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Decentralized Scalable Exploration via Emergent Adaptive Lévy Walks on Minimal-Sensing Platforms
Wai Lun Leong, Teo Swee Huat Rodney
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%
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Summary
This paper introduces the Sensor-Driven Lévy Walk (SDLW) controller, a lightweight, decentralized algorithm for autonomous exploration by palm-sized nano-UAVs. The controller combines discrete Lévy step-length sampling with a sensor-reactive heading policy using a von Mises distribution. By adapting the heading bias based on local range measurements (openness), the system achieves scalable multi-robot exploration with improved coverage and reduced collisions compared to baseline methods, all while operating within the strict computational and sensing constraints of sub-50g platforms like the Bitcraze Crazyflie.
Entities (7)
Relation Signals (6)
SDLW → uses → von Mises distribution
confidence 95% · The method combines discrete Lévy step-length sampling with a sensor-reactive heading policy using directional range measurements... selects headings using a von Mises distribution
SDLW → targets → nano-UAV
confidence 92% · We present a lightweight sensor-driven Lévy walk (SDLW) controller for aerial robots weighing under 50 grams
SDLW → improves → Coverage
confidence 90% · Simulation results show coverage improvements of 79.6% in open arenas
SDLW → reduces → collision
confidence 90% · with collision reductions of 13.0%, 7.1%, and 1.4%, respectively
Bitcraze Crazyflie → uses → Multi-ranger deck
confidence 90% · Crazyflie setups use a Multi-ranger deck for four directional distance readings
SDLW → evaluatedin → IR-SIM
confidence 85% · We evaluate the proposed Sensor-Driven Lévy-Walk (SDLW) controller in the open-source IR-SIM simulator
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Abstract
Abstract:Efficient autonomous exploration with palm-sized nano-UAVs remains challenging due to severe limitations in sensing, computation, and flight endurance. We present a lightweight sensor-driven Lévy walk (SDLW) controller for aerial robots weighing under 50 grams and equipped with sparse local sensing. The method combines discrete Lévy step-length sampling with a sensor-reactive heading policy using directional range measurements. Each robot independently samples its Lévy exponent from a uniform prior to diversify exploration without inter-robot communication for exploration control. Each robot then selects headings using a von Mises distribution that biases motion toward open directions while preserving superdiffusive exploration properties. The controller operates at constant computational cost, enabling scalable multi-UAV exploration. Simulation results show coverage improvements of 79.6% in open arenas, 43.1% in rooms-and-corridors layouts, and 13.6% in cluttered environments, with collision reductions of 13.0%, 7.1%, and 1.4%, respectively, relative to a uniform-heading Lévy walk baseline. This work provides a practical framework for scalable multi-robot exploration on minimal-sensing, resource-constrained nano-UAVs.
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- Source: https://arxiv.org/abs/2607.25195v1
- Canonical: https://arxiv.org/abs/2607.25195v1
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Decentralized Scalable Exploration via Emergent Adaptive Lévy Walks on Minimal-Sensing Platforms Wai Lun Leong1 and Teo Swee Huat Rodney2 Additional material including the open-source code is available at https://github.com/williamleong/sdlw.1,2Wai Lun Leong and Teo Swee Huat Rodney are with the National University of Singapore, Singapore william.leong, tsltshr@nus.edu.sg Abstract Efficient autonomous exploration with palm-sized nano-UAVs remains challenging due to severe limitations in sensing, computation, and flight endurance. We present a lightweight sensor-driven Lévy walk (SDLW) controller for aerial robots weighing under 50 g50\,g equipped with sparse local sensing. The method combines discrete Lévy step-length sampling with a sensor-reactive heading policy using directional range measurements. Each robot independently samples its Lévy exponent from a uniform prior to diversify exploration without inter-robot communication for exploration control. Each robot then selects headings using a von Mises distribution that biases motion toward open directions while preserving superdiffusive exploration properties. The controller operates at constant computational cost, enabling scalable multi-UAV exploration. Simulation results show coverage improvements of 79.6% in open arenas, 43.1% in rooms-and-corridors layouts, and 13.6% in cluttered environments, with collision reductions of 13.0%, 7.1%, and 1.4% respectively, relative to a uniform-heading Lévy walk baseline. This work provides a practical framework for scalable multi-robot exploration on minimal-sensing, resource-constrained nano-UAVs. I Introduction Palm-sized nano-UAVs offer a critical capability for time-sensitive search-and-rescue missions in hazardous post-disaster environments, such as structurally unstable buildings, confined spaces with toxic atmospheres, or rubble-filled passages where human access is dangerous or impossible, yet autonomous exploration remains challenging due to severe constraints in onboard sensing, computation, and flight endurance. These constraints often rule out SLAM-centric or optimization-heavy planning. Recent work has demonstrated that lightweight SLAM can run onboard nano-UAVs using minimal time-of-flight (ToF) sensors and Cortex-M microcontrollers [3, 9], but such systems still require careful algorithm optimization; for missions where only coverage rather than detailed mapping is required, simpler reactive approaches remain attractive. In such regimes, reactive controllers that rely only on local measurements are appealing: they incur constant computational cost, avoid map maintenance, and maintain constant-time complexity with multiple agents without inter-robot communication. Among minimalist search processes, Lévy walks provide a principled balance between short local probes and occasional long relocations via heavy-tailed step lengths that yield superdiffusive dispersion; the model and its broad relevance have been surveyed in depth in physics and biology [12]. Recent theory on the discrete two-dimensional grid ℤ2Z^2 shows that for parallel search there is an optimal exponent α∈(2,3)α∈(2,3) that depends on team size k and search scale ℓ . Sampling each agent’s exponent independently and uniformly in (2,3)(2,3) achieves near-optimal parallel search performance over wide ranges of k and ℓ (within polylog factors) . The same line of work formalizes the discrete Lévy walk with integer jump distances distributed as P(d=0)=1/2P(d=0)=1/2 and P(d=i)∝i−αP(d=i) i^-α for i≥1i≥ 1 [2]. Preserving this discrete formulation helps keep execution lightweight while remaining aligned with theoretical guarantees. Translating these ideas to resource-constrained robots has taken several directions. One approach biases headings using a priori target densities, selecting directions from a von Mises distribution centered on the gradient ∇P∇ P of a known field; this bias improves search when a reliable prior exists, but it presupposes access to that prior, which nano-UAVs commonly lack [7]. A second approach designs information-correlated Lévy walks in which each step’s heading maximizes predicted mutual information with an occupancy map under construction; this improves mapping but requires maintaining a map and evaluating information gain at each step [10]. A third approach modifies Lévy motion using potential fields for obstacle avoidance and inter-robot spacing [11]. Related work also explores reactive Lévy-like dispersion without communication to speed up coverage, and collective Lévy-walk mechanisms to preserve heavy-tailed properties at larger swarm sizes [1, 6]. Gap and Goal We propose a fully reactive, map-free controller combining discrete Lévy steps with sensor-driven von Mises heading selection. A sensor-weighted resultant from four directional ranges biases motion toward open space via an openness-to-concentration mapping, preserving superdiffusion. The design requires O(1)O(1) computation, no inter-robot communication, and maintains constant-time complexity across team sizes. I-A Problem Statement and Assumptions We consider a team of k palm-sized nano-UAVs tasked with coverage-oriented exploration of a bounded, cluttered 2-D domain. This work targets platforms such as the Bitcraze Crazyflie nano-UAV (mass around 27 g to 33 g27\,g33\,g)[4, 8], which exemplifies the sub-50 g50\,g minimal-sensing constraint. In prior indoor exploration deployments, Crazyflie setups use a Multi-ranger deck for four directional distance readings and a Flow deck for optical-flow motion estimation [8]. Sensing. Each UAV acquires four directional distance measurements in its local frame (front, left, right, back) per control cycle. This sparse sensing provides essential environmental information while maintaining a minimal computational burden. Critically, there is no global localization, no map building, and no access to priors such as target distributions or occupancy models. Each agent must decide reactively, based exclusively on current local distance measurements. Computation. Onboard compute is severely constrained. All control updates must execute in constant time O(1)O(1) with kilobyte-scale memory. This rules out map maintenance, global optimization, and complex state estimation, placing strong emphasis on lightweight, reactive controllers. Communication and coordination. Search behavior is fully decentralized and does not rely on inter-robot communication for exploration control. Lightweight message passing may still be available for mission-critical events (e.g., safety or failsafe alerts), but it is not used for search decisions. This preserves scalable emergent multi-robot behavior while avoiding communication-dependent exploration logic. I-B Contributions This work contributes: 1. Sensor-Driven Lévy-Walk search controller for nano-UAVs. We propose a map-free, constant-time controller using only sparse local directional ranging to stochastically bias headings via von Mises distribution while executing discrete Lévy steps. 2. Theory-informed exponent randomization. Following established results that α∼Uniform(2,3)α (2,3) yields near-optimal parallel search performance, we realize this strategy on minimal-sensing nano-UAVs. 3. Sensor-adaptive stochastic steering. We introduce an openness-to-κ mapping that adapts von Mises concentration to local structure, preserving superdiffusive behavior while reducing collisions. 4. Comprehensive simulation evaluation. Evaluation across three arena types and five team sizes demonstrates 13%–65% coverage gains and 1%–29% collision reduction relative to baseline; simulation code is released to enable reproducibility and further exploration. 5. Design for nano-UAV resource constraints. We provide a constant-time implementation relying only on four directional readings and lightweight sampling suitable for sub-50 g50\,g platforms. I-C Related Works Theory of Lévy search. Clementi et al. establish that per-agent α∼Uniform(2,3)α (2,3) is near-optimal for parallel search on ℤ2Z^2 across unknown team sizes and scales. We adopt this result and validate its feasibility on resource-constrained platforms [2]. Biasing directions: prior fields vs. reactive sensing. Marthaler et al. bias headings using a known target-density gradient and a von Mises directional model, but their method requires priors [7]. Ramachandran et al. maximize mutual information for mapping, which requires maintaining a map and evaluating information gain each step [10]. Our reactive sensor-weighted von Mises achieves directional bias without priors or maps, suitable for constant-time nano-UAV control. Potential-field Lévy hybrids and reactive dispersion. Works combining Lévy motion with potential fields offer practical collision avoidance but rely on deterministic steering. Our stochastic von Mises policy maintains controlled randomness tunable via κ, better preserving superdiffusive properties. Reactive Lévy-like dispersion results support scalability without communication [11, 1, 6]. Minimal navigation for nano-UAV swarms. McGuire et al. demonstrate exploration with Crazyflie swarms using wall-following and RSSI-homing (SGBA), employing deterministic bug-algorithm steering [8]. Our work differs from this by using reactive stochastic heading selection throughout exploration, preserving Lévy walk superdiffusive properties without return-to-home infrastructure, focusing on coverage-oriented search rather than outbound-return missions. The above approaches lack a fully reactive, map-free, minimal-sensing controller that simultaneously (i) preserves superdiffusive Lévy properties, (i) exploits per-agent exponent randomization, and (i) adapts heading reactively to local geometry in constant time. We address this gap by combining discrete Lévy steps with a sensor-driven von Mises heading policy that biases motion toward open space while retaining controlled randomness. The controller requires no inter-robot communication and no shared map, enabling implicit cooperation through decentralized motion rather than explicit coordination. I Method This section formalizes the Sensor-Driven Lévy-Walk (SDLW) controller as a constant-time reactive pipeline. Each control cycle uses four local range measurements to estimate open directions, samples a discrete Lévy segment length to preserve heavy-tailed exploration, and selects a stochastic heading from a sensor-conditioned von Mises distribution. The resulting command is executed by a two-state Rotate/Move controller. The subsections follow this pipeline. Section I-A defines the minimal agent and sensing model. Section I-B specifies the discrete Lévy step-length sampler used to generate exploratory motion segments. Section I-C defines the sensor-weighted heading policy that biases those segments toward open space while retaining stochasticity. Section I-D then combines these components into the full reactive controller. I-A Agent and Sensing Model Consider k identical palm-sized nano-UAVs operating in a bounded, cluttered 2-D domain. Each agent i∈1,…,ki\!∈\!\1,…,k\ maintains a planar pose (xi,yi,ψi)(x_i,y_i, _i), where ψi _i is the yaw (heading). Per control cycle, the agent acquires a fixed set of directional distance measurements ℛi≜rF,rL,rR,rB,R_i \r_F,r_L,r_R,r_B\\!, corresponding to front (0)(0), left (+π/2)(+π/2), right (−π/2)(-π/2), and back (π)(π) directions in the agent frame (Fig. 1). There is no global localization and no mapping; search decisions rely only on ℛiR_i and constant-size state, without explicit coordination. I-B Discrete Lévy Step-Length Sampling Each agent performs motion in segments (“jumps”) of length d≥0d\!≥\!0. Let the agent’s Lévy exponent αi _i be sampled once at initialization, αi∼Uniform(2,3), _i (2,3), to diversify search across the team without explicit coordination. Given bounds dmin>0d_ \!>\!0 and dmax>dmind_ \!>\!d_ , we adopt the discrete law: Pr[d=0] [d=0] =12, = 12, (1) Pr[d=j] [d=j] =j−αi∑ℓ=jminjmaxℓ−αi,j∈jmin,…,jmax, = j^- _i _ =j_ ^j_ ^- _i, j∈\j_ ,…,j_ \, (2) where jmin=⌈dmin⌉j_ \!=\! d_ and jmax=⌊dmax⌋j_ \!=\! d_ . We retain Pr[d=0]=1/2 [d=0]=1/2 exactly to match the discrete formulation in [2] rather than introduce an extra design parameter. Operationally, a d=0d=0 draw yields a rotate-only cycle: the agent reorients to a new heading without forward motion, then samples a fresh step length d for the subsequent move phase. The same obstacle-threshold checks apply during rotation, so small axial or lateral nudges can occur if any range is below the safety threshold. Algorithm 1 provides the complete sampling procedure, which executes in constant time due to the fixed support size. Algorithm 1 Discrete Lévy Step-Length Sampler 1:α∈(2,3)α∈(2,3), dmin>0d_ >0, dmax>dmind_ >d_ 2:jmin←⌈dmin⌉j_ ← d_ ; jmax←⌊dmax⌋j_ ← d_ 3:With probability 1/21/2, return 0 4:Z←∑ℓ=jminjmaxℓ−αZ← _ =j_ ^j_ ^-α 5:Sample j∈jmin,…,jmaxj∈\j_ ,…,j_ \ with Pr[j]=j−α/Z [j]=j^-α/Z 6:return j I-C Sensor-Driven Stochastic Heading Selection RrFr_FrRr_RrLr_LrBr_B Figure 1: Sensor geometry (top-down view). The robot acquires four orthogonal distance measurements (rF,rL,rR,rBr_F,r_L,r_R,r_B) in its local frame, corresponding to front, left, right, and back directions. Let the four sensor directions in the world frame be Θ≜ψi,ψi+π2,ψi−π2,ψi+π. \ _i,\, _i+ π2,\, _i- π2,\, _i+π\. This sensing architecture matches platforms such as the Bitcraze Crazyflie, whose Multi-ranger deck provides exactly these four orthogonal distance measurements. We compute a sensor-weighted resultant that favors open directions and mildly penalizes moving backward. Define per-direction multipliers β=1,1,1,βBβ\!=\!\1,1,1, _B\ with 0≤βB≤10\!≤\! _B\!≤\!1 (backward penalty), and weights ws≜βsrs2,s∈F,L,R,B.w_s _s\,r_s^2, s∈\F,L,R,B\. The resultant vector is ≜∑sws[cosΘssinΘs],W≜∑sws,v _sw_s bmatrix _s\\ _s bmatrix, W _sw_s, with mean direction μ≜atan2(vy,vx)μ 2(v_y,v_x) and openness (see Fig. 2 for examples) (a) Open Corridor (b) Constrained Junction obstaclewFw_FwLw_LwRw_RwBw_Bv‖ large\|v\| large; o≈0.47o≈ 0.47 obstaclewFw_FwLw_LwRw_RwBw_Bv‖ small\|v\| small; o≈0.22o≈ 0.22 Figure 2: Sensor-weighted resultant in contrasting geometries. (a) Open corridor with large forward distance yields dominant wFw_F (proportional to rF2r_F^2), producing a strong unidirectional resultant v with high openness o. (b) Constrained T-junction with obstacles nearby in multiple directions yields more balanced weights and a weak, ambiguous resultant v with low openness o. oκ(o)κ(o)constrainedopen011κmin _ κmax _ Figure 3: Openness-to-concentration mapping. The linear mapping in (3) decreases von Mises concentration as openness increases: open spaces use lower κ for wider exploration, while constrained spaces use higher κ for more cautious steering. Markers indicate example openness values from Fig. 2. o≜‖W+ε,o∈[0,1],o \|v\|W+ , o∈[0,1], where ε>0 \!>\!0 is a small numerical guard that keeps the denominator nonzero in degenerate cases, such as when all usable range measurements are zero. The metric o quantifies the degree to which the weighted resultant is unidirectional; high openness indicates strong directional consensus (open space), while low openness reflects ambiguous or conflicting sensor signals (tight geometries). To preserve randomness in wide spaces yet be cautious in tight areas, we map openness to the von Mises concentration: κ(o)≜κmax−(κmax−κmin)o,κ(o) _ -( _ - _ )\,o, (3) with constants 0<κmin≤κmax0\!<\! _ \!≤\! _ (illustrated in Fig. 3). This linear mapping balances exploration and safety: in open regions where the weighted resultant is strong, lower κ values permit wider directional variance, allowing exploration of unvisited space. Conversely, in constrained corridors where geometry is ambiguous, higher κ values concentrate the distribution toward the strongest geometrical cue, reducing collision-inducing tangential excursions. This empirical adaptive strategy complements the discrete Lévy framework by making reactive headings responsive to local structure. Low κ (Exploration) Moderate κ High κ (Caution) μκ≈1κ≈ 1 μκ≈5κ≈ 5 μκ≈10κ≈ 10 Figure 4: Von Mises heading distributions at increasing concentration. Each panel shows sample angles (blue dots) drawn from VonMises(μ,κ)VonMises(μ,κ) with mean μ directed to the right (orange arrow). Low κ (left) permits wide directional exploration; high κ (right) concentrates samples tightly around μ, suitable for constrained navigation. The heading command θ for the next segment is sampled as θ∼VonMises(μ,κ(o)),θ (μ,\,κ(o) ), where the effect of varying κ on the heading distribution is shown in Fig. 4. The complete sensor-driven heading selection procedure is given in Algorithm 2. Algorithm 2 Sensor-Driven von Mises Heading 1:Ranges (rF,rL,rR,rB)(r_F,r_L,r_R,r_B), heading ψ, params (βB,κmin,κmax,ε)( _B, _ , _ , ) 2:Θ←ψ,ψ+π2,ψ−π2,ψ+π ←\ψ,\ ψ+ π2,\ ψ- π2,\ ψ+π\ 3:β←1,1,1,βBβ←\1,1,1, _B\; R←rF,rL,rR,rBR←\r_F,r_L,r_R,r_B\ 4:ws←βsRs2w_s← _s\,R_s^2; W←∑swsW← _sw_s; ←∑sws[cosΘs,sinΘs]⊤v← _sw_s[ _s, _s] 5:μ←atan2(vy,vx)μ 2(v_y,v_x); o←‖/(W+ε)o←\|v\|/(W+ ) 6:κ←κmax−(κmax−κmin)clip(o,0,1)κ← _ -( _ - _ )\,clip(o,0,1) 7:return θ∼VonMises(μ,κ)θ (μ,κ) I-D Control State Machine Fig. 5 depicts the two-state reactive controller structure. |wrap(θ−ψ)|≤δψ|wrap(θ-ψ)|≤ _ψRotateyaw →θ→ motionreached d or rF<rthr_F<r_th enter Move ⇒ sample d enter Rotate ⇒ θ←VonMises(μ,κ)θ (μ,κ) Inputs: rF,rL,rR,rB,ψr_F,r_L,r_R,r_B, : (μ,o)(μ,o), κ(o)κ(o)Safety (Rotate): axial nudges if rFr_F or rBr_B smallProgress: accumulate traveled distanceSafety (Move): lateral nudges if rLr_L or rRr_R small Figure 5: Two-state reactive controller. Agents alternate between Rotate, where heading error is reduced via yaw, and Move, where forward motion progresses until distance d is reached or an obstacle is detected (rF<rthr_F<r_th). The sensor-driven von Mises policy recomputes heading on each Rotate entry, adapting concentration κ(o)κ(o) to local geometry. We employ a two-state controller per agent: Rotate → Move. Let δψ _ψ be the heading tolerance, and τ the control period. Controllers initialize in Rotate with θ=0θ=0 and sample the first step length d at the first Rotate→ transition. Rotate If |wrap(θ−ψi)|>δψ|wrap(θ- _i)|> _ψ, apply a saturated yaw rate toward θ. During rotation, all four ranges are checked and small axial or lateral nudges are applied when any range falls below the safety threshold to create immediate clearance. Move Advance at constant speed until either (i) the traveled distance reaches d, or (i) an imminent obstacle is detected (rFr_F below threshold). In either case, switch to Rotate and resample heading via the von Mises policy. On the next Rotate→ transition, sample a new d via (1)-(2). Algorithm 3 presents the complete reactive Lévy-walk controller integrating discrete step sampling, sensor-driven heading selection, and the two-state control structure. Algorithm 3 Reactive Lévy-Walk Controller (per agent, per cycle) 1:if initialization then sample αi∼Uniform(2,3) _i (2,3) 2:if state = Rotate then 3: if |wrap(θ−ψ)|≤δψ|wrap(θ-ψ)|≤ _ψ then 4: d←d← sampleDiscreteLevy(αi,dmin,dmax)( _i,d_ ,d_ ) ⊳ Alg. 1 5: reset distance accumulator; state ← Move 6: else 7: apply yaw toward θ; axial or lateral nudges if any range is small 8: end if 9:else if state = Move then 10: update traveled distance from odometry/estimate 11: if (traveled ≥d≥ d) or (rF<rthr_F<r_th) then 12: (μ,o)←(μ,o)← sensorResultant(rF,rL,rR,rB,ψ)(r_F,r_L,r_R,r_B,ψ) 13: κ←κ(o)κ←κ(o); θ←sampleVonMises(μ,κ)θ (μ,κ) ⊳ Alg. 2 14: state ← Rotate 15: else 16: apply forward velocity; lateral nudges if rLr_L or rRr_R small 17: end if 18:end if I-E Collision Handling and Safety We adopt conservative thresholds on front/side ranges for emergency slowdown/stop and small nudges that push away from close obstacles. The openness mapping (3) increases κ in tight spaces, narrowing the von Mises spread and reducing collision-inducing grazing. Backward motion is discouraged by βB<1 _B<1 but permitted when necessary. I-F Implementation for Nano-UAVs The control design is amenable to efficient execution on resource-constrained microcontrollers. Computation employs fixed-size four-element vector operations and scalar arithmetic, eliminating dynamic memory allocation. Trigonometric functions employ lookup tables or polynomial approximations to reduce latency; random sampling for discrete Lévy and von Mises distributions uses lightweight generators with precomputed probability tables to minimize normalization overhead. These techniques preserve constant-time operation across all control cycles. The Bitcraze Crazyflie platform (STM32F405 ARM Cortex-M4, 168 MHz, 192 kB SRAM) exemplifies the target hardware; the minimal state requirements (only pose and heading estimates) are well within its memory constraints, supporting operation at the typical update rates (10–20 Hz) of nano-UAV flight control. I Experimental Setup We evaluate the proposed Sensor-Driven Lévy-Walk (SDLW) controller in the open-source IR-SIM simulator, a lightweight Python framework for navigation, control, and multi-robot scenarios with configurable robots, sensors, and environments [5]. Evaluation focuses on coverage efficiency and collision robustness across three representative arenas and five team sizes. We compare against a baseline (Uniform Heading Lévy Walk) under identical sensing, kinematics, and safety constraints to isolate the contribution of sensor-adaptive heading selection. I-A Simulator and Configuration Simulator. IR-SIM v2.9.0 provides collision detection, configurable holonomic kinematics, 1D time-of-flight range sensing, and scenario specification via YAML. Scenarios execute with physics integration and rendering disabled for high-throughput, repeatably randomized trials [5]. Arenas (all 20 m × 20 m): We evaluate on three environments representative of indoor nano-UAV operations: (1) Open—rectangular boundary, no internal obstacles; (2) Rooms-and-corridors—three rectangular rooms connected by a 2 m-wide horizontal corridor and a 4 m-wide vertical corridor with 1 m door openings; (3) Cluttered-50—50 randomly placed non-overlapping circular obstacles with radii in [0.2, 0.6] m. These span from geometrically coherent (open/structured) to geometrically ambiguous (random), testing heading adaptation across structure diversity. Representative layouts for the structured and cluttered arenas are shown in Fig. 6. (a) Rooms & Corridors (b) Cluttered (50) Figure 6: Representative arena layouts: (a) three rooms connected by a 2 m-wide horizontal corridor and a 4 m-wide vertical corridor with 1 m door openings; (b) 50 randomly placed obstacles (seed 42 example). Robot model. Holonomic kinematics with fixed forward speed 0.5 m s−10.5\,m\,s^-1, saturated yaw rate |ψ˙|max=0.5 rad s−1| ψ|_ =$0.5\,rad\,s^-1$ (28.6 ° s−128.6\, \,s^-1), and collision radius 0.10 m0.10\,m. These parameters reflect typical nano-UAV capabilities, with conservative speed and turn limits to allow safe operation in tight spaces and at low update rates. Sensing. Four orthogonal 1D distance readings (front, left, right, back) in the agent’s local frame, maximum range 4 m4\,m, simulating the Bitcraze Crazyflie Multi-ranger deck. Parameters. Step bounds dmin=0.5 md_ =$0.5\,m$, dmax=20 md_ =$20\,m$ span feasible segment lengths for sub-50 g50\,g platforms in 20 m20\,m×20 m20\,m arenas. Von Mises parameters κmin=0.6 _ =0.6, κmax=10 _ =10 provide directional spread in open areas while narrowing in confined spaces. Backward penalty βB=0.3 _B=0.3, heading tolerance δψ=5 ° _ψ=$5\, $, and obstacle threshold rth=0.4 mr_th=$0.4\,m$ use conservative safety margins suitable for 10–20 Hz onboard control. Baseline. Uniform Heading Lévy Walk (UHLW): identical discrete Lévy steps and safety-handling as SDLW, but heading selected uniformly from (−π,π)(-π,π) and the sensor-adaptive von Mises branch is bypassed. This isolates the contribution of sensor-adaptive heading selection. Experimental protocol. Team sizes: k∈1,2,4,8,12k∈\1,2,4,8,12\ agents. 50 independent random trials per condition, 15 minute horizon, grid-based coverage metric (0.25 m cells). IV Results We present results across three representative arenas and five team sizes. SDLW consistently outperforms UHLW, with gains correlated to environmental geometry coherence. IV-A Coverage Performance Fig. 7 shows that SDLW substantially accelerates coverage accumulation relative to UHLW across all conditions, achieving 79.6% higher mean coverage in Open, 43.1% in Rooms and Corridors, and 13.6% in Cluttered (50 obstacles) arenas consistently across all team sizes. Coverage gains are largest in structured environments and modest in random obstacles. Open arena Rooms & Corridors Cluttered (50) Figure 7: Coverage over time for k∈1,4,8,12k∈\1,4,8,12\ agents (columns); results with k=2k=2 omitted for brevity. Coverage is defined as the fraction of free-space grid cells (0.25 m0.25\,m resolution) visited by any team member. Mean coverage with standard-deviation shading over 50 trials. Blue: SDLW (sensor-adaptive); Purple: UHLW (uniform heading). SDLW substantially outperforms in structured environments, achieving 79.6% higher coverage in Open and 43.1% in Rooms & Corridors, with 13.6% advantage in cluttered layouts where sensor-adaptive heading benefits geometry-driven exploration. IV-B Safety and Robustness Fig. 8 summarizes collision robustness, showing consistent SDLW advantages across environments. In the Open arena, SDLW incurs 13.0% fewer mean collisions than UHLW across all team sizes, with the benefit particularly pronounced at larger k: at k=12k=12, SDLW achieves 4.08 collisions compared to UHLW’s 4.80. The Rooms and Corridors environment shows a moderate SDLW advantage, with 7.1% lower mean collisions and consistent improvements across most team sizes tested. In the Cluttered (50 obstacles) arena, SDLW maintains a modest collision advantage with 1.4% fewer mean collisions than UHLW overall. At moderate team sizes (k=8k=8), collision rates are comparable (2.92 vs. 2.94), while at k=12k=12 collision counts show SDLW with 5.72 and UHLW with 5.54. Collision reduction benefits are substantial in open and structured spaces, and modest in random obstacle layouts. The current logging pipeline records aggregate per-robot collision flags rather than classifying contacts as obstacle or inter-agent events, so these counts should be interpreted as overall collision robustness rather than type-specific failure rates. Figure 8: Collision events per trial across arenas and team sizes. Mean collisions for SDLW (ours, blue) and Uniform Heading Lévy Walk (UHLW, purple), with error bars showing standard error. SDLW demonstrates consistent collision reduction across all environments: Open shows a particularly strong 13.0% mean reduction, while Rooms & Corridors achieves 7.1% fewer collisions. Even in the cluttered arena, SDLW maintains a modest 1.4% collision advantage. The sensor-adaptive strategy provides collision benefits across environments, with the magnitude varying based on geometric structure coherence. IV-C Limitations Key limitations: (i) simulation assumes perfect noiseless sensing; real sensors exhibit noise and measurement artifacts; (i) 2-D planar model abstracts vertical dynamics and 3-D obstacles; (i) fixed parameters throughout execution; adaptive tuning could reduce parameter sensitivity by learning κ values from brief exploration phases, at the cost of increased computational overhead; (iv) hardware validation on actual nano-UAVs with real sensing and actuation latencies remains essential. V Conclusion This work presents a Sensor-Driven Lévy-Walk (SDLW) controller for palm-sized nano-UAVs, combining discrete Lévy step lengths with sensor-adaptive von Mises heading selection. 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