Strategy Forest: Decentralized UAV Exploration

• Strategy Forest is a decentralized UAV exploration method that builds voxel maps and dynamically switches between Explorer and Collector modes to manage large and residual unknown areas.
• It uses dual cost functions that incorporate A* path lengths and turning penalties to optimize target selection in cluttered forest settings.
• Experimental simulations show up to 65% faster completion times and significant increases in explored volume compared to baseline methods.

Searching arXiv for the core paper and closely related forest-strategy/planning work. Strategy Forest denotes a decentralized UAV exploration strategy for cluttered forest environments in which each robot builds a voxel map from depth + odometry, extracts and clusters frontiers, classifies frontier clusters, selects an execution mode, chooses a target viewpoint, and sends that target to a trajectory generator. Its defining feature is online switching between Explorer mode, which prioritizes large, informative frontiers and movement toward unexplored territory, and Collector mode, which prioritizes small “trail” clusters caused by occlusions and clears leftover islands of unknown space inside already explored regions. The method is motivated by the observation that forests generate many thin, disconnected pockets of unknown space through trunks, branches, shrubs, limited sensing range, and frequent occlusions, so a pure “go to the biggest frontier” policy often induces expensive revisits later (Bartolomei et al., 2023).

1. Problem formulation in cluttered forest exploration

Strategy Forest is designed for previously unknown large spaces in which autonomous navigation and exploration remain difficult because the environment is cluttered and exhibits large and frequent occlusions due to high obstacle density. Forests are the canonical case. The approach targets both single-UAV missions and small swarms, with explicit attention to long-distance wireless communication limits, collision risk, and the need to exploit fast UAV motion while still being safe and complete (Bartolomei et al., 2023).

The method is organized around three coupled difficulties. First, high obstacle density and frequent occlusions generate many frontier fragments; because the sensor range is limited, the map contains narrow slivers and hidden pockets of unknown space. Second, a safety-versus-speed trade-off arises because standard frontier planners tend to produce cautious stop-and-go motion near unknown boundaries, which is safe but underuses UAV dynamics. Third, in multi-UAV settings, radio links can be blocked or weakened, making centralized approaches that assume always-on connectivity unrealistic. Strategy Forest therefore uses a point-to-point decentralized architecture with a maximum communication range rather than a centralized controller (Bartolomei et al., 2023).

A common misconception is to treat forest exploration as a conventional frontier-selection problem with only one behavioral mode. The formulation underlying Strategy Forest rejects that simplification. It treats the residual unknown patches created by occlusions as structurally important decision objects rather than as incidental artifacts of mapping. This suggests that the approach is not merely a heuristic acceleration of frontier exploration, but a reformulation of the exploration objective around the joint management of frontier advance and residual-space cleanup.

2. Local pipeline and frontier semantics

Each UAV executes the same local pipeline: build a voxel map from depth + odometry, extract and cluster frontiers, classify frontier clusters, choose an execution mode, select a target viewpoint, and send that target to a trajectory generator (Bartolomei et al., 2023). The central representation is therefore not a global task allocation map but a local, incrementally updated frontier structure.

After frontiers are clustered, each cluster is labeled either as a normal frontier or as a trail. A cluster is considered a trail if its convex hull is surrounded by free space or it has only one neighboring cluster. This heuristic is intended to capture frontier fragments that are likely to remain as leftover unexplored patches if the robot only pursues large outer frontiers. In operational terms, trails encode the local signature of occlusion-induced incompleteness.

The mode selector then decides whether the UAV should remain in its current mode, switch to Explorer, or switch to Collector, based on the nearby frontier/trail structure. Collector is chosen when there is a minimum number of nearby trails that should be cleared locally. Explorer is chosen when those smaller islands have been cleared, or when trails are too far away to justify a detour. The paper describes this as a lightweight state machine driven by local map structure (Bartolomei et al., 2023).

The significance of this pipeline lies in the role assigned to frontier classification. Frontier clustering is not only a preprocessing step for goal generation; it is the mechanism by which the environment is partitioned into exploratory and exploitative subproblems. Explorer mode covers the main unknown volume, while Collector mode removes the small residual unknown regions that naive frontier methods tend to ignore.

3. Execution modes and cost functions

For a cluster $c \in \mathcal{C}$, Strategy Forest defines a viewpoint

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$

where $\mathbf{x}_c$ is the 3D position and $\gamma_c$ the yaw/orientation (Bartolomei et al., 2023). Target selection is mode-dependent.

In Explorer mode, the selected cluster minimizes

$$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$

where $J_D$ is the A* path length from current robot position to the viewpoint, $J_V$ is a turning / heading change penalty, $J_L$ is a penalty for choosing a trail instead of a true frontier, and $\omega_D,\omega_V,\omega_L$ are weights (Bartolomei et al., 2023). The turning term is

$$J_V(\xi_c) := acos\!\left( \mathbf{v}_R^T \frac{\mathbf{x}_c - \mathbf{x}_R}{|| \mathbf{x}_c - \mathbf{x}_R ||_2} \right),$$

with $\xi_c := \{\mathbf{x}_c, \gamma_c\},$0 the current velocity and $\xi_c := \{\mathbf{x}_c, \gamma_c\},$1 the current position. The label penalty is

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$2

The chosen target is

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$3

If the UAV is trapped or no forward cluster exists, the method falls back to a greedy local selection within a radius $\xi_c := \{\mathbf{x}_c, \gamma_c\},$4, ignoring velocity alignment: $\xi_c := \{\mathbf{x}_c, \gamma_c\},$5

In Collector mode, trail clusters $\xi_c := \{\mathbf{x}_c, \gamma_c\},$6 are ranked by

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$7

where

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$8

and

$\xi_c := \{\mathbf{x}_c, \gamma_c\},$9

The Collector then greedily clears nearby trails one by one until no close-by trails remain. Because it operates in mostly known free space, the paper doubles the maximum velocity in Collector mode compared with Explorer mode (Bartolomei et al., 2023).

These two costs instantiate the balance between exploration and exploitation. Explorer mode penalizes trail selection and heading change in order to keep forward progress toward major unknown regions. Collector mode instead reduces the problem to efficient clearing of local residual structures. A plausible implication is that the method’s performance advantage in forests comes from this asymmetry: Strategy Forest does not attempt to use one scalar objective for both frontier expansion and residual-space cleanup.

4. Decentralized multi-UAV coordination

The multi-UAV extension is decentralized rather than centralized. Each agent exchanges local sub-maps, odometry, current target pose, and current execution mode. The design assumes a maximum pairwise communication range; if two UAVs move too far apart, communication is lost and coordination degrades, while later map synchronization is possible if communication is regained (Bartolomei et al., 2023).

Coordination is only encouraged between compatible roles. Explorer–Explorer coordination is used to cover more unknown space. Collector–Collector coordination is used to clear trails. Explorer–Collector interaction uses a leader-follower behavior, where the Explorer leads and the Collector follows and clears the leftover trails. The mechanism is implemented as soft cost shaping rather than hard task assignment (Bartolomei et al., 2023).

For robot $\mathbf{x}_c$0, the Explorer and Collector costs are augmented as

$\mathbf{x}_c$1

and

$\mathbf{x}_c$2

with

$\mathbf{x}_c$3

The attraction term is

$\mathbf{x}_c$4

with

$\mathbf{x}_c$5

The repulsion term is

$\mathbf{x}_c$6

where

$\mathbf{x}_c$7

and $\mathbf{x}_c$8, $\mathbf{x}_c$9 is the collision threshold, and $\gamma_c$0 is the desired separation scale (Bartolomei et al., 2023).

This coordination design is notable because it does not require persistent global consistency. Instead, it biases local target selection so that communication retention, safety, and role compatibility shape the emergent team behavior. That design directly addresses the paper’s claim that centralized methods assuming always-on connectivity are unrealistic in forests.

5. Experimental setup and quantitative results

The evaluation is simulation only. The system uses a depth camera with a $\gamma_c$1 m range and a UAV dynamics model with

$\gamma_c$2

Maps are voxel grids with resolution $\gamma_c$3 m or $\gamma_c$4 m depending on size (Bartolomei et al., 2023).

For single-UAV experiments, the forest sizes are synthetic forests of $\gamma_c$5 m and a real forest reconstruction of $\gamma_c$6 m, with densities $\gamma_c$7, $\gamma_c$8, $\gamma_c$9, and $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$0 trees/m$$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$1. The baseline is FUEL. Compared with FUEL, Strategy Forest achieves much faster completion times and higher average speeds, though often at the cost of longer traveled distances. In the real forest, completion time is 500.7 ± 14.8 s versus 757.7 ± 47.9 s, and speed is 1.3 ± 0.5 m/s versus 0.7 ± 0.4 m/s. In the synthetic forests, completion times are 665.4 ± 32.7 s versus 1114.1 ± 97.4 s in sparse forest, 779.6 ± 110.9 s versus 954.1 ± 28.8 s at average density, 613.2 ± 16.2 s versus 1130.2 ± 28.8 s in dense forest, and 658.2 ± 57.2 s versus 904.1 ± 109.5 s in very dense forest. The paper summarizes this as up to 65% speed up in some settings (Bartolomei et al., 2023).

For multi-UAV experiments with 2 UAVs in fixed-density forests, the map size is $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$2 m, the maximum communication range is $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$3 m, and densities are $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$4, $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$5, $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$6, and $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$7 trees/m$$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$8, with a centralized map-splitting method using FUEL as baseline. The method is generally comparable to the centralized split-map baseline, but with higher per-agent speed and more balanced workload. Completion times are 780.3 ± 32.2 s versus 834.3 ± 64.3 s in sparse forest and 838.5 ± 64.4 s versus 848.1 ± 98.5 s at average density, while the baseline is slightly better in some dense cases: 786.3 ± 40.7 s versus 754.0 ± 23.9 s in dense forest and 803.7 ± 52.8 s versus 705.8 ± 73.2 s in very dense forest (Bartolomei et al., 2023).

For 2 and 3 UAVs in a non-homogeneous forest of map size $$J_{E}(\xi_c) := \omega_D J_D(\xi_c) + \omega_V J_V(\xi_c) + \omega_L J_L(c),$$9 m with regional densities $J_D$0, $J_D$1, and $J_D$2 trees/m$J_D$3, maximum communication range $J_D$4 m, and mission time limit $J_D$5 s, Strategy Forest consistently beats map-splitting FUEL in explored volume over time. One reported comparison gives 542.3 vs 514.6 m³ at 300 s, 1062.8 vs 840.0 m³ at 600 s, 1400.0 vs 1145.3 m³ at 900 s, 1626.7 vs 1330.1 m³ at 1200 s, and 1816.0 vs 1437.8 m³ at 1500 s. Increasing from 2 to 3 UAVs improves coverage at all timestamps, including 1208.0 ± 91.6 m³ versus 1108.2 ± 54.7 m³ at 300 s and 3621.8 ± 321.0 m³ versus 3453.0 ± 849.9 m³ at 1500 s. The abstract characterizes the multi-UAV outcome as a 40% increase in explored area for the same mission time (Bartolomei et al., 2023).

These results indicate that the method’s principal strength appears in cluttered single-UAV exploration and in decentralized coverage of non-homogeneous forests. The denser fixed-density two-UAV cases show that communication-aware motion constraints can offset some of the benefits of local mode switching.

6. Scope, limitations, and relation to other “forest strategy” usages

The main limitations stated for Strategy Forest are that local decision-making can lengthen travel distance; decentralized coordination depends on agents staying within a finite radio range; dense forests can reduce multi-UAV effectiveness because maintaining communication range constrains motion freedom; and the evaluation is simulation only, including a real-forest reconstruction, with onboard real-world deployment identified as a natural next step (Bartolomei et al., 2023).

The term “forest strategy” is used more broadly in arXiv literature, but those usages refer to substantively different objects. In forest management, one paper redesigns the harvesting strategy of the Toruń Forest District through a five-player non-zero-sum game and a Nash equilibrium over criteria including CO2 sequestration, biodiversity, harvested wood volume, native species fraction, and protective forest functions; the final strategy is obtained by swapping specific harvested stands while essentially maintaining planned timber output (Kotlarz, 2024). In large-scale spatial-temporal forestry planning, another line of work formulates the problem as an MDP with a black-box simulator and uses policy gradients to compare an explicit policy with an abstract spatially stationary policy; there the “forest strategy” is a long-horizon planning policy over cells and timesteps rather than a frontier-based exploration controller (Crowley et al., 2012). In probability and geometry, the “Directed Spanning Forest” and the “Hyperbolic Directed Spanning Forest” are random graph constructions in Euclidean and hyperbolic spaces, not operational exploration or management strategies (Flammant, 2019).

This terminological variation matters because Strategy Forest, in the strict sense established by the UAV exploration work, is neither a timber-harvesting optimization framework nor a generic spatial-temporal planning policy nor a spanning-forest object from stochastic geometry. It is a decentralized forest-exploration method in which dynamic switching between Explorer and Collector modes operationalizes the balance between aggressive advance into unexplored territory and systematic cleanup of occlusion-induced residual unknown space.