Mathematical representation of cooperative UAV planning

For a system of N unmanned aerial vehicles (UAVs), define the agent set as N = { 1 , ⋯ , N } . The state and control input of UAV i are denoted by x i ( t ) ∈ ℝ n i and u i ( t ) ∈ ℝ m i , respectively. The motion of each vehicle is governed by

The general planning problem in cooperation may be stated as

where the cost is decomposed into

where

and

where the non-negative weighting coefficients λ t , λ e , λ s , λ r , and λ c regulate the relative importance of mission duration, energy consumption, trajectory smoothness, collision risk, and communication performance. The optimization is subject to the vehicle dynamics, prescribed initial and terminal conditions,

and actuator and flight-envelope constraints,

For a possibly time-varying obstacle O k ( t ) , collision avoidance requires

where p i ( t ) is the position component of x i ( t ) , r i is the effective physical radius of UAV i , and s i k obs ( t ) is the additional obstacle-clearance margin. Pairwise separation is imposed through

The safety margin s i j ( t ) should not be treated as an arbitrary tuning constant. It must account for the principal sources of uncertainty affecting vehicle separation and may be represented conceptually as

where the individual terms represent localization uncertainty, trajectory-tracking error, motion-prediction error, communication delay or packet loss, and aerodynamic or wake-interaction effects, respectively. The effective radius r i should already incorporate the physical dimensions of the airframe and any necessary geometric buffer.

Calibrate localization bounds from held-out ground-truth residuals at the relevant update rate and in representative occlusion/GNSS conditions; estimate tracking bounds from flight logs over wind, payload, battery, controller latency, and actuator saturation; and use prediction residual quantiles or conservative reachable sets at each forecast horizon. Bound communication displacement using measured end-to-end age-of-information and packet-loss bursts multiplied by bounded relative speed/acceleration, including clock error. Estimate aerodynamic exclusion volumes from measured vertical/horizontal disturbance and attitude/altitude recovery tests at the tested rotor spacing, rather than treating downwash as a uniform sphere. Use simultaneous confidence bounds or a clearly budgeted risk allocation across errors and agent pairs; naive addition of sample standard deviations is not a deterministic bound. Report calibration sample size, quantile/confidence method, update interval, extrapolation horizon, and observed bound exceedances. If a bound expires or cannot be established, do not claim assured separation: execute a pre-verified braking, hover, loiter, altitude-separation, or landing contingency only if its own reachable tube is known to remain conflict-free; otherwise stop autonomous mission progression and defer to controlled separation/abort procedures.

If the uncertainty is modeled stochastically, deterministic separation can be replaced with the chance constraint

where d i j min is the required minimum separation and ε i j is the maximum acceptable probability of constraint violation. If the underlying probability distribution is itself uncertain, a distributionally robust formulation may be adopted:

where

denotes an ambiguity set containing plausible probability distributions. Risk may alternatively be quantified using conditional value-at-risk, probabilistic occupancy maps, reachability tubes, or robust controlled-invariant sets. These formulations demonstrate why nominal shortest-path solutions cannot be transferred directly to uncertain and dynamically evolving airspace: a geometrically valid route may still become unsafe when sensing errors, prediction uncertainty, communication imperfections, and closed-loop tracking dynamics are considered.

A centralized planner has global state information and is able to optimize for the entire problem, but the decision dimension and pairwise constraints become large and there is a single point of delay or failure of the coordinator. Decentralized planners distribute computation and offer automatic scalability and fault isolation properties, but need coordination protocols for intent exchange, priority, reciprocity or conflict resolution. Distributed optimization techniques let agents solve local subproblems and coordinate by means of consensus, alternating direction, sequential negotiation or safe corridor construction [27]. Hybrid approaches explicitly employ different techniques for mission, route, trajectory and safety levels [19][20][28]-[33]. Figure 2 translates these complementary roles into a hierarchical autonomy loop. Mission-level objectives guide global coordination, local prediction and trajectory generation, and safety-critical control before commands reach the vehicles. Feedback links the execution layer to subsequent planning decisions. The diagram represents a proposed integration architecture; its practical value depends on compatible interfaces, timely feedback, and feasible safety interventions, rather than implying an independently established end-to-end guarantee.

Figure 2. Recommended hierarchical architecture coupling mission planning, global coordination, local prediction, safety-critical control, and vehicle execution. Original schematic created for this review.

Minimum acceptable metrics include mission success, collision and near-miss rate, minimum separation, cost of paths or trajectories, makespan, energy consumption proxy, latency of planning cycle and tail latency, memory and CPU/GPU load, communication bytes and age of information, constraint violations, deadlock rate and recovery mechanism. Scalability must be analyzed as a function of the number of UAVs, number of neighbors, obstacle density, map size, and horizon. Experiments for robustness must include perturbation of localization, dynamics, wind, sensing range, packet delay, packet losses and unmodeled agent behaviors. Hardware tests should reveal onboard CPU, estimator, communication graph, control rate, safety radius and criteria for intervention.

Predeclared event definitions: A collision is physical contact or a measured signed surface separation ≤ 0 , including vehicle-obstacle contact. A near miss is 0 < signed surface separation < s_req(t), where s r e q is the prespecified pair- or obstacle-specific operational buffer; count contiguous excursions as one event and also report minimum clearance, duration, and time-to-collision. Mission success requires every assigned mandatory waypoint/task to be completed within its prespecified deadline, with no collision, geofence breach, energy-reserve violation, or operator rescue. Deadlock is simultaneous lack of mission progress for at least τ D = max ( 10 ,   s   2 T H ) , where T_H is the planning-horizon duration, while goals remain feasible, using displacement toward the assigned goal < 0.1 m for each blocked vehicle in the window. Livelock is repeated replanning or route/velocity reversal at least twice in the same τ_D window with net goal progress < 0.1 m and no mission completion. Report thresholds in metres and seconds, frame rate, uncertainty of separation measurement, timeouts, trial denominator, censored runs, and whether simultaneous near-miss pairs are counted separately. The 0.1 m and 10 sdefaults should be adapted before a test to vehicle size/speed and then held fixed across algorithms.

Table 1 compares the 14 algorithm families using a common set of descriptors covering representation, vehicle dynamics, environmental assumptions, information requirements, safety claims, and computational or communication limits. It distinguishes formal guarantees from conditional properties and empirical results, making clear why a method that performs well under one model may not retain the same properties under different sensing, dynamics, or coordination conditions. The comparison is intended to guide method selection rather than provide a numerical ranking.

Table 1 appraisal key: F = formal under stated assumptions, C = conditional on feasibility and model/bounds, E = empirical; NR = not reported. Each row summarizes the source method, not a guarantee for an untested UAV. Evidence type for individual implementations is reported in Table 2. An R/P/NR checklist for the eight criteria is defined in Section 2; these rows are qualitative and unweighted.

Table 1.Algorithm-family comparison for multi-UAV cooperative planning and collision avoidance.

D* and A* are appealing when it is possible to construct an occupancy map and apply efficient heuristics for the search. D* Lite and other incremental algorithms reuse search work performed before the map change, while jump-point algorithms eliminate symmetric expansions on uniform maps. In the multi-agent case, naïve sequential planning followed by conflict correction is incomplete and introduces loops of replanning. MAPF introduces time into the model and forbids both vertex collisions and edge swap collisions. CBS decomposes the problem into the high-level constraint tree and the low-level single-agent planning problem and produces an optimal solution, ECBS and focal-search variations sacrifice optimality for speed [9]-[12].

The mismatch with UAV physics is significant. Classical MAPF models agents as point masses, with unitary moves, synchronous decisions, and discrete collisions. Continuous-time, kinematic, heterogenous geometry, and kinodynamic extensions alleviate the discrepancy but raise the complexity of search [13][14][35]. Hence, in a practical pipeline for UAVs, one could use CBS to compute the order of routes and time windows and refine trajectories with continuous collision checking using a polynomial approach. Thus, it preserves the combinatorial nature of MAPF while avoiding pretending that paths in grids are flyable.

PrPMSM provides efficient solutions for repeated problems in a mostly static environment, while RRT-like algorithms quickly explore the high-dimensional space of possibilities. RRT* gives asymptotic optimality, while informed, bi-directional, kinodynamic, and safe-corridor variants improve convergence and feasibility, respectively. The interaction of multiple UAVs could be considered either in the joint configuration space, by means of prioritized planning, or by sampling individual routes and scheduling time separately. Joint-space planning is conceptually elegant but suffers from the curse of dimensionality. On the other hand, prioritized planning scales better, although it might be incomplete and affected by the order of priorities [36]-[38]. Finally, sampling is particularly relevant in serving as a global frontend for discovering homotopy classes of routes amidst difficult obstacles. The sampled route should normally be smoothed and time parameterized with B-splines, Bézier curves, minimum snap polynomials, or some sort of constrained optimization. In dynamic environments, a local replanner or safety controller would still be needed because building a global tree on sensor rate is seldom possible.

Trajectory optimization represents each route in terms of states, controls, waypoints, splines, or polynomial coefficients and tries to minimize time, energy, smoothness, exposure, or formation error [67][68]. The pairwise separation constraint makes the feasible set non-convex. SCP, sequential quadratic programming, alternating minimization, difference of convex programming, and separating-hyperplanes reformulation convert the non-convex problem into a series of solvable subproblems [19][29][39]-[41]. Their performance depends on initialization, trust region, penalty construction, and collision detection methods. MADER algorithm is an example of a decentralized asynchronous scheme. Each agent is trying to optimize a piecewise polynomial trajectory using convex outer approximations of trajectory segments; separating planes between polyhedra are made optimization variables, making possible time continuous collision detection with static obstacles, moving obstacles, and other agents [19]. RMADER uncovers the communication assumption that has been implicit so far: a trajectory optimized on the basis of outdated information about neighbors might be unsafe until they get the information and update. Its delay checking and two stages of publication make sure that the last committed safe trajectory will survive a bounded-delay verification period [20]. Dynamic feasibility follows only if a dynamically valid trajectory is returned and validated at the intended controller rate; nonconvex initialization or infeasibility can defeat this condition. RMADER’s guarantee depends on a known delay bound and successful delay check. In its published hardware evaluation, the 50 ms bound was exceeded for approximately 25% of mesh-network delays, so collision-free observed flights in those cases are E, not guaranteed [20].

Particle swarm optimization, genetic algorithms, differential evolution, ant colony optimization, artificial bee colony, grey wolf and wolf pack algorithms are popular due to the ease of encoding the problem with multiple objectives and arbitrary cost for threat, while requiring no gradient computation. The candidate solution generally consists of waypoint coordinates or spline control points. Hybrid versions include chaotic initialization, opposition learning, adaptive parameters, local search, or deterministic smoothing [43]-[49][69]. Their adaptability is real, although many comparisons are poorly conducted. New metaheuristics are often compared with untuned canonical alternatives on a limited number of synthetic scenarios, reporting convergence iterations without wall clock latency or flight dynamics feasibility. Stochastic planners should provide several repeated runs, confidence intervals, sensitivity analysis of population and penalty parameters, constraint repair overhead, and inference time. For online replanning, a deterministic solver with a warm start might beat a metaheuristic when the latter just barely finds a slightly shorter offline route.

Figure 3 illustrates how piecewise Bézier trajectories negotiate static threat regions in two planning scenarios [48]. The curved routes demonstrate the geometric relationship between trajectory smoothness and obstacle clearance. These examples help explain the role of continuous trajectory representations, but the displayed paths alone do not establish performance under moving obstacles, inter-UAV conflicts, or uncertain vehicle dynamics.

Figure 3. Example of optimization-based UAV path planning around static full-coverage threat regions using piecewise Bézier trajectories. Reproduced from Zhang, Liu and Feng (2023) [48], Scientific Reports 13, 16453, under the Creative Commons Attribution 4.0 licence; panels show two task scenarios from the source article’s Figure 2.

Potential fields use attraction to goals and repulsion from obstacles and neighbors. They are often inexpensive locally but can oscillate, become trapped, or deadlock in clutter; modifications such as tangential forces and virtual targets do not establish general completeness [50][51]. DWA scores velocity commands reachable over a short horizon; the modeled velocity and acceleration limits condition whether a command is flyable [56]. Chang et al. [57] report MATLAB 2019b simulations with three UAVs in each of two tasks (aggregation and target search), five randomly generated groups per task. Across the 10 groups, Table 1 gives success of 2/10 for DWA, 1/10 for APF, and 10/10 for the improved DWA-ORCA method, with average distance 19.91, 16.75, and 14.35 m and mean planning times 56.46, 36.95, and 48.75 ms per instance, respectively. The publication does not provide per-trial timing variance or processor specification for that comparison. These descriptive, small-sample simulation differences do not establish a general improvement or real-time flight safety.

Velocity obstacles consist of velocities resulting in a collision within a preselected horizon if another agent holds its estimated velocity. Reciprocal Velocity Obstacles distribute the avoidance responsibility, while ORCA transforms pairwise constraints into half-planes whose intersection determines allowed velocity. The algorithm is decentralized and efficient, being a de facto local multi-agent baseline [52]-[55]. Three assumptions warrant highlighting: estimates of states and velocities must be sufficiently accurate; agents must reciprocate in a reasonable manner; and the selected command must be dynamically trackable. Non-cooperative traffic, delayed intent information, narrow passages, and high-density infeasibility may break those assumptions. V-RVO and Voronoi-based variants reduce oscillations and incorporate local free space. Extensions for priority awareness and non-holonomy improve applicability. For UAVs, vertical clearance, anisotropic safety volumes, downwash, and acceleration constraints must be explicitly represented rather than projecting a planar disc model to 3-D. ORCA’s collision-avoidance result applies to reciprocal agents satisfying its constant-velocity, sensing, horizon, and feasible-velocity assumptions; UAV flight with delay and acceleration limits requires separate validation.

MPC repetitively predicts the evolution of the system, solves a finite-horizon optimization problem with constraints, applies the resulting first control and shifts the horizon. Distributed MPC allows each UAV to solve an optimization problem based on the predicted trajectories of neighboring agents. Distributed MPC unifies tracking, separation, obstacle avoidance, formation preservation, input limitations, and energy optimization into a single objective and constraint set [30]-[32][58]. Warm-starting and sparse nonlinear programming enable real-time processing for modest-sized teams. However, the computational complexity is not the only limitation. Recursive feasibility breaks when several hard collision constraints become incompatible with each other, late prediction comes in, or horizon cutting hides a looming dead-end. Slack variables ensure feasibility but degrade hard safety guarantees if there is no separate invariant fallback. Terminal sets, safe corridors, priority negotiation, tube MPC, and distributed consensus alleviate those problems. Mean solve time without worst-case analysis and deadline-miss statistics is inadequate as evidence for safety-critical claims. Constraint satisfaction refers to feasible, completed optimization under the modeled disturbance and communication bounds; real-time completion and recursive feasibility must be demonstrated or separately proved.

Control barrier functions h(x) define the safe set C = {x:h(x) ≥ 0}. Ensuring ḣ(x,u) + α(h(x)) ≥ 0 by means of quadratic programming yields the minimal change of a nominal command sufficient for maintaining forward invariance provided that the model is correct and the QP stays feasible. Higher-order CBFs accommodate relative degree constraints, while collision-cone CBFs capture relative motions. Multi-UAV safety can be made decentralized by imposing pairwise barrier constraints between local neighbors [59]-[63]. Large swarms expose the core limitation: several barrier constraints and actuator constraints may become mutually incompatible. Priority assignment, adaptive relaxation, responsibility allocation, backup controllers, and feasibility-aware CBFs are actively studied topics. Reachability analysis and Hamilton-Jacobi approaches offer stronger guarantees but suffer from a dimensionality curse. However, a practical design can employ reachability analysis offline to build invariant safety envelopes and CBF-QP online to enforce them. Forward invariance holds only on the certified safe set when the barrier inequality is continuously enforceable, state estimation and dynamics satisfy the assumptions, and the QP remains feasible; a relaxed or infeasible QP removes the claim. Figure 4 extends the geometric illustration to moving threat regions by showing successive receding-horizon path segments [48]. Updating the planned route as the threat configuration changes highlights the need to couple prediction with repeated replanning. The figure illustrates this planning mechanism; it does not by itself demonstrate a multi-UAV safety guarantee under sensing errors or communication delay.

Figure 4. Receding-horizon path segments generated against moving threat regions, illustrating the need to couple prediction and repeated replanning. Reproduced from Zhang, Liu and Feng (2023) [48], Scientific Reports 13, 16453, under the Creative Commons Attribution 4.0 licence.

Table 2 complements the algorithm-family comparison with 14 representative systems and their deployment evidence. It relates each mechanism to its dynamics, communication assumptions, claim level, validation setting, and remaining limitations. Separating simultaneous multi-UAV flight from simulation, transferable multi-robot evidence, and single-UAV demonstrations prevents results obtained under different experimental conditions from being treated as equivalent evidence of field readiness.

Table 2 appraisal key: UF = simultaneous multi-UAV flight; US = multi-UAV simulation or HIL; MR = transferable multi-robot; SU = single-UAV. F/C/E have the meanings in Section 2. A grouped row may mix evidence types; individual numerical outcomes inherit the exact source setting. NR means not reported or not verifiable from the cited source. This representative table does not constitute an independently screened cohort.

Table 2.Representative multi-UAV systems and their deployment evidence.

MARL models a cooperative navigation task as a decentralized partially observable Markov decision process. Centralized learning uses joint state and reward representations, while decentralized execution translates local observations into actions. Value-based methods fit well for discrete actions, while actor-critic methods like PPO, MAPPO, SAC, and TD3 fit better for continuous commands. Parameter sharing enables homogeneous swarms, while curriculum learning grows the team size, obstacle density or dynamics [21]-[26]. Learning resolves implicitly interaction problems that can hardly be solved manually, and ensures constant inference time. However, a poorly designed reward function may make a trade-off between rare collisions and average progress invisible. Training distributions typically exclude sensor failures, extreme density, non-reciprocal agents, actuator faults, and wind. Average success rate alone does not bound worst-case risk. Evaluation should thus cover out-of-distribution maps, randomized dynamics and latency, adversarial agents, uncertainty calibration, and confidence intervals over random seeds.

Swarm is naturally a dynamic graph: UAVs are nodes and sensing or communication relations are edges. GNN aggregates local neighbor features using the same weights, providing permutation invariance and an option for scaling team sizes. Attention mechanisms learn which neighbors or obstacles affect the action the most, while recurrent networks encode temporal context. Learned communication reduces intent exchange overhead but becomes brittle to topology changes, packet loss, or malicious communications [24][65].

The important comparison is not between GNN and non-GNN, but between learned messages and explicit exchange of relative-state and predicted-trajectory information at the same bandwidth and latency. Ablations need to include variations in neighbor-radius, graph-degree, drop-rate, quantization, and unseen team-size. Safety-critical systems require detection of graph-distribution shift and falling back to a provably safe local controller.

Hybridization is the most credible path to practical use. A global optimizer or learned policy suggests a route; trajectory optimization guarantees smoothness and satisfies actuator limitations; MPC tracking with replanning handles unexpected perturbations; ORCA, CBF-QP, or reachability provide the safety-critical fallback. Filtered reinforcement learning can project an unsafe action into the feasibility set in training and execution [66]. Residual learning learns a corrective term to a stable model-based controller, shrinking the space that must be learned. Smoothness and safety constraints in this architecture depend on feasible optimization, accurate models, valid uncertainty bounds, and a working fallback. The architecture itself provides no unconditional system-wide guarantee.

Nevertheless, safety filter is not a ceremonial end point. Feasibility region of the safety intervention, computation time deadline, switching transient effects, dependency on state estimation, and multiple constraint interactions must be analyzed. In case the learning policy frequently requests unsafe actions, the safety filter can induce deadlock or severe performance loss without collision. Rate and severity of safety interventions should be a reported metric, accordingly.

Figure 5 compares the success proportions and mean planning times reconstructed from the ten simulation groups reported by Chang et al. [57]. The improved DWA-ORCA method achieved success in all ten groups, while APF and DWA succeeded in one and two groups, respectively. APF had the lowest reported mean planning time, showing why computational cost and task success should be assessed together. The broad Wilson intervals reflect the small group count, and the absence of timing distributions and processor details limits conclusions about statistical superiority or real-time deployment.

Figure 5.Descriptive reconstruction of Chang et al. (2025) [57], Table 1: avoidance successes APF 1/10 (10%), DWA 2/10 (20%), improved DWA-ORCA 10/10 (100%), and mean planning time per instance APF 36.95 ms, DWA 56.46 ms, improved method 48.75 ms. The source reports 10 MATLAB 2019b multi-UAV simulation groups: five aggregation and five target-search tasks, each with three simulated UAVs, randomized starts/targets and obstacles, a 0.5 m obstacle radius, 1 m avoidance radius, 0.7 m/s maximum simulated speed, and 0.1 s default step [57]. Approximate post hoc 95% Wilson intervals for 1/10, 2/10, and 10/10 are 1.8% - 40.4%, 5.7% - 51.0%, and 72.2% - 100%, respectively; these intervals were calculated for this review, not reported by the source. The source does not disclose a hardware processor specification or trial-level timing spread, so timing uncertainty and deadline-miss probability cannot be estimated. The panels are descriptive within this benchmark, not a statistical superiority or flight validation claim.

Decentralized planner usually treats the latest obtained trajectory as up-to-date. Instead of considering only packet delay, we should consider age of information—a combination of sensing, estimation, computing, queuing, transmitting, and clock differences. Bounding delay can be achieved by robust tubes, bounded-prediction sets, asynchronous commitment protocol, event triggered updates, or conservative reachable sets. RMADER provides a good example: formally, the requirement is to check the time passed since the last observation at least once in a period equal to maximum possible communication delay [20]. In case the time passed is larger than the chosen bound, formal guarantee does not hold even if no collision happened experimentally. Complete packet loss is a special case which needs a special approach. Vehicle can reserve braking or loitering trajectories, increase uncertainty tubes, return to right-of-way rule, separate altitude layer, perform mission abort, etc. Communication-motion code design should solve both how to fly and what to communicate, because the geometry of flight determines link quality, and network load—safety [70].

Static map becomes outdated, dynamic object tracks are corrupted, and visual or lidar occlusions are correlated between nearby vehicles. Neighbor intent can be modeled as a communicated trajectory, constant velocity forecast, interaction model, Gaussian process, multimodal learned predictor, or bounded reachable set. Deterministic single mode forecast is dangerous in intersections as two individually plausible evasive actions can be incompatible. Chance-constrained or scenario MPC and belief-space planning allow trading efficiency for risk, requiring calibrated uncertainty. Statistical coverage or risk control requires explicit calibration and distribution/shift assumptions; unknown or expired bounds trigger the contingency specified in Section 3.1.

Point mass or double integrator models are helpful for algorithm development, but they might inflate the agility of the system. Fixed-wing UAVs have minimum speed, turn radius, and climb requirements; multirotors are differentially flat but have thrust, tilt, jerk, battery, and tracking bandwidth constraints. Downwash effects make safety anisotropic in vertical formations since the vertical separation volume is greater than the horizontal airframe radius. Downwash-aware trajectory planning has shown smooth trajectories for up to 200 simulated agents and 32 nanoquadrotor hardware experiments [37]. However, the offline-to-minutes planning approach contrasts with reactive unknown environment flights.

An energy model should incorporate more than just path length. Turns, acceleration, climbs, winds, payloads, communication, computations, and hovers cost energy. A swarm planner should reserve energy for contingencies, return to home base, or landing and should redistribute tasks if batteries are inconsistent. Multiobjective Pareto optimal analysis is preferable to combining all costs into unknown weights.

Heterogeneous swarms incorporate various radii, dynamics, sensors, endurance, and communication range. Symmetrical reciprocal algorithms and shared MARL policies may not work when avoiding capabilities differ. The responsibility must be allocated based on maneuverability, urgency, energy, and right-of-way. In a mixed airspace, cooperative UAVs need to coexist with unconnected drones, birds, helicopters, cranes, and emergency aircraft. Geofences, corridors, strategic de-confliction, remote identification, and contingency plans by standards and unmanned traffic management interfaces cannot be reduced to local obstacle avoidance anymore [71].

Table 3 converts the preceding comparisons into a proposed benchmark and reporting protocol spanning 14 evaluation dimensions. It pairs minimum metrics with reporting requirements and stress-test scenarios so that safety, mission completion, computational demand, communication, robustness, and deployment evidence can be assessed together. References attached to each dimension identify relevant methodological or application literature. The combined checklist, prescribed reporting requirements, and numerical event thresholds are recommendations of this review; they should not be interpreted as requirements or measurements reported by every cited source.

Benchmark definitions (prospective): Collision = physical contact or signed surface gap ≤ 0; near miss = positive gap below the prespecified safety buffer; mission success = mandatory objectives completed before the deadline with no collision, geofence or energy violation, or manual rescue; deadlock = goal progress < 0.1 m for each blocked agent over τ D = max ( 10 ,   s   2 T H ) , where T_H is the planning-horizon duration; livelock = ≥ 2 route or velocity reversals in the same τ D window with < 0.1 m net goal progress. Adapt numerical defaults to the platform before testing, hold them fixed for all methods, and report near-miss pairs and zero-success trials.

Table 3.Recommended benchmark and reporting protocol for deployable multi-UAV planning.

The current state-of-the-art moves from a deterministic clearance for a particular forecast to risk-constrained planning in a multimodal uncertainty. The scenario MPC, distributionally robust optimization, conformal prediction, and reachable-set learning are capable to deliver a coverage regardless of the unknown probability distributions. The challenge is computational—the number of pairwise uncertain constraints grows with the size of the swarm and the planning horizon. The local interaction graph, shared latent intention, and adaptive risk assignment might make this approach computationally feasible. Conformal or distributionally robust coverage depends on the particular assumptions about exchangeability or the ambiguity-set; they cannot be claimed under any distribution shift.

Large language and vision-language models are able to interpret mission rules, build a semantic cost map, resolve conflicts, or propose high-level contingency actions. The models are not meant to command collision-sensitive maneuvers without deterministic interface. The credible pipeline includes a foundation model that produces a goal, constraints, or plan candidates; a compiler to verify their syntax and policy; an optimizer to assure their feasibility; and a safety controller to guarantee safe execution. Hallucinations, prompt injection with an external message, timing uncertainties, and auditability have to be considered.

Simulations enable curriculum learning and generation of rare events, and digital twins can have platform-specific propulsion, sensors, networks, weather, and urban geometry. The differentiable physics and system identification allow better calibration. However, validation should not stop here—an assurance ladder approach is needed to move from unit tests and falsification through Monte Carlo simulations, software/hardware-in-the-loop, cage flight, controlled outdoor flight, and representative missions. The counterexamples discovered at every step are supposed to go back to training and validation phases.

Periodic broadcasting of the entire trajectory uses unnecessary bandwidth in the case of a predictable movement, overloads dense swarms. The event-driven broadcasting broadcasts changes once the prediction error, the collision risk, or the intent change passes a certain threshold. Semantic communication communicates latent task- or safety-relevant variables, not raw data. The planner and the network should be designed jointly such that the compression error and silence encode the safety signal. Security and authentication are crucial since spoofing of the intent can lead to intentional collisions and denial of service.

Delivery and inspection missions of dense swarms involve strategic deconfliction at minutes-to-hours timescale and tactical avoidance at seconds-to-milliseconds timescale. Corridor assignment, altitude stratification, vertiport capacity, weather, noise, energy pricing, and priority traffic produce a multi-layered optimization problem. The swarm planning algorithms should interface with the traffic management system while maintaining safety under network degradation. It requires compositional guarantees in the strategic, tactical, and control layers.

In the future, the teams will reconfigure themselves in response to failure, recharge, communication relaying, and sensing roles. Hence, the planning should focus not only on trajectory but on interaction graph, information value, and task redundancy. Meta-learning and graph policies will help in the adaptation process while formal contracts will define the expectations from the neighbors. The graceful degradation resulting in partial mission completion while preserving safety is a preferable objective to nominal optimality.