Exploration Path Planning

• Exploration path planning is the process of generating collision-free, dynamically feasible trajectories in unknown environments to maximize sensor coverage and ensure safe return.
• Techniques include frontier-based heuristics, Bayesian methods, sampling and graph-based strategies, and learning-based policies that integrate mapping with uncertainty estimation.
• These methods are applied in diverse scenarios such as planetary rover routing, hazard monitoring, and multi-robot target search, balancing operational constraints with mission objectives.

Exploration path planning is the problem of generating collision-free, dynamically feasible trajectories in partially known or unknown environments so that a robot or robot team maximizes coverage, information gain, or task-relevant discovery under constraints such as travel time, battery, actuation, sensing, traversability, and safe return-home. In current work, the problem appears in swarm target search, grid and voxel exploration, semantic inspection, hazard monitoring, planetary rover routing, wind-disturbed UAV search, and tethered cavity exploration. The resulting methods span frontier-based heuristics, Bayesian and information-theoretic objectives, sampling- and graph-based planners, hierarchical route-plus-trajectory optimization, and learning-based policies that integrate mapping, uncertainty estimation, and action selection (Ghassemi et al., 2019, Bouman et al., 2023, Deng et al., 2020).

1. Problem formulations and mission objectives

A recurring formal structure is a sequential decision problem over a robot state, an evolving world belief, and a finite action set or continuous trajectory family. In adaptive coverage planning, the state space is $S \coloneqq Q \times W$, where $Q$ is robot pose on an Information Roadmap and $W$ encodes traversability risk $p_r(n)$ and coverage probability $p_c(n)$; the planner seeks a horizon-$H$ policy maximizing discounted reward under a time budget, risk bounds, and dynamic constraints (Bouman et al., 2023). In planetary rover planning, the problem is cast as an MDP $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$ with state $s_t=(I_t,g_t,x_t)$, where $I_t$ is an orbital image, $g_t$ a goal pixel, and $Q$0 the rover location; the learned policy outputs one of eight motion directions (Zhang et al., 2018).

The mission objective varies with sensing and task semantics. Coverage-oriented formulations maximize the accumulated area swept out by a sensor footprint or the number of newly covered cells (Bouman et al., 2023, Snyder et al., 13 Feb 2025). Informative search formulations seek rapid reduction of uncertainty in an unknown spatial signal field or belief map while also moving toward likely target locations (Ghassemi et al., 2019, Choi et al., 27 May 2026). Other formulations couple exploration with additional mission criteria: semantic surface reconstruction and inspection quality in sparse-object environments (Dharmadhikari et al., 2023), object detection under battery and wind disturbances (Niaraki et al., 2019), or tether-length regulation in cavities (Petit et al., 29 Jun 2026).

A notable consequence is that “exploration” is not a single objective. In some systems, the planner is explicitly asked to classify all voxels in a bounded environment as free or occupied and to return home before battery expires (Dharmadhikari et al., 2020). In others, the planner must inspect every face of a reconstructed semantic mesh at a required image resolution and viewing angle (Dharmadhikari et al., 2023), or reduce the Kullback–Leibler divergence between a true hazard field and a maintained belief under limited flight endurance (Choi et al., 27 May 2026). This suggests that exploration path planning is best viewed as a family of constrained optimization problems whose common feature is decision making under partial observability.

2. Environment representations and uncertainty models

The dominant geometric substrate is the occupancy map. Recent planners use 2D occupancy grids, voxel maps, TSDFs, SDFs, OctoMaps, and elevation maps. In 2D frontier planning, frontier cells are unknown cells bordering at least one free cell (Deng et al., 2020). In 3D exploration, the map is often an incrementally built occupancy volume $Q$1 with voxels labeled free, occupied, or unknown, optionally accompanied by a signed-distance field for collision checking and graph construction (Dharmadhikari et al., 2020, Zacharia et al., 4 Mar 2026). Ground robots may also require a 2.5D height grid for slope-constrained traversability (Zacharia et al., 4 Mar 2026).

A second class of representations models latent spatial quantities rather than only occupancy. In decentralized swarm search, the unknown signal field $Q$2 is given a Gaussian-process prior,

$Q$3

with posterior mean and variance used for source seeking and uncertainty-guided path selection (Ghassemi et al., 2019). In hazard monitoring, the environment is represented as a spatial risk map $Q$4, stored in log-odds form $Q$5, and initialized from uncertain ROIs rather than confirmed targets (Choi et al., 27 May 2026). In dynamic grid worlds, a spatiotemporal predictor tensor is updated by cross-correlation kernels,

$Q$6

to capture temporal evolution such as wildfire spread (Yoon et al., 2021).

A third line of work encodes higher-level scene structure. Curiosity-based terrain exploration uses ROST, a realtime online spatio-temporal topic model in which each cell inherits a mixed topic prior from its neighborhood and observations are visual words such as ORB or texton indices (Girdhar et al., 2013). Hyperdimensional occupancy-grid mapping represents each cell by a $Q$7-dimensional hypervector and summarizes the entire occupancy grid by binding and bundling operations,

$Q$8

yielding a fixed-length representation that feeds downstream reinforcement learning (Snyder et al., 13 Feb 2025). Generative predictive models go further by hallucinating multiple plausible completions of a partially observed map: CogniPlan uses a conditional generative inpainting model to produce several layout hypotheses, averages the predicted occupancies, and interprets each unknown cell as a Bernoulli variable with entropy-driven uncertainty (Wang et al., 5 Aug 2025).

These representations imply different exploration semantics. Occupancy models support coverage and frontier discovery; Gaussian processes support posterior variance and source-location inference; topic models support semantic novelty; hazard maps support posterior risk reduction; and generative occupancy predictors support expected information gain over unobserved structure. The representation therefore largely determines what is considered “informative.”

3. Information gain, exploration–exploitation balance, and objective design

The core design choice in exploration path planning is the definition of utility. In frontier methods, utility is typically a visible-frontier count or a smooth surrogate of it. A differentiable formulation introduces a boundariness map $Q$9 and a fuzzy visibility filter $W$0, then defines single-view and path information gain as weighted sums of visible boundary cells. Because the gain becomes a smooth function of continuous robot poses, it can be optimized jointly with smoothness by automatic differentiation (Deng et al., 2020).

In Bayesian search, exploration and exploitation are combined explicitly. Bayes-Swarm assigns each robot $W$1 a next waypoint by maximizing a convex combination of source seeking and path-wise knowledge gain,

$W$2

subject to $W$3. The first term directs motion toward the GP predictive maximum; the second integrates posterior standard deviation along the path and incorporates other robots’ planned waypoints to discourage overlap (Ghassemi et al., 2019).

Information can also be defined semantically rather than geometrically. In terrain learning, the most successful curiosity signal is Topic Perplexity, computed from temporary topic assignments at a candidate neighbor and weighted against a revisitation penalty. High perplexity corresponds to rare topics relative to the robot’s path history and approximates expected reduction in topic entropy (Girdhar et al., 2013). In adaptive coverage, the reward is the marginal gain of a submodular set function $W$4, so later observations have diminishing returns by construction (Bouman et al., 2023). In ERRT, the planner minimizes

$W$5

where distance and actuation costs are offset by a negative information-gain term proportional to the number of newly visible unknown voxels (Lindqvist et al., 2021).

In hazard exploration, information gain is tied to belief reduction. One framework optimizes a differentiable expected detection score $W$6 for each B-spline edge path and later accepts online replanning only if a Jacobian-based expected information-gain score $W$7 improves beyond a threshold (Choi et al., 27 May 2026). A related bi-level planner minimizes the average posterior hazard probability $W$8 over a Voronoi cell, making path planning equivalent to maximizing entropy reduction under a Bayesian hazard-inference model (Choi et al., 31 Mar 2025).

Paper	Exploration signal	Optimization unit
(Ghassemi et al., 2019)	GP predictive maximum + path-integrated posterior standard deviation	next waypoint / trajectory
(Girdhar et al., 2013)	Topic perplexity with revisitation penalty	one-step neighbor choice
(Deng et al., 2020)	Differentiable frontier boundariness and visibility	continuous path
(Bouman et al., 2023)	Marginal submodular coverage gain	horizon-$W$9 policy
(Choi et al., 27 May 2026)	Expected detection and KL-reduction-driven replanning	per-edge B-spline
(Lindqvist et al., 2021)	Newly visible unknown voxels, plus distance and actuation terms	candidate RRT* branch

A common misconception is that exploration utility must be either frontier count or mutual information. The literature described here shows a wider spectrum: topic-level surprise, GP variance integrated over trajectories, semantic inspection completion, posterior hazard reduction, and entropy over generative occupancy hypotheses are all used as legitimate exploration surrogates when aligned with the task.

4. Planning architectures and algorithmic families

A major family consists of hierarchical local/global planners. MBPlanner separates a motion-primitives-based local exploration layer from a global graph search layer. The local planner samples dynamically feasible motion primitives within a fixed local subvolume, scores them by visible unknown-voxel gain, and declares local completion when no admissible gainful branch exists; the global planner then routes to a frontier node or to home via a sparse graph and optional trajectory refinement (Dharmadhikari et al., 2020). OmniPlanner generalizes the same bifurcation across aerial, ground, and underwater robots: a local graph in a bounding box is used for gain-maximizing short-horizon planning, while a persistent global roadmap enables frontier repositioning and return-home under morphology-specific admissibility checks (Zacharia et al., 4 Mar 2026).

A second family augments frontier planning with explicit viewpoint evaluation. OTO Planner updates frontiers selectively only in newly perceived regions, evaluates candidate viewpoints by information gain plus path-length, heading-change, and enclosed-subregion costs, and refines nearby viewpoints to reduce zig-zagging before sequencing them with an asymmetric TSP heuristic (Zhou et al., 2024). Semantics-aware exploration and inspection uses three behaviors—volumetric exploration, mesh-hole coverage, and semantic inspection—and switches among them rather than solving a single weighted objective; semantic hole edges act as frontiers in mesh space, and final inspection uses greedy set cover followed by a TSP over selected viewpoints (Dharmadhikari et al., 2023).

A third family integrates high-level routing with local continuous trajectory optimization. In hazard monitoring, one framework solves a vehicle-routing problem over uncertain ROIs, augments the route with pseudo-nodes via an edge-aware centroidal Voronoi tessellation, allocates the remaining distance budget across route segments with a line-segment Voronoi partition, and optimizes dynamically feasible B-spline trajectories on each edge (Choi et al., 27 May 2026). The related bi-level formulation performs essentially the same decomposition for known and unknown hazards, with edge-based CVT improving spatial coverage and route uniformity relative to node-based placement (Choi et al., 31 Mar 2025). TAPE adopts a two-level hierarchy for tethered aerial exploration: the global planner solves a frontier-based TSP to minimize distance, while the local planner evaluates up to five path options using an adjustable decision function over path cost, maximum tether length, final tether length, and number of contact points (Petit et al., 29 Jun 2026).

Sampling- and tree-based planners remain prominent. ERRT samples pseudo-random goals that are in free space and can observe at least one unknown voxel, grows an RRT* toward each goal, predicts actuation via nonlinear MPC, and selects the branch minimizing multi-objective cost (Lindqvist et al., 2021). Adaptive coverage planning uses Monte Carlo Tree Search over motion primitives on an Information Roadmap, leveraging the submodularity of coverage to guide horizon-limited sequential decision making at real-time rates (Bouman et al., 2023). NEXT replaces uniform expansion in high-dimensional tree search with a learned value–policy prior inside a UCB-style selection rule, yielding an explicit exploration–exploitation mechanism at the node-expansion level (Chen et al., 2019).

Distributed systems introduce another architectural axis. Bayes-Swarm is entirely asynchronous: each robot receives neighbors’ waypoints and observations, caps and refits a local GP, numerically solves its acquisition maximization, broadcasts a new waypoint plus recently collected measurements, and replans without waiting for all peers (Ghassemi et al., 2019). This design makes communication per decision minimal and directly couples distributed inference with decentralized informative path planning.

5. Learning-based and predictive approaches

Learning-based exploration path planning ranges from imitation learning to tabular RL, PPO, actor–critic graph policies, and meta-learned tree search priors. In planetary rover planning, DB-CNN learns from expert actions generated by offline planners and directly maps orbital images and goal maps to action scores without explicit environment mapping. The architecture uses a double branch to combine global context and local feasibility; on Martian images it reports $p_r(n)$0 versus $p_r(n)$1 for VIN, with faster convergence and lower epoch time (Zhang et al., 2018).

End-to-end reinforcement learning can absorb the planner entirely into the policy. In VSA-OGM, LiDAR returns are encoded into a hyperdimensional occupancy representation and fed to a PPO policy network that outputs discrete moves in MarsExplorer or continuous steering and throttle in RaceCarGym; no separate $p_r(n)$2 or sampling planner is used. Training performance is comparable to Bayesian Hilbert Maps, while generalization on unseen environments improves by approximately $p_r(n)$3 in RaceCarGym and by approximately $p_r(n)$4 higher reward on unseen MarsExplorer layouts (Snyder et al., 13 Feb 2025). For wind-disturbed UAV exploration, tabular Q-learning and SARSA use a reward that combines drag-induced energy penalty and object-detection bonus, with an $p_r(n)$5-greedy exploration schedule and action masking to prevent ping-pong loops; under moderate wind the RL policy detects approximately $p_r(n)$6 more targets than coverage sweep, and under high wind approximately $p_r(n)$7 more (Niaraki et al., 2019).

Other methods learn priors while retaining explicit search. NEXT learns a continuous-space value estimator $p_r(n)$8 and local sampler $p_r(n)$9, then combines them with a UCB score $p_c(n)$0 to select which node of a search tree to expand and where to expand it (Chen et al., 2019). CogniPlan combines a conditional WGAN-GP layout predictor with a graph-attention policy trained by Soft Actor-Critic. Multiple plausible inpainted maps are averaged into occupancy probabilities $p_c(n)$1, node features include these probabilities and frontier-related utility, and the planner chooses graph actions that trade path length against entropy reduction. On exploration benchmarks it reports a path length of $p_c(n)$2 px versus $p_c(n)$3 px for ARiADNE+ and $p_c(n)$4 px for TARE Local (Wang et al., 5 Aug 2025).

Learning can also operate above the motion planner. In the spatiotemporal exploration framework, a high-level DQN chooses among exploitation modes for specific states or an uncertainty-seeking exploration mode, while a short-term sample-based planner optimizes a horizon-$p_c(n)$5 path using the current belief map. After $p_c(n)$6 training epochs, the learned policy achieves an average reward per path of $p_c(n)$7, compared with $p_c(n)$8 for pure exploration, $p_c(n)$9 for pure exploitation, and $H$0 for random walk (Yoon et al., 2021).

These results indicate that learned components are used in three distinct roles: direct policy learning over structured map encodings, learned priors inside classical search, and learned mode selection on top of model-based short-horizon planning.

6. Empirical behavior, failure modes, and open directions

Reported gains are often substantial but task-specific. In swarm robotic search, Bayes-Swarm with $H$1 and $H$2 finds the primary source $H$3–$H$4 faster than exhaustive search and up to $H$5 faster than random walk, with mission time scaling nearly inversely with swarm size up to $H$6 robots before diminishing returns (Ghassemi et al., 2019). OTO Planner reports $H$7–$H$8 reductions in exploration time and movement distance relative to TARE, together with a $H$9–$$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$0 speed-up in frontier detection (Zhou et al., 2024). TAPE increases path length by only $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$1 relative to a pure-TSP baseline while keeping tether length below the maximum allowed value in $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$2 of simulated cases, versus $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$3 without the local tether-aware planner (Petit et al., 29 Jun 2026). OmniPlanner reports, for example, a $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$4 increase in AUC and $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$5 faster full exploration than ERRT in a multi-branch cave, and $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$6 AUC improvement plus $$\mathcal{M}=\langle \mathcal{S},\mathcal{A},P,R,\gamma\rangle$$7 faster completion than NBVP for underwater exploration (Zacharia et al., 4 Mar 2026).

Several studies also document characteristic failure modes. Word-perplexity exploration can overstay in visually complex regions with high word entropy and therefore miss other terrains; topic-perplexity is more effective because it operates at the latent-topic level (Girdhar et al., 2013). Pure coverage sweeps can become energy-inefficient or outright infeasible under strong wind fields, whereas reward shaping with drag-aware energy terms changes the preferred routes substantially (Niaraki et al., 2019). In large-scale unknown environments, repeated-path behavior and full-map frontier rescanning impose avoidable cost, motivating selective frontier updating and viewpoint refinement (Zhou et al., 2024). This suggests that poor alignment between the exploration signal and the operational constraint is a recurrent source of underperformance.

A second misconception is that stronger global optimality claims are standard. Several planners explicitly avoid such claims. The MBPlanner appendix states that it does not include formal completeness or optimality proofs and only gives an approximate local-completeness lemma as the number of sampled primitives tends to infinity (Dharmadhikari et al., 2020). OTO notes that global optimality is not guaranteed because the ATSP is solved heuristically and that dynamic obstacles are not explicitly handled (Zhou et al., 2024). DB-CNN requires offline expert paths and assumes static environments, while NEXT may degrade when new tasks lie far outside the training distribution (Zhang et al., 2018, Chen et al., 2019).

The open directions named across these works are similarly specific. They include adaptive parameter tuning and online learning of heuristic weights (Zhou et al., 2024), multi-robot coordination for curiosity-driven exploration and hazard monitoring (Girdhar et al., 2013, Niaraki et al., 2019), dynamic obstacle handling and chance-constrained rollouts (Bouman et al., 2023), continuous-state approximators for larger domains (Niaraki et al., 2019), real-time spool control and richer cable dynamics for tethered exploration (Petit et al., 29 Jun 2026), and extension of morphology-agnostic planning to additional sensing models and behaviors (Zacharia et al., 4 Mar 2026). A plausible implication is that future progress will depend less on a single universal utility function than on modular combinations of uncertainty representation, task-specific gain design, and architecture-level decomposition between local trajectory generation and global mission allocation.