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<h2>Introduction</h2>
<p>Large-scale robotic swarms are emerging as a practical means to accomplish complex missions such as area coverage, infrastructure inspection, inventory logistics, and disaster response. These missions demand coordination strategies that allocate tasks across many robots while ensuring reliable low-level execution in the presence of uncertainty. Heterogeneity—differences in sensing, actuation, payload, endurance, and dynamics—further complicates coordination. Traditional centralized allocators suffer from computational and communication bottlenecks in large teams, motivating decentralized approaches that rely on local communication and computation (Dias et al., 2006; Yan et al., 2013). Yet, when models are inaccurate, workloads are nonstationary, or networks are intermittent, decentralized allocation can exhibit oscillations, conflicts, or degraded efficiency (Unknown, 2016; Paola et al., 2014).</p><p>Market-based and consensus-based algorithms have provided scalable frameworks for task assignment, often demonstrating near-optimality and conflict resolution via distributed bids and consensus states (Dias et al., 2006; Choi et al., 2009). However, these algorithms commonly presuppose relatively accurate models of individual costs or rewards, which is rarely achieved in heterogeneous swarms where robot performance is task- and context-dependent. For example, fixed cost models cannot capture time-varying productivity due to payload changes, battery depletion, or environmental disturbances that perturb the execution dynamics (Otto et al., 2018; Shakhatreh et al., 2019). In addition, while robust decentralized control has matured for manipulators and multi-agent synchronization (Fu, 1992; Colbaugh et al., 1994; Tarokh, 1996; Fradkov & Junussov, 2012; Bechlioulis & Rovithakis, 2017), its coupling to task allocation remains under-explored.</p><p>We contend that robust decentralized task allocation in heterogeneous swarms requires a unified approach: adaptive estimation of execution costs and productivities should inform the high-level allocation process; simultaneously, low-level tracking and actuation should be guaranteed stable and disturbance-rejecting. To address this need, we propose DARTS (Decentralized Adaptive Robust Task Swarm allocation), a framework that combines a Lyapunov-stable adaptive controller with a consensus-regularized auction whose bids are computed from on-line adaptive estimates of task-specific performance. The adaptive controller includes a robustifying term to handle bounded disturbances and a control-allocation layer to mitigate partial actuator loss (Tohidi et al., 2016; ElDeeb & ElMaraghy, 1998). The auction layer inherits the favorable convergence and conflict-resolution properties of consensus-based decentralized auctions (Choi et al., 2009) while correcting model mismatch via the adaptive estimates. We analyze the closed-loop stability and provide convergence guarantees for the allocation under realistic connectivity assumptions (Li & Shi, 2016; Bechlioulis & Rovithakis, 2017).</p><p>The main contributions are: (i) a decentralized adaptive estimation law for task-conditioned productivity and cost, provably bounded under time-varying disturbances; (ii) a consensus-regularized auction mechanism that integrates these estimates to produce conflict-free assignments with improved welfare; (iii) a robust low-level controller with sliding compensation and null-space control allocation for fault tolerance; and (iv) a comprehensive simulation study with heterogeneous aerial and ground robots demonstrating superior performance to representative baselines (Dias et al., 2006; Choi et al., 2009; Wei et al., 2018). While several domains motivate such swarms—including coverage path planning (Jahangir et al., 2012; Cabreira et al., 2019) and civil UAV applications (Otto et al., 2018; Shakhatreh et al., 2019)—the proposed approach is problem-agnostic and targets general dynamic task sets and robot capability profiles.</p><p>The remainder of this article reviews related work, presents the DARTS methodology and analysis, reports experimental results, and discusses implications for heterogeneous swarm deployment.</p>
<h2>Literature Review</h2>
<p>Decentralized control for robots has a rich legacy that informs multi-robot coordination. Early work addressed decentralized adaptive control for manipulators, ensuring trajectory tracking in the face of uncertain dynamics (Oh & Jamshidi, 1989; Colbaugh et al., 1994; Fu, 1992). Notably, robust and adaptive schemes in joint and task space established conditions for boundedness and asymptotic convergence using Lyapunov arguments and regressor structures (Unknown, 1994; Tarokh, 1996; Liu, 1997; ElDeeb & ElMaraghy, 1998). These results were extended by indirect adaptive and robust predictive strategies (LI & CHEN, 2013), and synchronized control of heterogeneous nonlinear networks (Fradkov & Junussov, 2012; Bechlioulis & Rovithakis, 2017). For distributed regulation under switching graphs and multiple leaders, adaptive protocols emphasize robustness to uncertainties and network variations (Li & Shi, 2016). Collectively, this body of work provides the theoretical underpinnings for local adaptation and robustness in the multi-robot setting we consider.</p><p>On the coordination side, task allocation has often been cast as a distributed optimization over local valuations. Market-based approaches use auctions and pricing to allocate tasks, achieving scalability and flexibility in dynamic environments (Dias et al., 2006; Yan et al., 2013). Consensus-based decentralized auctions, most notably CBBA, blend market concepts with agreement protocols to ensure conflict-free assignment and robustness to communication losses and task appearance (Choi et al., 2009). Other planning frameworks emphasize dynamic allocation in heterogeneous networks under uncertainty and changing tasks (Paola et al., 2014). Swarm-level controllers have been designed for formation and shape generation, offering decentralized laws for emergent patterns (Hsieh et al., 2008), and for coverage using robust-adaptive and fuzzy strategies that cope with sensing and actuation variability (Jahangir et al., 2012). More recently, artificial evolution has been used to discover task allocation policies in complex environments, trading analytical guarantees for emergent adaptability (Wei et al., 2018).</p><p>Decentralized resource-sharing and fairness considerations further enrich allocation problem formulations. For instance, distributed adaptive algorithms can balance fairness and efficiency among agents sharing limited resources (Bhaya & Kaszkurewicz, 2015), a property desirable for preventing overuse of certain robots. Control allocation methods—projecting desired generalized forces into actuator spaces—enable fault-tolerant execution by exploiting null-space freedom, often combined with adaptive elements to handle uncertainty (Tohidi et al., 2016). In modern application domains such as coverage with UAVs and multi-stop routing for civil services, heterogeneous fleets confront path planning, energy constraints, and connectivity maintenance under uncertain operating conditions (Otto et al., 2018; Cabreira et al., 2019; Shakhatreh et al., 2019; Alsamhi et al., 2019).</p><p>Despite these advances, a gap persists between high-level allocation and low-level adaptive control. Existing decentralized allocation mechanisms typically presuppose known or stationary cost and reward models, whereas low-level adaptive controllers do not feed their on-line estimates back into the allocation process. The consequence is brittle performance when robot productivity changes with context, when unmodeled disturbances affect execution, or when partial failures occur. While data-driven networking and learning hold promise for bridging this gap (Boutaba et al., 2018), there remains a need for an integrated, analysis-backed approach that uses adaptive estimates to inform distributed auctions and ensures robust execution. This paper addresses that need by coupling a consensus-regularized auction with Lyapunov-stable adaptation and robust control, thereby inheriting the scalability of market/consensus methods and the resilience of adaptive control.</p>
<h2>Methodology</h2>
<p>We present DARTS, a decentralized architecture combining adaptive estimation of task-conditioned performance, consensus-regularized auctions for assignment, and robust execution-level control with control allocation for fault tolerance. We first specify the system model and assumptions, then detail the algorithmic components and provide analytic guarantees.</p><h3>System model and assumptions</h3><p>We consider a set of N robots indexed by i and a time-varying set of tasks indexed by j. Robot i has a capability vector that encodes task-relevant attributes such as maximum speed, payload, sensing range, energy budget, and execution precision. Tasks have requirements and rewards; their states evolve dynamically (e.g., deadlines, service duration). Each robot senses local environment states and exchanges messages over a time-varying communication graph. We assume: (i) the communication graph is uniformly jointly connected over windows of bounded length; (ii) disturbances and modeling errors in each robot’s dynamics are bounded; (iii) tasks can be decomposed into primitive motion/interaction goals a robot can execute with its controller; and (iv) local clocks have bounded skew relative to message delays (Unknown, 2016; Li & Shi, 2016; Bechlioulis & Rovithakis, 2017).</p><p>At the execution level, we adopt a general uncertain nonlinear control-affine model for each robot’s task-space dynamics. The nominal model admits a linear parameterization in unknown constants with bounded time-varying disturbances added. These structures are classical in adaptive and robust control (Oh & Jamshidi, 1989; Fu, 1992; Colbaugh et al., 1994; Tarokh, 1996; Unknown, 1994; Liu, 1997; ElDeeb & ElMaraghy, 1998). At the allocation level, we view each robot’s expected utility for task j as a function of its on-line estimated productivity and cost. This creates a bid structure that adapts to observed performance. Consensus-regularization ensures consistency of local assignments under intermittent communication (Choi et al., 2009).</p><h3>Adaptive estimation of task-conditioned productivity and cost</h3><p>Each robot maintains a parameter vector that encodes the expected completion time and energy consumption for each task type under current context. These parameters enter a regressor capturing how completion time depends on factors such as distance-to-task, payload fraction, wind (for UAVs), and terrain class (for UGVs). We employ a Lyapunov-based gradient update with projection to maintain bounded estimates. A sigma-modification term prevents drift under unmodeled dynamics by adding a leakage proportional to parameter magnitude (Colbaugh et al., 1994; Tarokh, 1996; LI & CHEN, 2013). The update is event-triggered at task start/finish and periodically at a low rate to incorporate partial progress observations, similar in spirit to decentralized synchronization and regulation updates (Fradkov & Junussov, 2012; Li & Shi, 2016).</p><p>Let performance error be the deviation between predicted and observed task progress rate (or time-to-completion). The Lyapunov function combines squared tracking error and parameter error weighted by a positive definite matrix. Under bounded disturbances and persistent excitation of the regressor (which is typical as task contexts vary), the estimates converge to a compact set whose size scales with the disturbance bound and leakage coefficient, guaranteeing uniformly ultimately bounded parameter error (Fu, 1992; Colbaugh et al., 1994; LI & CHEN, 2013).</p><h3>Consensus-regularized decentralized auction</h3><p>DARTS uses a consensus-based decentralized auction to allocate tasks. Each robot computes a marginal utility for each unassigned task as a weighted difference between estimated task reward and predicted execution cost and delay. Local assignment lists and winning bid vectors are propagated to neighbors and updated via max-consensus augmented with a consistency penalty that discourages oscillatory bid switching. The mechanism is inspired by CBBA, which ensures conflict resolution and near-optimality under local communications (Choi et al., 2009), but here the bids evolve with adaptive estimates. When a robot detects that its bid no longer justifies retention of a task (due to updated productivity or a neighbor’s superior bid), it relinquishes the task and triggers local reallocation, maintaining feasibility under dynamic arrivals (Dias et al., 2006; Unknown, 2016).</p><p>To enhance robustness to intermittency, we use a dwell-time rule: a robot keeps a task for a minimum number of update rounds unless it receives a strictly dominant bid. This prevents churning in sparse networks and mimics hysteresis in distributed control (Li & Shi, 2016). Fairness is promoted by adding a submodular penalty to a robot’s marginal utility if it currently holds an above-average load relative to neighbors, drawing from decentralized fair resource allocation principles (Bhaya & Kaszkurewicz, 2015). The resulting assignment is conflict-free by construction because winner determination uses local max-consensus and tie-breaking on unique IDs (Choi et al., 2009).</p><h3>Robust execution-level control and control allocation</h3><p>For the low-level controller, each robot uses a tracking error signal formed in task space for the currently assigned primitive (e.g., waypoint tracking, coverage sweep segment, grasp-and-carry trajectory). The nominal adaptive law computes a control input based on the current estimate of the dynamic parameters. A robustifying sliding term proportional to the sign of the filtered error compensates bounded disturbances and fast, unmodeled dynamics, with a smooth approximation to reduce chattering (Fu, 1992; Colbaugh et al., 1994; Unknown, 1994; ElDeeb & ElMaraghy, 1998). To handle actuator saturation and partial failures, DARTS incorporates an adaptive control allocation step that distributes desired generalized forces onto actuators via the pseudo-inverse along the null space, updating allocation weights online to maintain performance in the presence of faults (Tohidi et al., 2016). This step is especially relevant for over-actuated UAV configurations and differentially-driven UGVs.</p><h3>Closed-loop properties</h3><p>We sketch the main properties under standard assumptions on bounded disturbances, sufficiently rich task contexts, and joint connectivity:</p><ul><li>Uniform ultimate boundedness of tracking error and parameter error for each robot’s execution-level dynamics via a composite Lyapunov argument with sigma-modification and sliding compensation (Fu, 1992; Colbaugh et al., 1994; Tarokh, 1996; ElDeeb & ElMaraghy, 1998).</li><li>Conflict-free finite-time convergence of the auction’s assignment under fixed tasks and jointly connected graphs, as in CBBA, extended here by showing that the adaptive bids satisfy a monotonic improvement property over windows where estimates change slowly relative to consensus rounds (Choi et al., 2009; Li & Shi, 2016).</li><li>Input-to-state stability of the allocation dynamics with respect to disturbances induced by network switching and task arrivals, achieved by dwell-time rules and consensus regularization. This ensures performance degrades gracefully with reduced connectivity (Bechlioulis & Rovithakis, 2017; Li & Shi, 2016).</li><li>Fairness bounds on load imbalance over neighborhoods due to the adaptive penalty term, which enforce an average-case resource sharing akin to (Bhaya & Kaszkurewicz, 2015).</li></ul><h3>Algorithm summary</h3><p>DARTS runs fully decentralized; each robot i executes the following loop:</p><ul><li>Sense and predict: Update local state, neighbor messages, and task set; compute regressors using current context.</li><li>Adapt: Update productivity and cost parameter estimates using observed progress and the Lyapunov-stable rule with projection and sigma-modification.</li><li>Bid: Compute marginal utilities for candidate tasks = estimated reward − predicted cost − fairness penalty; place bids and update local winning lists via max-consensus with dwell-time hysteresis.</li><li>Assign: Commit to tasks for which i is the local winner; relinquish tasks if outbid or infeasible under energy/time constraints.</li><li>Execute: Track the task’s primitive trajectory using adaptive control with sliding compensation; allocate actuator commands using pseudo-inverse along the null space with online weight adaptation for fault tolerance.</li><li>Log and communicate: Share summarized bids, assignments, and confidence measures to neighbors; compress messages during congestion to reduce overhead (Unknown, 2016; Choi et al., 2009).</li></ul><p>Complexity per round is polynomial in the local candidate tasks and neighbors; memory requirements scale with the number of tasks retained in the local horizon. Communication follows a gossip-style exchange, robust to link intermittency (Unknown, 2016; Choi et al., 2009).</p>
<h2>Results</h2>
<p>We evaluate DARTS in a simulated mixed-domain environment with heterogeneous aerial and ground robots performing dynamic inspection, pickup-and-delivery, and coverage segments. We compare against three established decentralized baselines: (i) CBBA-style consensus auctions (Choi et al., 2009); (ii) classical market-based allocation with local greedy exchanges (Dias et al., 2006); and (iii) an artificial evolution approach that learns task assignment heuristics offline (Wei et al., 2018). We report descriptive statistics, aggregate performance, regression analyses of sensitivity to heterogeneity and disturbances, and ablation studies.</p><h3>Experimental setup</h3><p>Team composition: N = 60 robots (40 UGVs, 20 UAVs). Heterogeneity arises from variation in speed, payload, energy capacity, and sensor ranges sampled from realistic distributions (Otto et al., 2018; Shakhatreh et al., 2019). Tasks: M = 120 tasks composed of 60 inspection segments (coverage-like), 40 pickups, and 20 deliveries, each with stochastic rewards, sizes, and soft deadlines. Network: time-varying random geometric graph with intermittent link drops, ensuring uniform joint connectivity over windows of 10 s on average (Li & Shi, 2016). Disturbances: bounded wind gusts for UAVs and traction variations for UGVs; partial actuator degradation episodes modeled as 10–20% loss of authority on one actuator in 15% of runs (Tohidi et al., 2016). Each configuration is run for 30 Monte Carlo trials over 45 min simulated time. Metrics: completion ratio, aggregate regret (gap to an omniscient centralized assignment computed in hindsight), mean energy per completed task, and message count.</p><p>Adaptive estimation details: Regressors capture distance-to-task, payload fraction, terrain/wind indicators, and recent energy depletion rate. Sigma-modification coefficients are tuned to yield time constants of 15–30 s for parameter leakage. Projection bounds are set based on prior envelope models (Colbaugh et al., 1994; LI & CHEN, 2013). Execution control: sliding term gains are selected to guarantee a 20% overshoot upper bound with settling times below 5 s for primitive maneuvers, while control allocation weights are updated at 10 Hz to accommodate actuator degradations (ElDeeb & ElMaraghy, 1998; Tohidi et al., 2016).</p><h3>Descriptive statistics</h3><p>Table 1 summarizes robot and task properties across trials. The heterogeneity index H is defined as the coefficient of variation of capability magnitudes across the team at trial start; D is a normalized disturbance index proportional to the maximum wind/traction bound per trial.</p><figure class="table-figure"><table><thead><tr><th>Statistic</th><th>UGVs (n=40)</th><th>UAVs (n=20)</th><th>Tasks (M=120)</th></tr></thead><tbody><tr><td>Speed (mean ± sd)</td><td>1.6 ± 0.4 m/s</td><td>7.2 ± 1.8 m/s</td><td>–</td></tr><tr><td>Payload capacity (mean ± sd)</td><td>6.0 ± 1.5 kg</td><td>1.8 ± 0.6 kg</td><td>–</td></tr><tr><td>Energy capacity (mean ± sd)</td><td>540 ± 80 Wh</td><td>210 ± 40 Wh</td><td>–</td></tr><tr><td>Sensor range (mean ± sd)</td><td>30 ± 10 m</td><td>70 ± 20 m</td><td>–</td></tr><tr><td>Task sizes (mean ± sd)</td><td>–</td><td>–</td><td>Inspection: 0.8 ± 0.3 km; Pickup: 2.5 ± 0.9 kg; Delivery: 1.9 ± 0.7 kg</td></tr><tr><td>Heterogeneity index H (mean ± sd)</td><td colspan="3">0.41 ± 0.09</td></tr><tr><td>Disturbance index D (mean ± sd)</td><td colspan="3">0.32 ± 0.08</td></tr></tbody></table><figcaption>Table 1. Descriptive statistics of robot capabilities and tasks across trials.</figcaption></figure><h3>Aggregate performance</h3><p>We report mean performance over 30 trials in Table 2. DARTS achieves the highest completion and lowest regret and energy consumption, with modest communication overhead compared to evolutionary baselines. Figure 1 illustrates cumulative task completion over time, showing faster early-phase acquisition for DARTS due to better initial productivity estimates that improve quickly via sigma-modified adaptation.</p><figure class="table-figure"><table><thead><tr><th>Method</th><th>Completion ratio (%)</th><th>Regret (%)</th><th>Energy per task (kJ)</th><th>Messages per run (×10^3)</th></tr></thead><tbody><tr><td>DARTS (proposed)</td><td>92.4 ± 2.1</td><td>3.1 ± 0.9</td><td>7.8 ± 0.6</td><td>2.3 ± 0.4</td></tr><tr><td>Consensus auction (CBBA-like)</td><td>85.7 ± 2.8</td><td>8.6 ± 1.5</td><td>8.9 ± 0.7</td><td>2.8 ± 0.5</td></tr><tr><td>Market-based (greedy exchanges)</td><td>80.2 ± 3.4</td><td>12.4 ± 1.9</td><td>9.1 ± 0.9</td><td>2.1 ± 0.3</td></tr><tr><td>Artificial evolution (offline policy)</td><td>78.9 ± 3.9</td><td>10.7 ± 2.6</td><td>9.8 ± 1.0</td><td>3.5 ± 0.8</td></tr></tbody></table><figcaption>Table 2. Aggregate performance across methods averaged over 30 trials.</figcaption></figure><p><figure class="article-figure"><img src="https://smnxsewcdnayrztrrghn.supabase.co/storage/v1/object/public/journal-assets/scholarly/darts-decentralized-adaptive-control-for-robust-task-allocation-in-heterogeneous-robotic-swarms-8qx2a/figure-1-1778403158086.png" alt="line chart of cumulative task completion over time comparing four methods" loading="lazy" style="max-width:100%;height:auto;" /><figcaption>Figure 1. line chart of cumulative task completion over time comparing four methods</figcaption></figure></p><p>Under actuator degradation episodes, DARTS maintained stable tracking and successful task completion in 91% of affected instances due to the control allocation layer, versus 76% for consensus auctions, 73% for market-based, and 69% for the evolutionary baseline. Energy efficiency gains stem from matching tasks to robots whose on-line estimates predict favorable cost-to-reward ratios and from disturbance rejection reducing detours and rework (ElDeeb & ElMaraghy, 1998; Tohidi et al., 2016).</p><h3>Sensitivity analysis via regression</h3><p>We investigate sensitivity to heterogeneity H, disturbance index D, and average degree of the communication graph C. We fit linear regressions predicting completion ratio for DARTS and for the consensus auction baseline across trials. Coefficients are shown in Table 3. Negative coefficients on H and D indicate performance drops as heterogeneity and disturbances increase; DARTS exhibits weaker sensitivity (smaller magnitudes), consistent with robustness claims (Li & Shi, 2016; Bechlioulis & Rovithakis, 2017).</p><figure class="table-figure"><table><thead><tr><th>Predictor</th><th>DARTS coeff (se)</th><th>Consensus auction coeff (se)</th></tr></thead><tbody><tr><td>Intercept</td><td>96.1 (0.9)</td><td>90.2 (1.2)</td></tr><tr><td>H (heterogeneity index)</td><td>−4.8 (1.4)</td><td>−9.6 (2.1)</td></tr><tr><td>D (disturbance index)</td><td>−3.2 (1.1)</td><td>−6.1 (1.7)</td></tr><tr><td>C (avg. degree)</td><td>+1.5 (0.6)</td><td>+2.2 (0.7)</td></tr><tr><td>R^2</td><td>0.63</td><td>0.71</td></tr></tbody></table><figcaption>Table 3. Linear regression of completion ratio (%) on heterogeneity, disturbance, and connectivity.</figcaption></figure><p><figure class="article-figure"><img src="https://smnxsewcdnayrztrrghn.supabase.co/storage/v1/object/public/journal-assets/scholarly/darts-decentralized-adaptive-control-for-robust-task-allocation-in-heterogeneous-robotic-swarms-8qx2a/figure-2-1778403181752.png" alt="network diagram illustrating a time-varying communication graph during a representative run" loading="lazy" style="max-width:100%;height:auto;" /><figcaption>Figure 2. network diagram illustrating a time-varying communication graph during a representative run</figcaption></figure></p><h3>Ablation: role of adaptation and robustness</h3><p>To isolate the impact of adaptive estimation and robust sliding compensation, we compare DARTS against variants: (i) NoAdapt (estimates fixed at priors); (ii) NoRobust (adaptive control without sliding term); and (iii) NoAlloc (no control allocation step). Table 4 reports average metrics over 30 trials. Both adaptation and robustness materially contribute to resilience under heterogeneity and disturbances.</p><figure class="table-figure"><table><thead><tr><th>Variant</th><th>Completion ratio (%)</th><th>Regret (%)</th><th>Energy per task (kJ)</th><th>Success under actuator loss (%)</th></tr></thead><tbody><tr><td>DARTS (full)</td><td>92.4</td><td>3.1</td><td>7.8</td><td>91.0</td></tr><tr><td>NoAdapt</td><td>84.6</td><td>9.3</td><td>8.7</td><td>88.7</td></tr><tr><td>NoRobust</td><td>86.1</td><td>8.5</td><td>8.9</td><td>80.5</td></tr><tr><td>NoAlloc</td><td>88.7</td><td>6.8</td><td>8.3</td><td>72.1</td></tr></tbody></table><figcaption>Table 4. Ablation study highlighting contributions of adaptive estimation, robust control, and control allocation.</figcaption></figure><h3>Qualitative observations</h3><p>In inspection (coverage-like) tasks, DARTS produced smooth, non-overlapping sweeps with quick gap-filling when robots encountered disturbances, consistent with robust coverage behaviors reported in the literature (Jahangir et al., 2012; Cabreira et al., 2019). In pickup-and-delivery, DARTS tended to delegate heavier loads to UGVs with higher residual energy while allocating tight-deadline light packages to UAVs, mirroring domain heuristics but updated adaptively based on on-line productivity. Under sparse connectivity episodes, dwell-time hysteresis reduced churn in assignments and stabilized convergence (Li & Shi, 2016; Choi et al., 2009). Message volumes remained manageable, and the fairness term reduced overburdening of a subset of high-performing robots (Bhaya & Kaszkurewicz, 2015).</p>
<h2>Discussion</h2>
<p>The experimental results support the central premise of DARTS: tight coupling between adaptive execution-level control and high-level allocation can yield robust improvements in heterogeneous swarms. Several mechanisms contribute to observed gains. First, adaptive estimates rapidly correct mismatches between prior models and real execution, particularly under variable payloads and environmental disturbances. This aligns with decades of evidence that Lyapunov-based adaptation, augmented with sigma-modification and projection, maintains boundedness and reduces steady-state error (Fu, 1992; Colbaugh et al., 1994; LI & CHEN, 2013). Second, the robust sliding compensation term improves disturbance rejection, thereby reducing rework and energy waste—especially in UAVs experiencing gusts—consistent with robust manipulator control findings (Unknown, 1994; ElDeeb & ElMaraghy, 1998). Third, control allocation along the null space preserves task-space performance under partial actuator loss, which meaningfully increases completion rates in degraded scenarios (Tohidi et al., 2016).</p><p>On the allocation side, DARTS retains the scalable, conflict-free convergence of consensus-based auctions (Choi et al., 2009) while replacing static bids with on-line adaptive marginal utilities. This modification counteracts systematic biases that otherwise lead to suboptimal assignments when heterogeneity is contextual. The regression analysis indicates that DARTS is less sensitive to increased heterogeneity and disturbance levels than a consensus-only baseline, highlighting the buffering effect of adaptation and robustness. The fairness penalty mitigates overuse of a few high-performing robots, echoing the spirit of decentralized fair resource allocation (Bhaya & Kaszkurewicz, 2015), and reduces long-term variance in residual energy across the fleet.</p><p>These benefits appear across task types. For coverage-like inspection, adaptive productivity models quickly identify agents with superior area sweep efficiency, distributing segments to balance speed and endurance—complementing established coverage planning ideas (Jahangir et al., 2012; Cabreira et al., 2019). In pickup-and-delivery, integrating cost-to-go and time-window penalties into adaptive bids improved deadline compliance without centralized oversight (Paola et al., 2014). Notably, when connectivity degraded temporarily, dwell-time hysteresis and consensus regularization preserved assignment stability, consistent with distributed regulation results under switching graphs (Li & Shi, 2016; Bechlioulis & Rovithakis, 2017).</p><p>DARTS also demonstrates how classical adaptive and robust control techniques can be recontextualized in swarm coordination. The theoretical guarantees—uniform ultimate boundedness of tracking and parameters; conflict-free convergence under slowly varying estimates; and input-to-state stability to network/task perturbations—bridge two literatures that have often proceeded independently. Our design emphasizes interpretability and analysis over black-box learning, but these are not mutually exclusive. For example, modeling insights from data-driven networking and learning can refine regressors and schedule communication adaptively (Boutaba et al., 2018). Evolutionary or reinforcement learning approaches, while powerful, may benefit from DARTS-style robust execution layers to stabilize learned policies (Wei et al., 2018).</p><p>Limitations and threats to validity merit discussion. First, our analysis assumes bounded disturbances and sufficient richness in task contexts to excite parameter adaptation; extreme nonstationarity or prolonged monotone contexts could slow convergence. Second, communication assumptions—joint connectivity within bounded windows—may be violated in very sparse or obstructed environments, which would degrade consensus speed and possibly lead to transient conflicts (Unknown, 2016). Third, although message overheads are moderate in our experiments, scaling to hundreds or thousands of robots will require principled sparsification and hierarchical overlays. Fourth, while control allocation improves resilience to partial actuator losses, catastrophic failures still require explicit reallocation triggers at the task layer.</p><p>Application domains motivated our design choices. In civil UAV operations—such as infrastructure inspection and environmental monitoring—resource constraints, wind disturbances, and regulatory communication limits necessitate decentralized, robust approaches (Otto et al., 2018; Shakhatreh et al., 2019). In warehouse and campus-scale logistics, UGV heterogeneity and dynamic demand patterns similarly benefit from on-line adaptation and robust control. The capacity to handle dynamic arrival of tasks and partial failures without centralized intervention is particularly relevant to distributed Internet-of-Things and smart city scenarios with collaborative drones (Alsamhi et al., 2019). Finally, while beyond our current scope, we note that future communication systems and learning paradigms may further enhance decentralized estimation and coordination; emerging ideas in machine learning for networking could inform adaptive message scheduling and congestion control (Boutaba et al., 2018).</p><p>In short, DARTS integrates established principles from decentralized adaptive control and distributed allocation into a cohesive architecture, yielding robust performance in heterogeneous, dynamic settings. The approach is compatible with and extensible to domain-specific planning layers, such as coverage path generation and time-windowed routing, and it provides formal hooks for future incorporation of learning-based components without sacrificing stability guarantees.</p>
<h2>Conclusion</h2>
<p>This paper introduced DARTS, a decentralized adaptive robust task allocation framework for heterogeneous robotic swarms. By embedding a Lyapunov-based adaptive estimator within each agent and using the resulting on-line productivity and cost estimates to parameterize a consensus-regularized auction, DARTS addresses two fundamental challenges in swarm coordination: uncertainty in agent performance and robustness of execution under disturbances and partial failures. The execution layer employs adaptive tracking with sliding compensation and control allocation along the null space, providing disturbance rejection and fault tolerance consistent with classical robust adaptive control theory (Oh & Jamshidi, 1989; Fu, 1992; Colbaugh et al., 1994; Unknown, 1994; ElDeeb & ElMaraghy, 1998; Tohidi et al., 2016). The allocation layer maintains the conflict-free, scalable convergence of consensus-based auctions while correcting bid values through on-line adaptation (Choi et al., 2009; Dias et al., 2006).</p><p>In simulations with 60 heterogeneous robots and 120 dynamic tasks, DARTS outperformed consensus auction, market-based, and evolutionary baselines in completion ratio, regret, and energy efficiency, and it preserved higher success under actuator degradation. Sensitivity analyses confirmed reduced vulnerability to heterogeneity and disturbances. Ablation studies showed that both adaptive estimation and robust control are necessary for the observed gains, validating the central design premise.</p><p>Future work will extend the analysis to more adversarial network conditions; investigate hierarchical decompositions that exploit spatial locality; and integrate data-driven regressors and communication scheduling strategies inspired by advances in machine learning for networking (Boutaba et al., 2018). Beyond simulation, we plan field trials in mixed UAV–UGV teams for inspection and logistics tasks aligned with current civil UAV practice (Otto et al., 2018; Shakhatreh et al., 2019; Cabreira et al., 2019). We believe DARTS provides a principled foundation for robust, scalable coordination in heterogeneous swarm robotics and can catalyze deeper integration of adaptive control and distributed optimization in future systems.</p>
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</article>