on the attitude-dependent directional channel gain. To ensure covertness, we derive a per-slot constraint based on the Kullback--Leibler (KL) divergence at the warden. We then formulate a joint trajectory and attitude optimization problem to maximize the average achievable covert rate subject to covertness, motion, thrust-magnitude, attitude-smoothness, and acceleration-domain safety constraints induced by roll and pitch limits. The resulting problem is non-convex because the channel gains depend jointly on position, acceleration, and attitude. To solve it, we develop a minorization--maximization (MM)-based algorithm that constructs a concave lower bound on the transmission rate and a convex upper bound on the covert constraint at each iteration. We further extend the framework to imperfect attitude control and develop a robust design against attitude tracking errors caused by actuator limitations, sensor noise, and control delays. Numerical results demonstrate the effectiveness of the proposed dynamics-consistent design and highlight the benefit of jointly optimizing UAV trajectory and attitude for covert communications.

I. INTRODUCTION

Point-mass trajectory designs overlook how UAV maneuvers change attitude and antenna orientation, potentially overestimating covert performance. This paper proposes dynamics-consistent trajectory-attitude co-design for rotary-wing UAVs and describes a system in which the UAV serves Bob while Willie attempts to detect its transmission.

I. INTRODUCTION

  • Point-mass designs can overestimate achievable covert performance because they neglect the coupling between UAV maneuvers, attitude, antenna orientation, and channel gains.Acceleration-induced attitude changes can affect both the legitimate link and the warden’s received power.Source: §I · p. 1

A. Related Studies

  • Prior covert-UAV studies optimize mobility and related resources, but generally use point-mass models that omit acceleration-induced attitude effects.Attitude-aware UAV communication had been studied for secrecy, but its impact on covert detection and performance remained unexplored.Source: A. Related Studies · pp. 2–3

B. Main Contributions

  • The proposed framework models acceleration-induced attitude and directional antenna gains, then uses MM-based optimization and a robust extension for bounded attitude-tracking errors.The formulation includes covertness, kinematic, thrust, attitude-smoothness, and acceleration-domain safety constraints.Source: B. Main Contributions · p. 3

II. SYSTEM MODEL

  • The system model considers a rotary-wing UAV transmitting confidential information to ground receiver Bob while warden Willie attempts to detect the transmission.The UAV operates in 3D, maintains a minimum altitude, and must travel between prescribed initial and final locations during a discretized mission.Source: §II · p. 3

A. Dynamics-Consistent Attitude Model

The UAV’s required acceleration determines its reduced attitude, which in turn sets the downward-facing antenna’s boresight. The channel model incorporates this attitude dependence into the directional LoS gain.

A. Dynamics-Consistent Attitude Model

  • The body vertical axis, or reduced attitude, is uniquely determined by translational acceleration, so antenna orientation is adjusted indirectly through UAV maneuvers.The directional antenna is mounted downward, with boresight −ω[n].Source: A. Dynamics-Consistent Attitude Model · p. 4
  • For physically realizable flight, acceleration is constrained by conservative safety inequalities representing allowable airframe angular limits.Yaw is prescribed by a high-level guidance module rather than optimized explicitly.Source: A. Dynamics-Consistent Attitude Model · p. 4

B. Dynamics-Consistent Rician Channel Model

1) Attitude-Dependent LoS Gain:

  • The LoS gain uses a peak-normalized directional antenna pattern, with gain equal to 1 at zero off-boresight angle.The pattern is parameterized by its half-power beamwidth and maximum side-lobe attenuation.Source: 1) Attitude-Dependent LoS Gain · p. 4

2) Averaged NLoS Gain:

The channel model treats NLoS propagation as averaged power from scattering sub-paths and models the received signals used for Bob’s rate and Willie’s detection.

2) Averaged NLoS Gain:

  • NLoS propagation is modeled using scattering clusters and unresolved sub-paths whose transmit- and receive-side off-axis angles depend on scatterer geometry.The angular-scattering power contribution uses normalized reflection or scattering coefficients and the antenna pattern.Source: 2) Averaged NLoS Gain · p. 5
  • Independent sub-path phases or delay-resolvable paths make cross terms vanish after ensemble averaging, yielding averaged NLoS power.The effective NLoS gain represents the variance, equivalently the averaged power, of the aggregate NLoS component.Source: 2) Averaged NLoS Gain · p. 5

3) Received Signals at Bob and Willie:

  • Bob’s received signal supports the achievable-rate model, while Willie tests whether the UAV is transmitting under silent and transmitting hypotheses.The received-signal models are used to characterize Willie’s detection performance and derive the covert communication constraint.Source: 3) Received Signals at Bob and Willie · p. 5

III. ANALYSIS OF THE COVERTNESS MEASURE

The analysis models Willie’s per-slot detection as a binary test and uses KL divergence to measure distinguishability. In the low-SNR regime, a conservative upper bound yields a stricter covertness constraint.

III. ANALYSIS OF THE COVERTNESS MEASURE

  • Willie tests whether the UAV is transmitting from a length-L observation sequence, with H0 and H1 denoting the silent and transmitting cases.The observations are assumed independent and identically distributed, with zero-mean complex Gaussian distributions under both hypotheses.Source: §III · pp. 5–6
  • The per-slot KL divergence measures distinguishability between the hypotheses and is derived using its additivity across observations.The analysis adopts KL divergence as the covertness metric at Willie.Source: §III · pp. 5–6
  • When Willie’s received SNR is much less than 1, the per-slot KL divergence is conservatively upper-bounded in the low-SNR regime.The approximation uses Taylor expansions.Source: §III · p. 6
  • For finite but small γw[n], the quadratic approximation upper-bounds the exact KL divergence, making the covert constraint stricter at some performance cost.The approximation is asymptotically exact as γw[n] approaches zero.Source: §III · p. 6

IV. PROBLEM FORMULATION AND SOLUTIONS

The problem jointly optimizes UAV trajectory and attitude to maximize covert transmission rate while meeting covertness and flight constraints. Coupled channel and attitude dependencies make the problem non-convex, motivating an iterative MM solution.

A. Problem Formulation

  • The proposed objective is to maximize the covert transmission rate to Bob while satisfying covertness at Willie and physical flight constraints.The design jointly optimizes UAV trajectory and attitude.Source: A. Problem Formulation · p. 6
  • The formulation fixes the UAV’s initial and final positions and imposes discrete-time kinematics, velocity, acceleration, and minimum-altitude requirements.These are specified by constraints (40b)–(40f).Source: A. Problem Formulation · p. 6
  • Covertness is enforced at Willie, while acceleration-attitude coupling and maximum thrust constrain the maneuver.These requirements are represented by constraints (40h)–(40j).Source: A. Problem Formulation · p. 6
  • Unit-norm and inter-slot smoothness requirements constrain the UAV attitude.They are represented by constraints (40k) and (40l).Source: A. Problem Formulation · p. 6
  • Acceleration-domain safety constraints encode the roll and pitch angle limits.These requirements are represented by constraints (40m)–(40p).Source: A. Problem Formulation · p. 6
  • The problem is non-convex because channel gains depend jointly on position and attitude, while attitude is coupled to acceleration.Unit-norm and attitude-smoothness constraints also produce a non-convex feasible set.Source: A. Problem Formulation · p. 7

IV. PROBLEM FORMULATION AND SOLUTIONS

  • The coupled non-convex objective, covertness constraint, and feasible set motivate an MM-based iterative reformulation.The framework is developed to obtain a locally optimal solution.Source: §IV · p. 6, A. Problem Formulation · p. 7

B. Proposed Solution

The proposed MM algorithm eliminates attitude through the acceleration–attitude mapping, then uses local bounds to solve the resulting non-convex trajectory and attitude design. The reformulation yields channel gains dependent on position and acceleration.

B. Proposed Solution

  • The MM algorithm eliminates attitude, minorizes the average covert rate, upper-bounds covert and angular-smoothness constraints, and solves trust-region convex subproblems until convergence.Its lower- and upper-bound constructions preserve feasibility and guarantee monotonic objective improvement.Source: B. Proposed Solution · p. 7

1) Attitude Elimination and Reduced Channel Reformulation:

2) Minorizing the Achievable-Rate Objective:

The method constructs a local concave lower bound for the achievable-rate objective and a conservative convex upper bound for the covert constraint, enabling MM updates within a trust region.

2) Minorizing the Achievable-Rate Objective:

3) Majorizing the Covert Constraint:

  • Because the covert metric is non-convex, the method constructs a convex local upper bound within a trust region and conservatively enforces the covert constraint.Local curvature parameters are selected so the upper bound holds throughout the trust region.Source: 3) Majorizing the Covert Constraint · pp. 7–8

4) Local Convexification of the Angular Smoothness Constraint:

The algorithm locally convexifies angular smoothness and solves a trust-region convex approximation of the original problem. Its per-slot surrogate construction scales linearly with the number of time slots, while the convex solve is the main computational cost.

4) Local Convexification of the Angular Smoothness Constraint:

  • A convex local upper bound conservatively enforces the angular-smoothness constraint within the trust region.The bound is constructed from the original angular-smoothness function at the current iteration.Source: 4) Local Convexification of the… · p. 8

5) MM-Based Convex Approximation of Problem (P1):

  • Trust-region constraints support the MM convex approximation, whose concave objective and convex constraints make it solvable by standard CVX solvers.The section identifies the resulting subproblem as a convex optimization problem.Source: 5) MM-Based Convex Approximation of… · p. 8

C. Algorithm Summary and Complexity Analysis

  • Per-slot evaluations of reduced attitudes, channel gains, and surrogate gradients have O(N) complexity, while solving the convex approximation is the main computational cost.The approximation has approximately 9N real-valued variables, and its equality, affine-inequality, and second-order-cone constraint counts scale linearly with N.Source: C. Algorithm Summary and Complexity… · p. 8
  • Algorithm 1 repeats surrogate construction and convex-subproblem solves, updates position, velocity, and acceleration, and returns the converged solution.The procedure starts from a feasible initialization and stops upon convergence.Source: C. Algorithm Summary and Complexity… · p. 8

V. ROBUST DESIGN WITH IMPERFECT ATTITUDE CONTROL

The robust extension models attitude-control error as a perturbation of the nominal reduced attitude and designs against worst-case perturbations. It accounts for how attitude error changes channel gains and enforces covertness under the uncertainty set.

V. ROBUST DESIGN WITH IMPERFECT ATTITUDE CONTROL

  • The robust model represents the actual reduced attitude as a perturbed nominal attitude, with the perturbation constrained to the nominal attitude’s tangent space.The actual body vertical axis is denoted separately from the nominal attitude.Source: §V · p. 8, A. System Model Under Imperfect… · p. 8

A. System Model Under Imperfect Attitude Control

  • The actual body vertical axis may deviate from the nominal reduced attitude because of tracking errors, actuator imperfections, and sensing inaccuracies.The attitude-control error is restricted to the nominal attitude’s tangent space.Source: A. System Model Under Imperfect… · p. 8
  • Attitude perturbations affect the transmitter-side off-axis angle, while the receiver-side angle remains fixed by UAV-node geometry and ground-antenna orientation.The averaged NLoS gain is modeled as a distance-dependent residual scattering term and is not directly affected by attitude perturbation.Source: A. System Model Under Imperfect… · p. 8
  • The design uses worst-case Rician-averaged gains and imposes a per-slot covert constraint that holds under the worst-case attitude perturbation in the uncertainty set.The exact attitude-control error realization is unknown.Source: A. System Model Under Imperfect… · p. 9

B. Robust Problem Formulation

The robust problem is non-convex because its worst-case rate, covert constraint, angular smoothness, and coupled position–acceleration channel gains are non-convex. The MM solution uses local bounds within trust regions to produce convex approximations.

B. Robust Problem Formulation

  • P2 is non-convex because its worst-case rate objective, robust covert constraint, and angular-smoothness constraint are non-convex in the coupled position and acceleration variables.Both robust channel metrics depend on position and acceleration through Rician-averaged gains and the acceleration-induced attitude mapping.Source: B. Robust Problem Formulation · p. 9

C. Robust MM-Based Solution

  • The method bounds attitude uncertainty through angular deviation, using perturbations in the nominal body axis’s tangent space with norm at most ε_ω.Directly optimizing over all attitude perturbations is described as generally intractable.Source: C. Robust MM-Based Solution · p. 9
  • The robust LoS model conservatively lower-bounds Bob’s gain and upper-bounds Willie’s gain.The antenna gain is non-increasing with off-boresight angle.Source: C. Robust MM-Based Solution · p. 9
  • The robust Rician-averaged gain bounds retain the averaged NLoS component, whose explicit attitude dependence is absorbed into a scenario-level coefficient.The lower bound is for Bob and the upper bound is for Willie.Source: C. Robust MM-Based Solution · p. 9
  • The robust gain bounds represent worst-case degradation of Bob’s effective channel and worst-case enhancement of Willie’s.These bounds inform the robust rate and covert metrics, respectively.Source: C. Robust MM-Based Solution · p. 9
  • At each iteration, MM constructs a concave local lower bound for the robust objective and a convex local upper bound for the robust covert metric within a trust region.The covert upper bound is selected to dominate the robust covert metric within that region.Source: C. Robust MM-Based Solution · p. 9
  • The algorithm initializes a feasible solution, solves successive robust convex approximations, and returns the iterates at convergence.The angular-smoothness and trust-region constraints are handled as in the nominal-attitude case.Source: C. Robust MM-Based Solution · pp. 9–10
  • With properly chosen curvature parameters, the robust MM approximation is convex and can be solved by standard convex solvers.The robust worst-case attitude-error formulation accounts for bounded perturbations but generally yields a more conservative trajectory than ideal-attitude design.Source: C. Robust MM-Based Solution · p. 10

D. Algorithm Summary and Complexity Analysis

The section evaluates the proposed dynamics-consistent designs against point-mass benchmarks, including their covert-rate performance, covertness estimates, and convergence. It also reports the algorithm’s computational complexity and the performance–robustness tradeoff under attitude-control errors.

D. Algorithm Summary and Complexity Analysis

  • At each robust MM iteration, gain and gradient evaluations scale as O(N), while solving the robust convex approximation problem has worst-case complexity on the order of O((9N)^3).The robust design has the same asymptotic complexity as the nominal case, with robust evaluations increasing only the per-iteration constant factor.Source: D. Algorithm Summary and Complexity… · p. 10

VI. NUMERICAL RESULTS

  • Within the enforced covert operating region, the quadratic KL approximation closely follows the exact divergence and slightly upper-bounds it, making the resulting covert constraint conservative.The passage characterizes the approximation error as small in that region.Source: §VI · pp. 10–11, Figure 3 · p. 11
  • All methods stabilize within a limited number of iterations; Algorithm 1 achieves the highest average covert rate, while robust Algorithm 2 trades some rate for attitude-error protection.The point-mass design converges faster because its structure is attitude-agnostic; with ϵω = 0.1, the robust design maintains a rate comparable to the point-mass model’s predicted performance.Source: §VI · p. 11, Figure 4 · p. 11
  • The perfect attitude-control design achieves the highest cumulative covert throughput, while robust designs slightly reduce throughput but outperform the Point-mass Actual-Attitude benchmark.The robust designs account for worst-case attitude deviations and retain antenna pointing that favors Bob while limiting power received at Willie.Source: §VI · pp. 11–12
  • The risk map marks the covert threshold at normalized Willie-side metric 1; co-design can pass near a high-risk region by steering the antenna away from Willie while maintaining a favorable link to Bob.A point-mass design with a downward-pointing antenna may violate the covert constraint above that region because it ignores attitude-dependent antenna reorientation.Source: Figure 5 · p. 11, §VI · p. 12, Figure 7 · p. 12
  • Re-evaluating a point-mass trajectory under its actual acceleration-induced attitude reveals a discrepancy in Willie-side covert risk; in the considered setup, actual attitude reduces the metric and creates additional covertness margin.The point-mass abstraction therefore does not accurately characterize Willie’s received power when maneuvers alter antenna orientation.Source: §VI · p. 12, Figure 8 · p. 12

VII. CONCLUSIONS

The proposed trajectory-attitude design achieves higher covert transmission rates than conventional point-mass designs, while explicitly modeling acceleration-induced attitude and its effect on directional channel gains. The study is limited to rotary-wing UAVs, a single-antenna model, and perfect CSI.

  • The proposed trajectory design achieves higher covert transmission rates than conventional impractical point-mass designs.Source: §VII · p. 12
  • The framework models acceleration-induced UAV attitude and directional channel gains, then maximizes covert rate under covertness, motion, thrust, attitude-smoothness, and safety constraints.Source: §VII · p. 12
  • An MM-based algorithm addresses the non-convex optimization, and a robust extension accounts for imperfect attitude control.Source: §VII · p. 12
  • The study focuses on rotary-wing UAVs; extending it to fixed-wing systems would require considering aerodynamic constraints, bank-angle dynamics, and minimum-speed requirements.Source: §VII · p. 12
  • The current model uses a single directional antenna; a MIMO extension would jointly optimize trajectory, attitude, and transmit beamforming.Source: §VII · pp. 12–13
  • Although bounded attitude-control errors are considered, the study assumes perfect CSI and identifies uncertain warden-channel or location information as a direction for more robust designs.Source: §VII · p. 13

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