IAES Inter national J our nal of Robotics and A utomation (IJRA) V ol. 15, No. 3, September 2026, pp. 621 ∼ 638 ISSN: 2722-2586, DOI: 10.11591/ijra.v15i3.pp621-638 ❒ 621 Consensus-based path planning f or U A V swarms under multiple constraints: A r e view Y ana Lu, Lianpeng Li, Hui Zhao, Xu Zhao School of Automation, Beijing Information Science and T echnology Uni v ersity , Beijing, China Article Inf o Article history: Recei v ed Feb 9, 2026 Re vised Apr 27, 2026 Accepted May 22, 2026 K eyw ords: Classical path search Consistenc y constraints Deep reinforcement learning Intelligent optimization algorithms P ath planning Unmanned aerial v ehicle sw arm ABSTRA CT Unmanned aerial v ehicle (U A V) sw arms are essential for emer genc y response, logistics, reconnaissance, and en vironmental monitoring, yet achie ving safe and scalable path planning under dynamic conditions and comple x constraints re- mains challenging. Unlik e e xisting surv e ys that cate gorize algorithms by theo- retical foundations, this paper systematically re vie ws U A V sw arm path planning through the lens of spatial, temporal, and task-le v el consistenc y constraints . W e classify recent adv ances into classical path search, intelligent optimization, and deep reinforcement learning, emphasizing ho w each addresses geometric con- tinuity , beha vioral coordination, and full-chain perception–decision–planning consistenc y under multi-constraint coupling. W e further identify critical limita- tions in scalability , dynamic adaptability , and heterogeneous sw arm cooperation, and outline future directions, including distrib uted control, multi-source per - ception fusion, cross-platform coll aboration, and rob ust autonomous decision- making. This re vie w pro vides a unique, application-centric taxonomy based on consensus constraints, of fering actionable insights for de v eloping consistenc y- a w are U A V sw arm path planning technologies. This is an open access article under the CC BY -SA license . Corresponding A uthor: Li Lianpeng School of Automation, Beijing Information Science and T echnology Uni v ersity Beijing, China Email: llp@bistu.edu.cn 1. INTR ODUCTION W ith the rapid e v olution of autonomous intelligent systems, Unmanned aerial v ehicle (U A V) sw ar ms — composed of multiple U A Vs with autonomous perception, distrib uted decision-making, and cooperati v e interaction capabilities — ha v e sho wn transformati v e potential in emer genc y rescue, logistics, monitoring, and military reconnaissance [1], [2]. Recent breakthroughs in deep learning and sw arm intelligence ha v e further enhanced their situational a w areness and cooperati v e control [3]. As the foundation of sw arm cooperation, path planning directly determines mission safety and has become a k e y indicator of system intelligence. Ho we v er , research on U A V sw arm path planning under multiple consensus constraints remains in its early stages, with only a fe w studies ha ving just be gun to e xplore this challenging area [4]. U A V sw arm path planning aims to generate a set of feasible trajectories for the entire sw arm in c om- ple x en vironments while satisfying mission requirements. It must simultaneously ensure trajectory continuity , temporal synchronization, and task-le v el decision consistenc y , t hereby enabling coordinated mission e x ecution [5] and a v oiding ener gy inef cienc y or e v en obstacle a v oidance f ailures. When performing comple x missions in dynamic and uncertain en vironments, U A V sw arms are required to satisfy consensus constraints across mul- tiple dimensions, including spatial, temporal, and cooperati v e task aspects. J ournal homepage: http://ijr a.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
622 ❒ ISSN: 2722-2586 Specically , spatial constraints [6] require planned paths to be continuously e x ecutable [7], safe, and capable of ef fecti v e obstacle a v oidance; temporal constraints [8] emphasize mission synchronization, forma- tion maintenance [9], and consistenc y in action timing [10]; and cooperati v e task constraints [11] are reected in information e xchange [12], beha vior coordination, and strate gy unication among agents. W ith the increas- ing en vi ronmental dynamics, the strengthening coupling among heterogeneous constraints, and t he continuous gro wth of sw arm scale [13], path planning under multiple constraints has progressi v ely e v olv ed into a highly comple x problem characterized by high dimensionality , nonlineari ty , strong coupling, and multi-objecti v e op- timization. Consequently , the applicability of traditional path planning methods in such scenarios has become increasingly limited. T o address the abo v e challenges, research ef forts ha v e focused on problem modeling, constraint inte- gration and solution strate gies [14]. In classical path search, impro v ed heuristic functions, dynamic cost update mechanisms, and local conict resolution enhance the ability to handle dynamic obstacles, spatiotem po r al con- icts, and limited cooperati v e beha viors. Intelligent optimization algorithms, le v eraging strong global search and adaptability , enable sw arm-le v el cooperati v e optimization under comple x constraints, mo ving path plan- ning be yond geometric feasibility to w ard multi consensus constraint handling. Meanwhile, deep reinforcement learning and multi-agent learning allo w U A V sw arms to achie v e continual learning and distrib uted cooperation in dynamic, uncertain en vironments, of fering more adapti v e solutions for multi-constraint path planning. Despite signicant progress in e xisting research, maintai ning consensus among U A V sw arms in dy- namic en vironments remains a primary challenge for path planning. F actors such as en vironmental dynam- ics, multi-source perception inconsistencies, and platform heterogeneity often lea d to de g r aded cooperati v e performance [15]. Therefore, it is necessary to conduct a systematic re vie w from the perspecti v e of con- sensus constraints, with the aim of pro viding important theoretical support and technical references for the de v elopment of highly autonomous U A V sw arm systems. Unlik e e xisting surv e ys that cate gorize algorithms by theoretical foundations [16], this paper pro vides a no v el application-centric taxonomy based on spatial- temporal-cooperati v e task consensus constraints. It systematically analyzes ho w classi cal search, intelligent optimization, and deep reinforcement learning methods maintain consensus under multiple conicting con- straints, critically e v aluating their scalability , real-time performance, and suitability for heterogeneous sw arms. T o impro v e the structural clarity of the re vie wed methodologies, the o v erall path planning process for U A V sw arms can generally be summarized into se v eral interconnected stages, including en vironment percep- tion, constraint modeling, cooperati v e task allocation, global path generation, local dynamic replanning, and consistenc y maintenance. Dif ferent planning approaches re vie wed in this paper mainly dif fer in their imple- mentation strate gies for these stages, particularly in balancing global optimality , real-ti me adaptability , and cooperati v e consistenc y under multi-constraint en vironments, sho wn in Figure 1. Furthermore, it discusses planning challenges under multi-constraint coupling, including scalability , real-time performance, and hetero- geneous sw arm cooperation, and concludes with major challenges, future research directions, and application prospects. Figure 1. Ov erall frame w ork of the proposed consistenc y-a w are path planning methodology for U A V sw arms The structures of the paper are as follo ws. Section 1 describes models spatial, temporal, and co- operati v e constraints. Section 2 re vi e ws classical search, intelligent optimization, and DRL methods. Section IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 621–638 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 623 3 highlights scalability , real-time consistenc y , and heterogeneous cooperation as future challenges. Finally , the conclusion summarizes the paper . 2. SP A TIAL-TEMPORAL-COOPERA TIVE T ASK CONSENSUS CONSTRAINTS 2.1. Spatial, temporal, and cooperati v e task constraints in path planning U A V sw arm path planning must satisfy three critical constraint types. Spatial constraints ensure that the sw arm operates continuously , feasibly , and without collisions within geometric and en vironmental limits [17]. T emporal constraints maintain stability and coordination in both path e x ecution and decision-making. Cooperati v e task constraints require that the sw arm’ s beha vi o r s do not conict and collecti v ely achie v e globally optimal performance [18]. T ogether , these three constraints constitute a consensus constraint frame w ork for U A V sw arm path planning. In terms of spatial constraints, U A V sw arms must operate within a predened three-dimensi onal airspace, a v oidi ng no-y zones and pre v enting collisions with obstacles [19] to ensure safe and ef cient mission e x ecution. Static obstacles require that planned paths ef fecti v ely a v oid them at the initial planning stage028, whereas dynamic obstacles dem and real-time perception [20] and adapti v e traj ectory adjustment [21]. Conse- quently , path planning algorithms must possess high-le v el predicti v e capabilities and ef cient update mecha- nisms to handle such challenges ef fecti v ely . Re g arding temporal constr aints, U A V sw arms missions must be e x ecuted in a sequential manner to pre v ent congestion or collisions caused by premature or delayed actions of indi vidual U A V sw arm. This is particularly critical in scenarios such as emer genc y response, disaster monitoring, and rapid inspection, where mission e x ecution must be temporally continuous and coherent. Such requirements place high demands on the real-time performance and computational ef cienc y of path planning algorithms [22]. T emporal constraints additionally require rapid replanning capability under limited computational resources. Cooperati v e task constraints represent a distincti v e feature of U A V sw arm path planning. I n di vidual U A V sw arm within the sw arm are required to maintain appropriate spatial distrib ution and safety separation during mission e x ecution to a v oid collisions due to e xcessi v e proximity . Dif ferent U A V sw arms must achie v e complementarity and coordination in task allocation [23]. Furthermore, the sw arm needs to maintain netw ork connecti vity through wireless comm unication to enable real-time information sharing and decision-making consistenc y . Consequently , path planning must consider not onl y geometric and temporal feasibility b ut also communication range constraints and topological rob ustness, ensuring that the sw arm can cooperate stably in dynamic en vironments. 2.2. Pr oblem classication dimensions The cooperati v e collision a v oidance problem for U A V sw arms e xhibits di v erse mission object i v es, algorithmic implementations, and operational en vironment charact eristics. T o systematically address the afore- mentioned multi-constraint path planning problem, e xisting research typically classies the approaches along the follo wing dimensions. In Figure 2, a three-dimensional classication is conducted from the perspecti v es of task types, algorithmic characteri stics, and en vironment (En v). The algorithmic cate gory includes determin- istic algorithms (DEA), randomized algorithms (RA), centralized algorithms (CA), and distrib uted algorithms (D A). Figure 2. Cluster problem classication dimension Consensus-based path planning for U A V swarms under multiple constr aints: A r e vie w (Y ana Lu) Evaluation Warning : The document was created with Spire.PDF for Python.
624 ❒ ISSN: 2722-2586 2.2.1. T ask types In tracking missions, U A V s w arms are required to collaborati v ely track mo ving tar gets [24]. These tasks are commonly encountered in securit y patrols [25] and traf c o w monitoring [26], [27]. Collision a v oidance strate gies need to balance tar get-tracking accurac y with sw arm safety separation, particularly when both tar gets and obstacles are in motion, imposing high real-time requirements on path planning. In search and rescue missions [28], such as disaster relief or maritime search operations, U A V sw arms must rapidly locate tar gets in comple x and dynamic en vironments [29]. Collision a v oidance st rate gies in these tasks must not only handle static obstacles b ut also adapt to dynamic disturbances such as debris, smok e, and mo ving rescue equipment, while completing mission co v erage in minimal time. In man y practical applications, missions may simultaneously in v olv e co v erage, tracking, and search- and-rescue objecti v es. F or e xample, post-disaster aerial inspection requires area co v erage, real-time tracking of k e y tar gets, and searching for potential trapped indi viduals. Collision a v oidance strate gies for such comple x missions must possess high e xibility and the capability to switch task priorities dynamically . 2.2.2. Algorithmic featur es From the perspecti v e of algorithmic features, U A V sw arm path planning methods can be primarily classied along tw o dimensions: deterministic v ersus stochastic and centralized v ersus distrib uted. Determinis- tic algorithms [30] produce consistent outputs under identical initial conditions [31], of fering high predictability and stability . The y are well suited for scenarios with well-dened en vironmental models and clear mission ob- jecti v es [32]. In contrast, stochastic algorithms [33] introduce probabilistic elements into the decision-making process, enabling more di v erse solutions in highly uncertain en vironments or lar ge search spaces. These algo- rithms are commonly emplo yed for global search, a v oidance of local optima, and adaptation to dynamically changing mission conditions. Re g arding decision-making architectures, centralized algorithms [34] rely on one or a fe w central nodes to aggre g ate i nformation and mak e global decisions. The y can maintain full a w areness of system states and achie v e globally optimal solutions; ho we v er , the y impose high requirements on communication links and computational resources, and f ailure of central nodes may result in mission interruption. Distrib uted algorithms [35], on the other hand, allo w indi vidual U A V sw arm to mak e autonomous decisions based solely on local information e xchange [36], of fering higher rob ustness and scalability , and are suitable for lar ge-scale sw arms and communication-constrained scenarios [37]. Ne v ertheless, distrib uted algorithms may e xhibit limitations in global optimi zation and con v er gence speed [38], which can be mitig ated by designing appropriate local rules and information-sharing mechanisms. 2.2.3. En vir onmental characteristics Classication based on en vironmental characteristics primarily depends on en vironmental stability , which can be di vided into static and dynamic en vironments. In static en vironments, the positions of tar gets and obstacles are x ed, as in inspection and mapping tasks, allo wing for pre-planned trajectories and relati v ely simple algorithms. In dynamic en vironments, tar gets, obstacles, or conditions change o v er time, as in maritime search and rescue or traf c monitoring, requiring real-time perception and trajectory adjustment, making path planning more challenging. Additionally , en vironments can be cate gorized according to the a v ailability of en vironmental infor - mation into kno wn and unkno wn en vironments [39]. In kno wn en vironments, information such as maps of the mission area, obstacle locations, and tar get characteristics is a v ailable before mission e x ecution, f acilitating the use of global planning strate gies [40]. In unkno wn en vironments, such information is not fully accessible prior to task e x ecution, necessitating the use of U A V sensors [41] and cooperati v e perception capabilities [42] to progressi v ely b uild an en vironmental model. Online decision-making and local path planning techniques are then emplo yed to respond to une xpected changes [43]. Dif ferent en vironmental char acteristics directly af fect the comple xity of mission planning, perception systems, and control strate gies, making this classication an essential dimension in U A V sw arms task design. 2.3. Constraint modeling In the mathematical modeling of path planning, the proper formulation of constraints directly deter - mines the feasibility and optimality of the planned trajectories. Based on mission e x ecution characteristics and sw arm coordination requirements, spatial, temporal, and cooperati v e task constraints need to be mathematically IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 621–638 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 625 modeled to accurately describe the states of U A V sw arms, including position, v elocity , and heading. P ath plan- ning solutions are then obtained through objecti v e optimization, enabling the sw arm to ef ciently coordinate [44], a v oid obstacles [45], and accomplish task allocation and e x ecution [46] during mission operations. 2.3.1. Mathematical modeling The mission space is modeled as a three-dimensional Euclidean space, consisting of a feasible i ght re gion and an obstacle set that do not o v erlap. The U A V sw arm contains a total of N unmanned aerial v ehicles. At an y time, the state of each U A V includes its position v ector , its v elocity , and its heading angle. In terms of spatial modeling, study [47] i n t roduces a h ybrid approach that combines discrete and con- tinuous states to describe U A V sw arms. By linking discrete sw arm e v ents with continuous state v ariables, this approach captures the dynamic motion and interaction of U A Vs in three-dimensional space. The mission objecti v e is commonl y dened by a path cost function J , which considers multiple performance metrics, in- cluding ight distance, ener gy consumption, mission duration, and risk. Accordingly , the o v erall objecti v e can be formulated as: min P J = N X i =1 ( α 1 L i + α 2 E i + α 3 T i + α 4 R i ) (1) Where P denotes the set of trajectories of all U A V sw arms, L i represents the total path length, E i denotes the ener gy consumption, T i is the mission e x ecution time, and R i corresponds to the risk cos t. a k denotes the weighting coef cients, which are assigned according to task priorities. The weighting coef cients α k in (1) allo w for mission-specic trade-of fs, e.g., prioritizing ener gy ( α 2 ) o v er path length ( α 1 ) for long- endurance missions. T o ensure the fea sibility of planned trajectories, dynamic constraints are introduced at the modeling stage to reect the kinematic characteristics and platform performance limitations of U A V sw arm [48]. T yp- ically , the v elocity , acceleration, and rate of change of heading angle of each U A V are required to satisfy: ν min ≤∥ ν i ( t ) ∥≤ ν max , ∥ ˙ ν i ( t ) ∥≤ a max , | ˙ ψ i ( t ) |≤ ψ max (2) In (2), v min , v max , a max , and ψ max represent the platform’ s limits on speed, acceleration, and turning rate, respecti v ely . These dynamic constraints ensure kinematic feasibility . Spatial constraints are introduced to ensure the safe ight of U A V sw arm within the mission space. Specically , spatial safety constraints require that the ight trajectories do not intersect with obstacle sets while maintaining a prescribed minimum safety distance d min . ∥ p i ( t ) − p j ( t ) ∥≥ d min , p i ( t ) / ∈ Ω o (3) This constraint ensures that U A Vs f o l lo w planned trajectories within admissible attitude and v el ocity limits. It pre v ents aggressi v e maneuv ers that may cause e xcessi v e ener gy consumption, ight instability , or control f ailure, thereby guaranteeing the ph ysical feasibility and safety of the trajectories. T emporal constraints describe time coordination among U A Vs during mission e x ecution. The y ensure mission completion within a gi v en time windo w while maintaining synchronization and cooperati v e beha vior . In U A V sw arm planning, time af fects task ef cienc y , coordination accurac y , and system stability . In U A V sw arm cooperati v e missions [49], temporal constraints in v olv e more than indi vidual timing. The y also capture task sequencing and synchronization within the sw arm. F or tasks requiring coordination, such as collaborati v e reconnaissance, formation ight, distrib uted monitoring, or mult i-point strik es, the fol- lo wing constraints must be satised: t ar r iv e i ≤ t ar r iv e j | t ar r iv e i − t ar r iv e j |≤ ∆ t sy nc (4) Here, ∆ t sy nc represents the allo w able time synchronization de viation. The former applies to scenarios with sequential task requirements; the latter applies to scenarios requiri ng simultaneous arri v al or synchronized Consensus-based path planning for U A V swarms under multiple constr aints: A r e vie w (Y ana Lu) Evaluation Warning : The document was created with Spire.PDF for Python.
626 ❒ ISSN: 2722-2586 e x ecution, ensuring that all U A V sw arms perform actions within the permissible time de viation, thereby main- taining o v erall mission coordination. Cooperati v e task modeli ng. Cooperati v e task constraints are introduced to ensure that U A V sw arm systems achie v e information s h a ring, motion coordination, and decision consistenc y during mission e x ecution, serving as k e y elements for realizing ef cient collecti v e intelligence beha vior [50]. F ormation-k eeping constraints are introduced to ensure that U A V sw arm maintain a prescribed spatial geometric relationship during formation or cooperati v e missions [51]. Let r ∗ i denote the relati v e position of U A V i with respect to the formation center in the ideal formation. During actual ight, the follo wing condition must be satised: ∥ ( p i ( t ) − p c ( t )) − r ∗ i ∥≤ ε f (5) where p c ( t ) represents the position of the formation center and ε f denotes the allo w able formation tolerance. This constraint enables the U A V sw arm to maintain o v erall shape during maneuv ers, obstacle a v oidance, or tar get tracking, pre v enting e xcessi v e dispersion or structural disorder of the formation. Cooperati v e task constraints capture functional di vision and complementarity among U A Vs at the task le v el. F or multi-objecti v e missions, task allocati on must be both unique and complete, enabling global opti- mization under sw arm cooperation. These constraints help the sw arm maintain structural stability , coordinated beha vior , and information consistenc y in comple x, dynamic en vironments, thereby impro ving operational ef- cienc y and rob ustness. T ogether with spatial and temporal constraints, the y form the foundational modeling frame w ork for U A V sw arm path planning. The planning of the path of the U A V sw arm must accommodate v arious application s cenarios and strik e missions, each imposing dif f erent requirements on co v erage ef cienc y , tar get prioritization, formation maintenance, as well as path optimality and threat a v oidance [52]. F or heterogeneous sw arms, dif ferences in platform e nd ur ance, payload capacity , and sensing capabilities must also be considered [53]. Consequently , this problem is inherently a multi-objecti v e constrained optimization task, whose c o m ple xity arises from high- dimensional state spaces, dynamic en vironments, and sw arm coupling. In practice, a balance must be struck between modeling accurac y and computational feasibility to ensure mission ef fecti v eness while maintaining real-time performance. 2.3.2. Objecti v e optimization In U A V sw arm cooperati v e path planning and scheduling, the proper formulation of optimization objecti v es directly determines system performance and mission ef cienc y [54]. These objecti v es typically encompass multiple dimensions, including path length, ener gy consumption, time ef cienc y , safety , and task co v erage. Owing to v arying mission requirements, these objecti v es often conict with one another , necessitat- ing the use of multi-objecti v e optimization methods to achie v e ef fecti v e trade-of fs [55]. At the path planning l e v el , minimizing ight distance or mission completion time is a k e y objecti v e for impro ving operational ef cienc y , particularly in time-sensiti v e tasks such as emer genc y response and in- spection. This problem is typically formulated as a shortest-path or optimal scheduling problem and is solv ed using enhanced methods such as A*, ant colon y optimizati on , or particle sw arm optimization, balancing com- putational ef cienc y with path feasibility . At the mission le v el, sw arm planning aims to maximize task completion and area co v erage ef ciently under time and ener gy limits. This is critical for area search, en vironmental monitoring, and agricultural inspection, typically achie v ed via re gion partitioning or information-g ain-based co v erage models. From the perspecti v e of ener gy utilizati on, minimizing ener gy consumption is a critical objecti v e in U A V path planning [56], [57]. Ener gy e xpenditure is inuenced by f actors such as path length, i g ht speed, v ehicle dynamics, and en vironmental disturbances. By incorporating ight dynamics models and optimizing speed proles and trajectory design, ener gy ef cienc y can be signicantly impro v ed, which is particularly important in scenarios with limited endurance. The aforementioned optimization objecti v es in practical missions are often coupled and in v olv e trade- of fs among multiple criteria. Consequently , multi-objecti v e optimizat ion frame w orks are typically emplo yed in modeling and solution processes [58], using weighting coef cients to achie v e a balanced compromise [59]. Such optimization strate gies enable coordination among dif ferent performance metrics, allo wing the U A V sw arm to achie v e o v erall mission ef fecti v eness in comple x en vironments. IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 621–638 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 627 3. CONSISTENCY -CONSTRAINED PLANNING METHODS Research on U A V sw arm path planning in v olv es v arious methods that dif fer in computational com - ple xity , adaptability , global optimal ity , and real-time performance, as summarized in T able 1. These methods can be broadly classied into classical path search, intelligent optimization, machine learning and deep rein- forcement learning, as well as h ybrid and multi-objecti v e approaches that combine multiple techniques. T able 1. Ov ervie w of typical path planning techniques and their characteristics T echnology cate gory Main methods Adv antages Limitations En vironment modeling Grid-based [60], T opological graph [61], Continuous model- ing [62], Semantic Map [63] Clear information representation, adaptable to multiple scenarios T rade-of f between modeling accu- rac y and real-time performance Classical search Dijkstra [64], A* [65], D* [66], Theta* [67] High interpretability , guaranteed optimality under certain condi- tions High computational cost in high- dimensional scenarios Sampling-based meth- ods RR T [68], RR T* [69], PRM [70] Suitable for high-dimensional continuous spaces, capable of handling non-con v e x en viron- ments Requires post-optimization, global optimality is dif cult to guarantee Intelligent optimiza- tion Genetic algorithm [71], P article sw arm optimization [72], Ant colon y optimization [73] Strong global search capability , suitable for multi-objecti v e opti- mization tasks Slo w con v er gence and sensiti vity to parameter settings Deep reinforcement learning DQN [74], PPO [75], SA C [76], End-to-end na vig ation net- w orks [77] High adaptability and scalability , suitable for dynamic en viron- ments High training cost and limited generalization capability 3.1. Classical path sear ch-based methods In path pl anning, graph sear ch methods ha v e long been central due to their clear structure, i nter - pretability , and good con v er gence, as sho wn in Figure 3. W ith adv ances in unmanned systems and more com- ple x scenarios, traditional frame w orks ha v e been e xtended to impro v e inte grated optimization under temporal, spatial, and dynamic consistenc y constraints. These enhancements allo w planning results to better mat ch real missions and en vironmental dynamics. Figure 3. Logic diagram of classical algorithm, including Dijkstra, A*, RR T , and PRM, and compares their respecti v e characteristics in global search, heuristic guidance, and sampling-based planning Consensus-based path planning for U A V swarms under multiple constr aints: A r e vie w (Y ana Lu) Evaluation Warning : The document was created with Spire.PDF for Python.
628 ❒ ISSN: 2722-2586 The de v elopment of classical path search algorithms under consistenc y constraints has progressed from static optimization to dynamic consistenc y maintenance and then to multi-objecti v e coordination. Early methods, based on the traditional Dijkstra algorithm [78], focused on nding optimal paths in static graphs. As tasks e xpanded to comple x en vironments with v arying attrib utes, In 2021 [79], proposed the re v erse-label Dijkstra algorithm, which separates road tra v el time from intersection w aiting time and dynamically updates costs using a re v erse-label mechanism, ensuring path timing aligns with en vironmental attrib utes. In 2023, consistenc y constraints were further applied to state-space search and sensor calibration path planning [80]. The impro v ed Dijkstra method uses observ ability as the path cost and emplo ys dynamic error estimation with multi-path iteration to align error con v er gence with observ ability e v aluation, enabling optimal path search in high-dimensional error space and impro ving the stability and accurac y of system-le v el calibration. As application demands shift to w ard higher dynamic responsi v eness and continuity , path smoothness and dynamic feasibility ha v e become k e y e xtensions of classical search algorithms. T o addres s the A* algo- rithm’ s limitations in ef cienc y and smoothness, study [81] proposed the self-adapti v e neighborhood search A* (SANSA) algorithm. SANSA impro v es ef cienc y by adjusting the se arch neighborhood and obstacle han- dling, and applies path smoothing after generation. This ensures trajectories maintain geometric and kinematic continuity , enabling coordinated preserv ation of consistenc y and feasibility , marking a shift from discrete paths to continuous trajectories. W ith t he rise of U A V sw arm planning, classical search algorithms ha v e been inte grat ed with coop- erati v e mechanisms to support global consistenc y and multi-agent coordination. In [82] proposed a 3D jump point search (3D-JPS) cooperati v e algorithm, using incremental conict resolution, dual-objecti v e cost func- tions, and consistenc y constraints to maintain conict-free trajectories. In [83] introduced a h ybrid genetic algorithm-D* (GA-D*) method, combining genetic algorithm s’ global search with D*’ s dynamic replanning. Probabilistic constraints and incremental consistenc y mechanisms enable coordinated task all ocation and path planning. In summary , while classical search algorithms lik e A* and Dijkstra of fer theoretical optimality and high i nterpretability under static conditions , their e xtensions to dynamic en vironments ofte n suf fer from e xpo- nentially increasing computational costs. As summarized in T able 2, their primary limitation lies in maintaining real-time trajectory continuity and scalability for lar ge sw arms , a g ap that intelligent optimization algorithms attempt to ll, albeit with their o wn con v er gence challenges. T able 2. Classic path search algorithms and their consistenc y characteristics Algorithm Core mechanism Manifestation of consistenc y constraint Dijkstra [78] Systematically tra v erses all reachable nodes in the graph to guarantee the optimal path Static optimality consistenc y Re v erse-Label Dijkstra [79] Separates static path cost from dynamic temporal cost to impro v e adaptability in time-v arying en vironments Cost consistenc y Impro v ed Dijkstra [80] Performs optimal path search in high-dimensional state spaces, such as error or augmented state spaces State consistenc y SANSA [81] Conducts heuristic search follo wed by path smoothing optimization to enhance trajectory feasibility Motion consistenc y 3D-JPS [82] Resolv es path conicts among multiple agents in an incremental and prioritized manner Multi-agent cooperati v e consistenc y GA-D* [83] Combines the global search capability of genetic al- gorithms with the dynamic replanning of heuristic methods Dynamic cooperati v e consistenc y 3.2. Intelligent optimization-based methods Intelligent optimization algorithms, grounded in sw arm intelligence and e v olutionary m echanisms, e xhibit rob ust global search capabilities and adapt ability , rendering them well-suited for multi-constraint path planning in U A V sw arms. Early genetic algorithm-based path planning focused on path geometry and feasibility consistenc y . In 2024 [84], proposed a h ybrid genetic algorithm-rapidly e xploring random tree (GA-RR T) method, using RR T to b uild the initial population and applying redundant node elimination and path backtracking to impro v e path smoothness, obstacle-a v oidance continuity , and e x ecutability , turning consistenc y constraints into e xplicit operations. As U A V sw arm applications demand partial information, high dynamics, and strong coupling, IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 621–638 Evaluation Warning : The document was created with Spire.PDF for Python.
IAES Int J Rob & Autom ISSN: 2722-2586 ❒ 629 consistenc y e xtends to strate gy and task coordination. In [85] used multi-agent proximal polic y optimization (MAPPO) with a centralized v alue netw ork to ensure beha vioral and strate gy consistenc y among agents, while dynamic cluster particle sw arm optimization (DCPSO) applied dynamic clustering, potential eld constraints, and receding-horizon replanning to align search direction, v elocity , and path con v er gence. These approaches enhance system-le v el consistenc y , impro v e stability in mul ti-agent s cenarios, and reduce issues of local optima and beha vioral oscillations. In dynamic, real-time tasks, intelligent optimization algorithms e xtend consistenc y to full-chain syn- chronization across information, decisions, and planning. Methods lik e online multi-iteration ant colon y with receding-horizon [86] update en vironmental perception, resource states, and local costs at eac h step, k eeping planned paths consistent with the changing en vironment. In [87] proposed a modied ant colon y optimization (MA CO) within a tw o-step frame w ork. ant colon y optimization (A CO) plans feasible paths for ground v ehicles, and a genetic algorithm optimizes U A V ight strate gies. By enforcing consistenc y constraints on tak eof f/landing order , endurance, and path coupling, it achie v es global coordination for heterogeneous systems under road netw ork limits. This reects the e v olution of intelligent optimization algorithms from single-step to full-process consistenc y . In summary ,intelligent optimization algorithms e xcel at global search and multi-objecti v e optimiz a- tion, making them suitable for com ple x multi-constraint path planning. As summarized in T able 3, the y ha v e e v olv ed from ensuring geometric path continuity to achie ving full-chain information–decision–planning con- sistenc y . Ho we v er , their slo w con v er gence, parameter sensiti vity , and high computational o v erhead limit their use in highly dynamic or real-time scenarios. F or lar ge-scale sw arms or rapidly changing en vironments, intel- ligent optimization alone is insuf cient, often requiring h ybrid or learning-based inte gration. T able 3. Intelligent optimization algorithms and their consistenc y characteristics Algorithm Core mechanism Manifestation of consistenc y constraints GA-RR T [84] Global optimization search using heuristic methods P ath geometric consistenc y MAPPO [85] Centralized learning during training and distrib uted decision-making during e x e- cution Multi-agent strate gy consistenc y DCPSO [85] Adapti v e optimization of particle s w arm in dynamic en vironments Search process consistenc y Online Multi-iteration ant colon y strate gy [86] Online planning strate gy based on a receding-horizon windo w Information-decision consistenc y MA CO [87] Cooperati v e use of multiple algorit hms to solv e comple x planning problems Full-chain consistenc y T o pro vide a clear and intuiti v e comparison across the three methodological streams, T able 4 sum- marizes their k e y characterist ics in terms of real-time performance, adaptabilit y to dynamics, multi-constraint handling, scalability , and computational cost. T able 4. Comparati v e summary of path planning methods for U A V sw arms Algorithm class Real-time perfor - mance Adaptability to dy- namics Multi-constraint han- dling Scalability Computational cost Classical search High Lo w to medium High Lo w Medium to high Intelligent optimization Lo w Medium High Medium High Deep reinforcement learning High High Medium High Lo w Be yond the qualitati v e comparison in T able 4, e xisting studies indicate that classical search algorithm s generally achie v e f aster deterministic con v er gence in lo w-dimensional static en vironments, whereas intelligent optimization methods pro vide superior global e xploration capability under coupled constraints. Deep reinforce- ment learning approaches demonstrate stronger adaptability and scalability in highly dynamic en vironments, although their training comple xity and simulation-to-reality transfer remain signicant challenges. Therefore, dif ferent planning methods e xhibit distinct trade-of fs in computational ef cienc y , adaptability , and cooperati v e consistenc y maintenance. Consensus-based path planning for U A V swarms under multiple constr aints: A r e vie w (Y ana Lu) Evaluation Warning : The document was created with Spire.PDF for Python.
630 ❒ ISSN: 2722-2586 3.3. Deep r einf or cement lear ning-based methods Deep reinforcement learning (DRL) has become a k e y approach for U A V path planning in unkno wn and dynamic en vironments due to its adaptability and abi lity to handle high-dimensional continuous states. T o address dynamic, multi-modal, and communication-constrained scenarios, researchers enhance DRL with im- pro v ed re w ard functions, e xploration strate gies, and en vironment-coupled models, impro ving path continuity , decision stability , and en vironmental consistenc y . Early DRL studies introduced consistenc y constraints using h ybrid approaches. In [88] proposed rey algorithm-enhanced deep Q-netw ork (F ADQN), whi ch incorporated rey-inspired guidance into the DRL frame w ork. By simulating rey attraction, it pro vided directional action preferences to the Q-netw ork, producing smoother and more continuous paths during initial training, marking a shift from free e xploration to geometric consistenc y . As research mo v ed from geometric features to dynamic en vironmental consistenc y , study [89] proposed instructed reinforcement Q-l earning algorithm (IR-QLA), embedding e n vi ronmental signal strength into the re w ard. This instructed reinforcement allo ws U A V sw arms to adjust paths in real time, main- taining dynamic compli ance with temporal and en vironmental changes, e v olving from stat ic state consistenc y to real-time en vironmental consistenc y . T o address DRL limitations lik e slo w training and local optima, study [90] int roduced a cumulati v e re w ard model and re gion se gmentation mechanism. The cumulati v e re w ard decomposes path progress and en- vironmental sparsity into continuous re w ards, impro ving temporal consistenc y and controllabil ity , while re gion se gmentation imposes soft global constraints to pre v ent local loops and enhance polic y stability . In [91] pro- posed the constrained-interfered uid dynamical system (C-IFDS) algorithm, inte grating U A V kinematics and constraints into a DRL-based reacti v e disturbance planning frame w ork, producing high-quality , lo w-conict trajectories with maintained trackability and consistenc y . This stage reects DRL ’ s e v olution from ra pid con- v er gence to global consistenc y , enhancing rob ustness in comple x en vironments. W ith the inte gration of unmanned systems and communication netw orks, consistenc y constraints ha v e e v olv ed to w ard real-w orld modeling. In [92] combined dueling double DQN (D3QN) with simultaneous na v- ig ation and radio mapping (SN ARM) to b uild an online 3D radio map, using urban communication channels as ph ysical consistenc y constraints. This allo ws U A V sw arms to coordinate obstacle a v oidance, signal quality , and ight time. As illustrated in Figure 4, e xisting U A V sw arm path planning approaches can be broadly c lassied into three cate gories: classical path search–based methods, intelligent optimization–based methods, and ma- chine learning and deep reinforcement learning (DRL)–based methods. DRL methods of fer high adaptability and scalability for dynamic en vironments, handling high-dimensional state spaces and decentralized e x ecution in T able 5. Ho we v er , the y suf fer from high training costs, poor sample ef cienc y , simulation-to-reality g aps, and lack of safety/consistenc y guarantees. T o address these limitations, h ybrid frame w orks combining classical search, intelligent optimization, and DRL ha v e emer ged le v eraging interpretabilit y , global search, and adapt- ability . While a systematic h ybrid solution remains an open challenge, it is a promising direction for balancing real-time performance, optimality , and multi-constraint consistenc y . Figure 4. Consistenc y constraint method IAES Int J Rob & Autom, V ol. 15, No. 3, September 2026: 621–638 Evaluation Warning : The document was created with Spire.PDF for Python.