Joint Trajectory, Sensing, and Computation Co-Design for UAV-Assisted Federated Edge Vision

arXiv:2611.00790v1 [cs.NI] 31 Oct 2026

Joint Trajectory, Sensing, and Computation Co-Design for UAV-Assisted Federated Edge Vision Kaichen Liu, Yueling Che, Sheng Luo

Jianhua Tang

College of Computer Science and Software Engineering Shenzhen University, Shenzhen, China 2400101033@mails.szu.edu.cn; {yuelingche, sluo}@szu.edu.cn

Shenzhen Smart City Technology Development Group Company, Ltd., Shenzhen, China jtang4@e.ntu.edu.sg

Abstract—This paper investigates UAV-assisted federated edge vision for training computationally heavy object detection models. Existing studies treat training data as static, ignoring the tight coupling between dynamic visual sensing and massive inplace computational burdens. To minimize the expected training time under battery constraints, we propose a four-phase joint trajectory, sensing, and computation co-design. To mitigate data heterogeneity, we use a uniform sensing probability to translate federated convergence requirements into UAV mobility constraints. Furthermore, a two-layer alternating optimization (AO) algorithm is developed to adaptively determine the local data workload, optimally balancing the required training rounds against in-place computation delays. Simulations validate the superiority of our approach in model convergence and accuracy over baselines. Index Terms—Unmanned aerial vehicles (UAV), federated edge learning (FEEL), mobile visual sensing, trajectory optimization, resource allocation.

I. I NTRODUCTION

U

NMANNED aerial vehicles (UAVs) equipped with highresolution cameras are emerging as ubiquitous platforms for industrial infrastructure inspection [1]. This naturally drives the evolution of UAV-assisted federated edge learning (FEEL) toward federated edge vision, a paradigm that collaboratively trains computationally heavy object detection models (e.g., YOLO11x) across distributed UAVs without sharing raw images [2]. However, unlike conventional federated learning with static datasets, the data acquisition in mobile vision is an active sensing process. The UAVs’ trajectories directly dictate the visual sensing quality and data volumes, which in turn determine the local computation workload and the ultimate learning convergence. Hence, isolated optimizations are inherently suboptimal, necessitating a rigorous joint trajectory, sensing, and computation co-design to minimize the total training time under stringent battery constraints. Existing studies on UAV-assisted FEEL largely take the training data as given. They primarily focus on embedding FEEL into UAV networks for communication efficiency and privacy (e.g., [3], [4]), or integrating UAV trajectory and resource scheduling into the FEEL process to accelerate model convergence (e.g., [5]–[7]). To explicitly model the data acquisition phase, recent advancements have introduced Integrated Sensing, Communication, and Computation (ISCC) to the FL paradigm. For instance, the authors in [8] and [9] studied UAV-

assisted ISCC for FEEL that jointly optimizes sensing and communication resources; however, [8] and [9] fundamentally considered a static UAV performing simple radar sensing. When applied to mobile visual sensing, these approaches fall short. As noted in [10] and [11], visual data quality and volume are inherently bounded by the UAVs’ flight trajectories, since their altitude and speed govern the camera footprint, ground sampling distance (GSD), and statistical data heterogeneity. To the best of our knowledge, existing ISCC frameworks have yet to accurately model this unique trajectory-sensing coupling in mobile vision, nor have they accounted for the massive inplace computational burden induced by modern deep vision models. As a result, developing a rigorous co-design that tightly couples the UAVs’ mobility with sensing, computation, and communication remains a critical open challenge. In this paper, we propose a joint trajectory, sensing, and computation co-design framework to minimize the expected training time in UAV-assisted federated edge vision. We propose a tractable four-phase operational model that quantifies the time and energy coupling across communication, dynamic visual sensing, and in-place computation. To mitigate sensing data heterogeneity, we enforce a uniform sensing probability across all UAVs, which translates the federated convergence requirements into strict UAV mobility constraints. We formulate the training time minimization problem as a mixedinteger nonconvex problem and develop a two-layer alternating optimization (AO) algorithm to solve it efficiently. In particular, our algorithm adaptively bounds the local data workload to optimally trade off the required training rounds against the heavy in-place computation delay. Extensive simulations demonstrate that our co-design substantially improves model convergence accuracy over baselines. II. S YSTEM M ODEL We consider a UAV-assisted FEEL system comprising an edge server (ES) located at S = (xs , ys , 0) and a set of UAVs denoted as K = {1, 2, . . . , K}. The UAVs collaborate to train a computationally intensive global object detection model, specifically YOLO11x. Each UAV k ∈ K enters its designated non-overlapping rectangular mission area Ak at a starting point pstart and finishes at an ending point pend k k . As illustrated in Fig. 1, to rigorously capture the synchronization delay inherent in training such a heavy model, each global

V1, 3

2 UAV 1

UAV k

V1, 4

p1end

W1

3 b1

a1 V1, 1

L1

4 p1start

⋯

1

V1, 2

1: Downlink Broadcasting 2: Distributed Sensing

ES 3: Local Computation 4: Model Uploading

image footprint

Fig. 1. Illustration of the four phases in a training round, depicted via the trajectory projection of each UAV.

training round is modeled as a sequence of four phases: 1) downlink broadcasting, 2) distributed sensing, 3) local computation, and 4) model uploading. Let Tk denote the total duration of these four phases for UAV k. Due to the synchronous protocol, the per-round completion time for the entire system is strictly bottlenecked by the slowest UAV, given by Tmax = maxk∈K Tk . A. Four-Phase Round Structure 1) Downlink Broadcasting: At the beginning of the round, the ES broadcasts the global model (size D0 bits) to all participating UAVs. Let db,k = ∥pstart − S∥ denote the k horizontal straight-line distance from the ES to the sensing starting point pstart . Suppose that UAV k flies at a constant k speed vb,k ∈ (0, vmax ] and altitude hk , where vmax denotes the maximal allowable speed. During this flight, the horizontal distance xb,k between UAV k and the ES increases from 0 to db,k . Assuming a line-of-sight (LoS) dominated air-to-ground channel, the average downlink transmission rate R̄b,k over this straight-line flight path is obtained as: ! Z db,k γb,k 1 Bc log2 1 + 2 dxb,k , R̄b,k = db,k 0 (hk + x2b,k )α/2 (1) where Bc is the total channel bandwidth, γb,k denotes the reference downlink signal-to-noise ratio (SNR) received at UAV k, and α ≥ 1 is the path-loss exponent. Since the UAV flies at a constant speed, the effective time-averaged transmission rate is equivalent to the spatial average over the flight distance in (1). To ensure the complete reception of the global model before the sensing task begins, UAV k’s received data volume within the broadcasting duration Tb,k = db,k /vb,k must satisfy the following data volume constraint: Tb,k · R̄b,k ≥ D0 . (2) 2) Distributed Sensing: To acquire a spatially diverse training dataset in parallel, the global sensing task is distributed across K UAVs. Upon reaching pstart , UAV k executes a k parallel-track (lawnmower) scanning trajectory over its designated area Ak (with length Lk and width Wk ). Note that pstart is heuristically chosen near the vertex of Ak closest to k the ES to minimize the approach distance. The sensing flight is performed at a constant sensing speed vs,k and altitude hk , subject to policy-mandated bounds: hmin ≤ hk ≤ hmax , vmin ≤ vs,k ≤ vmax , (3)

A downward-facing camera is equipped at each UAV to capture images at an interval of ∆timg . Given the horizontal and vertical fields of view (FOV) γa and γb , the rectangular footprint of a single image has width ak = 2hk tan(γa /2) and length bk = 2hk tan(γb /2). To guarantee seamless coverage along the track, the displacement between consecutive images must not exceed the footprint length, which yields vs,k ∆timg ≤ bk . (4) The lawnmower trajectory requires Nk,tr = ⌈Wk /ak ⌉ parallel tracks to fully cover Ak . Ignoring the negligible fractional track residuals for mathematical tractability, the total flight distance is tightly approximated by Lscan,k (hk ) ≈ Nk,tr Lk + Wk . Consequently, the sensing duration is Ts,k = Lscan,k (hk )/vs,k , and UAV k concludes the sensing at a determinable end point pend governed by the scanning geometry. k Since images are captured only along the tracks, the effective capture time is Tcap,k = Nk,tr Lk /vs,k . This distributed sensing process forms a unique local dataset Dk with size |Dk | = ⌊Tcap,k /∆timg ⌋ for UAV k. It is noted that increasing the altitude hk enlarges the footprint width ak , which effectively reduces the required tracks Nk,tr and shortens the sensing time Ts,k . However, a higher altitude degrades the image spatial resolution, quantified by the GSD, defined as GSDk = 200 tan(γa /2)hk /ra , where ra is the pixel resolution. The sensing quality directly affects the YOLO11x detection confidence. Based on empirical profiling [10], we model the successful participation probability of UAV k as: ps,k (vs,k , hk ) = min(1, max(0, Ck )), (5) where Ck is an empirical polynomial function of vs,k and (n) GSDk . Define a Bernoulli participation indicator Ik ∈ {0,1} (n) (n) with Pr(Ik = 1) = ps,k . A successful sensing with Ik = 1 validates the dataset, allowing UAV k to proceed to the subsequent computation and uploading phases; otherwise, it aborts the task and returns to the ES at maximum speed. (n) 3) Local Computation: For a participating UAV with Ik = 1, it hovers at the sensing end point pend to perform in-place k model training. To flexibly trade off computation delay against learning performance, UAV k selects a data subset of size Mk ∈ Z+ from Dk , and adapts its computation workload Mk within the practical bounds Nmin,k ≤ Mk ≤ Nmax,k , (6) where Nmax,k = ⌊|Dk |ps,k ⌋ is the total acquired valid samples and Nmin,k ≥ 0 guarantees a baseline training effectiveness. Let w(n) denote the global model parameters in the n-th round. The UAV computes the local updates via stochastic gradient descent (SGD) using its valid dataset of size Mk . Let ξ be the number of CPU cycles required to process one data sample, and fcpu be the CPU clock frequency. The local computation time is obtained as Tcp,k = Mk ξ/fcpu . During this phase, the UAV consumes hovering propulsion power but provides a stable environment for computationally intensive training. 4) Model Uploading: Upon completing the local training, the UAV flies back to the ES along the shortest straight line at a constant return speed vu,k to upload its model updates

(assumed to be of size D0 ). Let dup,k = ∥pend k −S∥ denote the horizontal upload flight distance. To avoid mutual interference, frequency division multiple access (FDMA) is adopted, where UAV k is allocated a bandwidth Bk , satisfying X Bk ≤ Bc , Bk ≥ 0, ∀k ∈ K. (7)

tion problem, we introduce a continuous surrogate variable Tmax to cap the expected completion time of every UAV. By (n) replacing the discrete indicator Ik with its success probability ps,k , the system bottleneck is effectively constrained by Tmax ≥ Tb,k + Ts,k + ps,k (Tcp,k + Tup,k ), ∀k ∈ K. (13)

k∈K

Similar to the broadcasting phase, the effective time-averaged uplink rate R̄u,k during this straight-line return flight can be expressed as a spatial average: ! Z dup,k γu,k 1 Bk log2 1+ 2 dxu,k , R̄u,k = dup,k 0 (hk +x2u,k )α/2 (8) where γu,k represents the reference uplink SNR received at the ES from UAV k at the unit distance. The uploading duration Tup,k = dup,k /vu,k must ensure the complete delivery of the updates, given by Tup,k · R̄u,k ≥ D0 , ∀k ∈ K. (9) Finally, the ES aggregates the received updates from all participating UAVs to generate w(n+1) . Given the abundant computational resources at the ES, the aggregation time cost is negligible compared to the lengthy physical phases. Note that under the synchronous protocol, this aggregation step strictly awaits the arrival of the slowest UAV. B. Energy Consumption and Round Time In each FEEL round, the total energy consumption of UAV k is decoupled into operational energy for communication, sensing, and computation, and propulsion energy for flying and hovering. Let Pr , Ps , and Pc denote the constant power for receiving, sensing, and uploading transmission at each UAV, respectively. The operational energy of a participating UAV is 3 Tcp,k + Pc Tup,k , where κ is Eop,k = Pr Tb,k + Ps Ts,k + κfcpu the effective switched capacitance of the CPU. The propulsion power of a rotary-wing UAV at s speed v is modeled as [12]:   2  3v v4 v 2  12 1 Pprop (v) = P0 1+ 2 +Pi 1 + 4 − 2 + Xv 3 , Utip 4v0 2v0 2 (10) where P0 , Pi , Utip , v0 , and X are hardware-specific aerodynamic constants. Since each phase involves either a constantspeed flight or a pure hover, the propulsion energy is evaluated in closed form as Eprop,k = Pprop (vb,k )Tb,k + Pprop (vs,k )Ts,k + Pprop (0)Tcp,k + Pprop (vu,k )Tup,k . For a (n) dropout UAV with Ik = 0, it aborts the task and returns directly, thus consuming strictly less energy than a participant. To guarantee battery safety over a total of N global training rounds, the worst-case energy must be bounded by the battery capacity Ek,max : N · (Eop,k + Eprop,k ) ≤ Ek,max , ∀k ∈ K. (11) Under the synchronous FEEL protocol, the round time is bottlenecked by nthe slowest participant:
o (n) T (n) = max Tb,k + Ts,k + Ik Tcp,k + Tup,k . (12) k∈K

However, minimizing the stochastic maximum of expectations is mathematically intractable. To derive a trackable optimiza-

III. C ONVERGENCE A NALYSIS AND P ROBLEM F ORMULATION A. Convergence Analysis Following standard federated learning literature [8], we assume that the global loss function FS (w) is L-smooth and µ-strongly convex, and let w∗ denote its optimal model parameters. We also assume unbiased local gradients with variance bounded by σk2 /Mk and bounded data heterogeneity Λ2k for all UAVs, since Mk data samples are computed. Theorem 1. Assume that the learning rate satisfies 0 < η < 1/(4L). After N > 0 global rounds, the expected optimality gap of the global model is bounded by:
G 1 − AN + AN λ, (14) E[FS (w(N ) ) − FS (w∗ )] ≤ µη(1 − 4Lη) where A = 1 − µη(1 − 4Lη), λ = E[FS (w(0) ) − FS (w∗ )] is the expected initial gap with w(0) being the initial model parameters, and G is the steady-state error with the expression given in [8, Theorem 1]. The proof closely follows [8] with minor algebraic adaptations for varying dataset sizes Mk , and is thus omitted due to space limits. Moreover, existing works reveal that unequal participant probabilities ps,k (vs,k , hk ) across devices severely inflate the steady-state error G through data heterogeneity. To eliminate this statistical bias and ensure stable convergence, we mandate a uniform successful sensing probability for any arbitrary UAV k ∈ K: ps,k (vs,k , hk ) = ps , ps,min ≤ ps ≤ 1, (15) where ps,min is the predefined minimum reliability threshold. Following (15), each UAV k must adaptively adjust its sensing speed vs,k and altitude hk to achieve global unified ps . We further obtain Corollary 1. Corollary 1. Under the uniform sensing probability ps , an upper bound Ḡ to the steady-state error G is found as  4Lη 2 X η X  σk2 G ≤Ḡ = + Λ2k + p−(K−2) Λ2k s K Mk K k∈K k∈K  2Lη 2 X  σk2 + 2 + 2Λ2k , (16) K χps Mk k∈K

where χ = 1 − (1 − ps )K . The proof to Corollary 1 is easy to obtain by applying the uniform ps , and thus is omitted here for simplicity. Note that Corollary 1 reveals the intrinsic system tradeoffs: increasing the computation workload Mk reduces the gradient variance σk2 /Mk in Ḡ, but prolongs the local computation time Tcp,k . Meanwhile, increasing ps suppresses the heterogeneity terms in Ḡ, but forces the UAV’s sensing parameters (vs,k , hk ) away

from their time-optimal sensing settings. Hence, the variables {Mk , vs,k , hk } must be jointly optimized. By replacing G with Ḡ, the RHS of (14) is upper bounded by Ḡ(1 − AN ) Φ({Mk }, {vs,k }, {hk }, N ) = + AN λ. µη(1 − 4Lη) Since 0 < A < 1, the initial error term AN λ vanishes as N increases, and Φ asymptotically approaches Ḡ/[µη(1 − 4Lη)]. To guarantee an ϵ-optimal global model, where ϵ > 0 is the predefined target optimality gap, we impose the following convergence constraint: Φ({Mk }, {vs,k }, {hk }, N ) ≤ ϵ. (17) B. Problem Formulation We aim to minimize the expected total training time N · Tmax , while guaranteeing the model convergence and meeting the multidimensional system limitations. Let Ω ≜  {vb,k , vs,k , vu,k , hk , Mk , Bk }k∈K , ps , Tmax , N . The training time minimization problem is formulated as follows: (P1): min N · Tmax Ω

s.t.

(2) − (4), (6), (7), (9), (11), (13), (15), (17), Mk ∈ Z+ ,

N ∈ Z+ ,

vb,k , vu,k ∈ (0, vmax ], ∀k ∈ K. (18) Due to the tight coupling of continuous variables (vs,k , hk ) and discrete variables (Mk , N ) in highly nonlinear constraints (e.g., (11) and (17)), Problem (P1) is a mixed-integer nonconvex program (MINLP), which is generally NP-hard. Next section proposes an efficient alternating optimization (AO) framework to decouple and solve it. IV. T WO -L AYER AO A LGORITHM To solve (P1), we propose the Two-Layer AO algorithm. The outer layer conducts a one-dimensional search over the rounds N to strictly enforce the energy limit. For any given N , the inner AO iteratively updates four decoupled blocks: deriving {vb,k } in closed form, optimizing {vs,k , hk } via successive convex approximation (SCA), determining {Mk } through an integer-aware bisection search, and allocating {vu,k , Bk } in closed form. A. Optimal Broadcasting Speeds Given {Mk , vs,k , hk , vu,k , Bk }, (P1) reduces to the broadcasting subproblem (SP-1), which naturally decouples across the K UAVs. For each UAV k, (SP-1) minimizes the broadcasting time Tb,k = db,k /vb,k over the speed vb,k , subject to the data constraint in (2) and the speed cap in (18). Substituting (1) into (2) directly cancels the flight distance db,k , reformulating the data constraint in (2) as an k) , where explicit upper bound on the speed vb,k ≤ Bc IDk (h 0  R db,k γb,k Ik (hk ) ≜ 0 log2 1 + (h2 +x2 )α/2 dxb,k is independent k b,k of vb,k . Because the objective Tb,k monotonically decreases as vb,k increases, the optimal closed-form solution is directly obtained by capping this bound at the maximum speed:   B I (h ) c k k ∗ vb,k = min vmax , . (19) D0

B. Optimization of Sensing Phase Given {Mk , Bk , vb,k , vu,k }, (P1) reduces to the sensing subproblem (SP-2), which minimizes Tmax over {vs,k , hk } subject to (3), (4), (13), (15), and (17). Problem (SP-2) is non-convex due to the fractional term Lscan,k /vs,k in (13), the nonlinear equality ps,k (vs,k , hk ) = ps in (15), the ceiling operation in the sensing distance, and the highly coupled variables in (17). The following addresses each constraint. First, substituting the bound (16) into (17), the term −(K−2) −(K−2) ps,k in (16) couples all UAVs. By replacing ps,k with −(K−2) its worst-case constant ps,min , we decouple the variables in (17), transforminghit into a lower bound on psi : 2 σk 2Lη 2 P 2 k∈K Mk + 2Λk K 2 χmin  2  , ps ≥ P P σk η 2 − 4Lη 2 2 A0 − K + Λ Λ K−2 k∈K Mk k∈K k k Kps,min (20) N ) K where A0 = (1−A)(ϵ−λA , χ = 1 − (1 − p ) . min s,min N 1−A Next, to handle (13), we remove the ceiling operation in Nk,tr and newly obtain that Lscan,k = Wk Lk /ak + Wk with sensing time Ts,k (vs,k , hk ) = Lscan,k /vs,k . Since both Ts,k and ps,k (vs,k , hk ) remain highly non-convex, directly solving (SP-2) is intractable. Hence, we employ SCA to replace these non-convex terms with their affine approximations. At the i(i) (i) th iteration around a local point (vs,k , hk ), their first-order Taylor expansions are derived as: ∂Ts,k ∂Ts,k (i) (i) (i) (i) (vs,k − vs,k ) + (hk − hk ), (21) T̂s,k = Ts,k + ∂vs,k ∂hk ∂ps,k ∂ps,k (i) (i) (i) (i) p̂s,k = ps,k + (vs,k − vs,k ) + (hk − hk ). (22) ∂vs,k ∂hk Substituting (21) and (22) into (13) successfully transforms the intractable expected time constraint into a linear inequality: (i) (i) Tb,k + T̂s,k + p̂s,k (Tcp,k + Tup,k ) ≤ Tmax , ∀k ∈ K. (23) Similarly, the nonlinear coupling (15) is linearized as (i) p̂s,k = ps , ps,min ≤ ps ≤ 1. (24) As a result, (SP-2) is approximated by the following convex problem at each iteration i: (SP-2.1): min [Tmax + Z] {vs,k },{hk },Tmax

s.t.

(3), (4), (20), (23), (24), (i)

ρ P

(i)

(i)

|vs,kh − vs,k | ≤ ∆(i) v , |hk − hk | ≤i ∆h , (i)

(i)

where Z = 2 k∈K (vs,k − vs,k )2 + (hk − hk )2 with ρ > 0 stabilizes the iteration, and the last two constraints (i) (i) define the trust region with step limits ∆v and ∆h . At each iteration, problem (SP-2.1) can be efficiently solved by CVX to obtain the optimal variables, which then serve as the (i+1) (i+1) local points (vs,k , hk ) for the next iteration. This SCA procedure repeats successively until the relative decrease of the objective Tmax falls below a predefined tolerance δ. C. Optimal Local Computation Workloads Given {vs,k , hk , vb,k , Bk , vu,k }, (P1) reduces to the workload subproblem (SP-3), which minimizes Tmax over {Mk } subject to (6), (13) and (17). Since Tb,k , Ts,k , Tup,k and ps,k

are constants, the bottleneck time is determined by Tcp,k , which increases with Mk . Let ek = Tb,k + Ts,k + ps Tup,k and c = ps ξ/fcpu > 0. The constraint in (13) is reduced to ek + cMk ≤ Tmax . For any candidate Tmax = T , the largest admissible integer workload  for UAV k is given  by T − e k ck (T ) = min Nmax,k , M . (25) c ck (T ) ≥ Nmin,k for all k and A candidate T is feasible if M ck (T )}. Since Φ in (17) is nonincreasing (17) holds under {M over Mk , the feasibility of (SP-3) is monotonic with respect to T . To obtain the exact integer global optimum, we sort all possible time thresholds and construct the following set: [ T = {ek + cm : m = Nmin,k , · · · , Nmax,k } , (26) k∈K

inside the operational range [maxk (ek + cNmin,k ), maxk (ek + cNmax,k )]. By performing a bisection search over the sorted set T , the smallest feasible element yields the optimal ∗ expected time Tmax and the optimal workloads Mk∗ = ∗ c Mk (Tmax ). D. Optimal Uploading Speeds and Bandwidth Given {vb,k , Mk , vs,k , hk }, (P1) reduces to the uploading subproblem (SP-4), which minimizes Tmax over the uploading speeds {vu,k } and bandwidth allocations {Bk }, subject to (7), (9), (13), and (18). Similar to the broadcasting phase, since Tup,k = dup,k /vu,k , substituting the uploading rate (8) into (9) directly cancels dup,k , reformulating the data constraint as an upper bound on the uploading speed: vu,k≤ Bk JDk0(hk ) ,  Rd γ where Jk (hk ) ≜ 0 up,k log2 1 + (h2 +xu,k dxu,k is the 2 )α/2 k u,k spatial integral independent of vu,k and Bk . To minimize Tup,k , UAV k must fly as fast as possible for any allocated bandwidth Bk . Thus, the time-optimal speed is tightly bounded by vu,k = min{vmax , Bk JDk0(hk ) }. Let Trem = maxk∈K (Tb,k + Ts,k + ps Tcp,k ) denote the fixed time budget consumed by the previous phases. According to the bottleneck constraint (13), the uploading time must satisfy Tup,k ≤ (Tmax − Trem )/ps . Consequently, for a target maximum time T , enforcing Tup,k ≤ (T −Trem )/ps dictates the required speed vu,k (T ) = ps dup,k /(T − Trem ) and the required p D0 dup,k minimum bandwidth Bk (T ) = Jk (hsk )(T −Trem ) . The target T P is globally feasible if and onlyP if both k Bk (T ) ≤ Bc and vu,k (T ) ≤ vmax hold. Since k Bk (T ) decreases with T , these two feasibility conditions give two lower bounds on the time variable as T ≥ Tbw and T ≥ Tcap , where Tbw ≜ Trem + dup,k ps D0 P k∈K Jk (hk ) , Tcap ≜ maxk∈K (Trem + ps dup,k /vmax ). Bc Therefore, problem (SP-4) admits the closed-form optimal p D d solutions: T ∗ = max{Tcap , Tbw }, Bk∗ = Jk (hks)(T0 ∗up,k −Trem ) , n o ps dup,k ∗ vu,k = min vmax , T ∗ −Trem . E. Overall Algorithm and Complexity Algorithm 1 summarizes the proposed two-layer AO algor r rithm. The outer layer searches N ∈ [Nmin , Nmax ], respectively bounded by the convergence and energy constraints. Since (SP-1), (SP-3), and (SP-4) are solved exactly and (SP-2)

Algorithm 1 Two-layer AO Algorithm Require: K, S, the sensing areas, ϵ, δ, and the system parameters. r r do 1: for N = Nmin to Nmax 2: Initialize the variables and set i = 0; 3: repeat 4: Update {vb,k } and {Bk , vu,k } in closed form, {vs,k , hk } by (SP-2.1), and {Mk } by (SP-3); 5: i = i + 1; (i) 6: until the relative decrease of Tmax (N ) is below δ 7: if Φ({Mk }, {vs,k }, {hk }, N ) ≤ ϵ and the energy budget holds for all k then (i) 8: Record Ttot (N ) = N Tmax (N ) and the variables; 9: end if 10: end for ∗ 11: N = arg minN Ttot (N ). ∗ , v ∗ , h∗ , M ∗ , B ∗ , v ∗ }. Ensure: N ∗ and the optimal {vb,k s,k k k k u,k

via SCA, the objective Tmax is non-increasing. Bounded below by zero, the inner loop converges; and the global minimum is obtained by evaluating Ttot = N · Tmax across all feasible N . r r Complexity: Let I and Nspan = Nmax − Nmin denote the inner iterations and outer search size. Each iteration evaluates integrals in O(KQ), solves (SP-2.1) in O((2K + 2)4 ), and bisects T in O(KNspan log(KNspan )). Thus, the overall com
plexity is O Nspan I ((2K+2)4 +KNspan log(KNspan )+KQ) , which remains scalable for practical UAV swarms. V. N UMERICAL R ESULTS AND P ERFORMANCE E VALUATION We evaluate the proposed system with two UAVs, each scanning a 200 × 200 m2 area. For the federated learning task, the YOLO11x architecture is adopted and trained on the dataset provided in [10]. The simulation parameters are listed in Table I. The proposed joint optimization yields N ∗ = 40 ∗ = FEEL rounds with an expected bottleneck time Tmax 458.96s per round. The per-UAV total energy consumption reaches 2.98 MJ at N ∗ = 40, rendering the 3.0 MJ battery constraint in (11) strictly tight. Fig. 2 and Fig. 3 compare our proposed algorithm against Baseline 1 with fixed sensing settings given in Table II and Baselines 2 and 3 with fixed learning or resource allocations, respectively. 1) Impact of Sensing Parameters: As compared to all the five settings in Baseline 1, Fig. 2 shows that our proposed algorithm always achieves the fastest convergence and highest accuracy. Baseline 1 with fixed high-altitude settings, such as (v-slow, h-high), is observed to converge noticeably slower. This is because that although a higher altitude enlarges the camera footprint and reduces the required lawnmower tracks (thus shortening the sensing flight), it usually coarsens the GSD and degrades image quality. Hence, the participation TABLE I S YSTEM PARAMETERS Parameter

Value

Number of UAVs K 2 Bandwidth Bc 6 MHz Pixel array ra × rb 4000 × 3000 CPU frequency fcpu 5 × 108 Hz Sensing speed vmin , vmax 0.5, 30 m/s Altitude hmin , hmax 8, 110 m Image interval ∆timg 1s Powers Pc , Ps , Pr 5, 0.5, 0.5 W

Parameter

Value

Model size D0 217.61 MB SNR γb,k , γu,k 52.5, 78.5 dB Diagonal FOV γd 84◦ Cycles per sample ξ 2.5 × 107 Participation ps,min 0.84 Energy budget Ek,max 3.0 MJ Path-loss exp. α 2.3 Hardware constant κ 10−28

(a) Accuracy

Speed (m/s) Altitude (m) Fixed (vs , h)

v-fast, h-high [7, 10.69] [70, 110.37] v-fast, h-low [7, 10.69] [8, 45] v-medium, h-medium [5, 8] [45, 70] v-slow, h-high [0.5, 4] [70, 110.37] v-slow, h-low [0.5, 4] [8, 45]

(9, 90) (9, 30) (5.5, 55) (1, 90) (1, 25)

(b) Loss

1.0

7

0.8

6

Training loss

Scenario

Validation mAP50

TABLE II BASELINE 1: UAV S ENSING S PEED AND H EIGHT I NTERVALS

0.6 0.4 0.2

VI. C ONCLUSION We investigated UAV-assisted federated edge vision. We conducted convergence analysis and enforced a uniform participation probability to mitigate sensing data heterogeneity. To minimize the total training time under per-UAV operation and energy constraints, we proposed the Two-layer AO algorithm to jointly optimize the training rounds, sensing mobility, computation workloads, and bandwidth allocations. Simulations validate that our design significantly accelerates model convergence and accuracy. Future work will relax the linear flight assumption, optimizing UAV trajectories during broadcast and upload phases for time minimization. R EFERENCES [1] W. Jiang, B. Han, M. A. Habibi, and H. D. Schotten, “The road towards 6g: A comprehensive survey,” IEEE Open Journal of the Communications Society, vol. 2, pp. 334–366, 2021. [2] P. Liu, G. Zhu, S. Wang, W. Jiang, W. Luo, H. V. Poor, and S. Cui, “Toward ambient intelligence: Federated edge learning with task-oriented sensing, computation, and communication integration,” IEEE Journal of Selected Topics in Signal Processing, vol. 17, no. 1, pp. 158–172, 2023.

4 3 2

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Training time (min) Proposed v-fast, h-high

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v-slow, h-high v-slow, h-low

Fig. 2. Comparison with Baseline 1 under fixed (vs,k , hk ) from Table II: (a) validation mAP50 and (b) loss versus training time. (a) Accuracy

(b) Loss

1.0

7

0.8

6

Training loss

Validation mAP50

probability ps drops, demanding more time to converge. Conversely, the (v-slow, h-low) setting yields the worst mAP50. This is because that the low altitude shrinks the footprint, resulting in a dense lawnmower trajectory. This inflates the sensing time, turning the UAV into a system straggler. Under a strict time budget, only a few aggregation rounds can be executed, severely limiting model generalization. Unlike Baseline 1, our proposed algorithm co-optimizes {vs,k } and {hk } along the ps,min boundary, effectively balancing data quality against time overhead. 2) Impact of Data Volume and Resource Allocation: While a large dataset generally improves per-round learning, training YOLO11x may incur large in-place computation delay. To balance this trade-off, our algorithm adaptively bounds the workloads, yielding optimal sizes M1∗ = 120 and M2∗ = 119 out of 227 and 228 captured samples. Unlike our proposed algorithm, utilizing a fixed data size in Baseline 2 fails to balance this trade-off. Specifically, as shown in Fig. 3, a large dataset with Mk = 200 severely prolongs the round time, causing a rightward convergence shift, whereas a small dataset with Mk = 100 fundamentally limits the final accuracy. Moreover, Baseline 3’s random bandwidth allocation preserves per-round accuracy but induces unoptimized uploading delays. This causes a system straggler that visibly shifts its training curve rightward. In contrast, our closed-form allocation optimally equalizes uploading times across UAVs, thereby eliminating this straggler effect.

5

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Training time (min) Proposed Mk = 100

0

100

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Training time (min) Mk = 150 Mk = 200

Random bandwidth

Fig. 3. Comparisons with Baseline 2 under fixed Mk ∈ {100, 150, 200} and Baseline 3 under a random bandwidth split: (a) validation mAP50 and (b) loss versus training time. [3] H. Zhang and L. Hanzo, “Federated learning assisted multi-uav networks,” IEEE Transactions on Vehicular Technology, vol. 69, no. 11, pp. 14 104–14 109, 2020. [4] T. Zeng, O. Semiari, M. Mozaffari, M. Chen, W. Saad, and M. Bennis, “Federated learning in the sky: Joint power allocation and scheduling with uav swarms,” in ICC 2020-2020 IEEE International Conference on Communications (ICC). IEEE, 2020, pp. 1–6. [5] H. Yang, J. Zhao, Z. Xiong, K.-Y. Lam, S. Sun, and L. Xiao, “Privacypreserving federated learning for uav-enabled networks: Learning-based joint scheduling and resource management,” IEEE Journal on Selected Areas in Communications, vol. 39, no. 10, pp. 3144–3159, 2021. [6] Y. Jing, Y. Qu, C. Dong, Y. Shen, Z. Wei, and S. Wang, “Joint uav location and resource allocation for air-ground integrated federated learning,” in 2021 IEEE Global Communications Conference (GLOBECOM), 2021, pp. 1–6. [7] C. Wang, X. Tang, Z. Xiong, D. Zhai, R. Zhang, D. Niyato, and Z. Han, “Uav-assisted federated learning with robust resource and trajectory optimization under location uncertainties,” IEEE Transactions on Cognitive Communications and Networking, 2025. [8] Y. Tang, G. Zhu, W. Xu, M. H. Cheung, T.-M. Lok, and S. Cui, “Integrated sensing, computation, and communication for uav-assisted federated edge learning,” IEEE Transactions on Wireless Communications, 2025. [9] N. Zhang, Q. Hu, D. Wen, Y. Mao, T.-M. Ma, G. Yu, and W. Wang, “Integrated sensing-communication-computation based online federated learning with limited cache in ofdm systems,” IEEE Transactions on Cognitive Communications and Networking, 2026. [10] L. Lanča, M. Mališa, K. Jakac, and S. Ivić, “Optimal flight speed and height parameters for computer vision detection in uav search,” Drones, vol. 9, no. 9, 2025. [Online]. Available: https://www.mdpi.com/2504-446X/9/9/595 [11] A. Al-Hourani, S. Kandeepan, and S. Lardner, “Optimal lap altitude for maximum coverage,” IEEE Wireless Communications Letters, vol. 3, no. 6, pp. 569–572, 2014. [12] M. Li, N. Cheng, J. Gao, Y. Wang, L. Zhao, and X. Shen, “Energyefficient uav-assisted mobile edge computing: Resource allocation and trajectory optimization,” IEEE Transactions on Vehicular Technology, vol. 69, no. 3, pp. 3424–3438, 2020.

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