Informative Path Planning

Autonomous exploration demands that robots continuously evaluate candidate viewpoints based on their expected information gain and execution cost. Sampling-based planners estimate this gain by volumetric raycasting and, due to its computational cost, evaluate candidates under an assumption of mutual independence, ignoring the overlap between viewpoints along the same path. This work presents a GPU-accelerated method for computing path-dependent marginal information gain, where instead of storing and merging the observed unknown voxels along each candidate path, previous observations are represented using depth buffers. Candidate rays are projected into the depth buffers of their ancestors to identify observation overlap and exclude regions expected to be observed. The planning tree is evaluated in depth order to maintain the dependency between viewpoints and their optimized yaws, while candidate nodes and rays at each level are processed in parallel on the GPU. The proposed method stays within 5-10% of the exact marginal gain computed using voxel hash maps, with speed-ups of up to 118x on a desktop GPU and 28x on an NVIDIA Jetson Orin NX. The method was integrated into two sampling-based exploration planners and evaluated in three simulation environments, where marginal gain reduced the time to 95% coverage in five of the six evaluated planner-environment combinations. Real-world experiments also showed a 30% reduction in the time to 95% coverage, as well as earlier exploration termination times.

Informative Path Planning for scalar field reconstruction uses predictive uncertainty to direct sensing vehicles toward maximally informative locations. Gaussian Processes provide this signal but their stationary isotropic kernels are misspecified for non-homogeneous phenomena such as oil spills, producing miscalibrated estimates that degrade planning. We investigate whether replacing the Gaussian Process with a well-calibrated Deep Ensemble improves path planning outcomes, and whether uncertainty quality interacts with the choice of planning algorithm. Five strategies ($ε$-Greedy, Value Greedy, Uncertainty Greedy, Monte Carlo Tree Search, and Receding Horizon Orienteering) share a common Deep Ensemble backbone trained on physics-based oil spill simulations. On held-out stochastic spill scenarios, the Deep Ensemble reduces normalised reconstruction error by $83\%$ relative to the Gaussian Process baseline. Crucially, well-calibrated uncertainty amplifies the importance of the planning strategy: the performance gap between algorithms is negligible under miscalibrated models but becomes substantial under the ensemble, where multi-step lookahead planners outperform greedy selection by up to $32\%$ in reconstruction error and achieve IoU above $0.85$. Monte Carlo Tree Search is the recommended planner, matching Orienteering in reconstruction quality at an order-of-magnitude lower computational cost.

Robots searching for a target from a natural-language description must determine not only where to search, but also which observed candidate is the desired target. These decisions reflect two distinct sources of uncertainty - spatial uncertainty over candidate locations and semantic uncertainty over target identity - that are often conflated in VLM-based search systems. We introduce a spatial-semantic uncertainty formulation that maintains separate beliefs over each component and integrates probabilistic VLM evidence into a global target-identity posterior, including probability mass for undiscovered targets. This decomposition allows an information-theoretic planner to independently value candidate discovery and target disambiguation through spatial and semantic expected information gain (EIG), providing an explicit mechanism for trading broader exploration against earlier identification. We evaluate six VLM uncertainty-elicitation interfaces on 500 synthetic targets and show that similar recognition accuracy can conceal substantial differences in calibration and false confidence. In degraded-observation search-and-identify experiments, EIG-based planners reach confident decisions in 75.0%-92.5% of trials, compared with 20.0% for Random search, while different spatial-semantic weightings achieve comparable identification accuracy once confidence is attained. Increasing semantic emphasis reduces unnecessary exploration and VLM queries, demonstrating that explicitly planning over semantic uncertainty can accelerate target resolution without sacrificing decision quality. These results highlight the distinct roles of uncertainty representation and uncertainty-driven planning in embodied VLM systems.

Hazardous robotic exploration requires robots to map spatial risks, such as unsafe terrain, radiation, fire, mines, or structural damage, while operating where collecting information can itself cause failure. A highly informative path may expose the robot to hazards, terminate execution, and prevent future observations. Hazardous exploration therefore requires deciding not only where uncertainty is largest, but when reducing it is worth the risk. This paper introduces a valuation-layer view of this problem. We keep the belief update, sensor model, physical risk model, and finite-horizon informative planner fixed, and change only the scalar objective used to rank feasible paths. Within this framework, we introduce a risk-augmented Behavioral Information objective based on Prelec probability weighting, yielding an interpretable family of conservative-to-aggressive information-risk valuations. Theoretically, we show that valuation parameters create switching boundaries between high-information/high-risk and lower-information/lower-risk paths, and induce a transformed Pareto-frontier structure over feasible exploration policies. Large-scale failure-truncated grid-world experiments show that valuation alone reshapes the information-risk frontier. Shannon information planning remains a strong raw-information baseline, while risk-aware objectives can reduce hazard exposure and robot losses by avoiding failures that truncate future sensing. Risk-augmented Behavioral valuation is Pareto-competitive with standard risk-aware baselines and provides interpretable conservative and intermediate regimes. These results support a framework in which robots reason not only about how much uncertainty an action reduces, but whether that reduction is worth the risk required to obtain it.

Environmental monitoring with unmanned aerial vehicles (UAVs) requires route planning methods that maximize covered area while handling energy limits, operational constraints, and geometric complexity. This paper reports the protocol and preliminary results of an ongoing systematic literature review (SLR) on autonomous UAV route planning for coverage-oriented environmental monitoring. The review follows the PRISMA 2020 framework and searches Scopus and Web of Science for studies published between 2015 and 2026. The protocol focuses on path planning, coverage path planning, and informative path planning, with emphasis on algorithmic families, coverage and energy metrics, obstacle handling, geometric environment representations, and environmental constraints. At the current stage, 562 records have been identified, 161 duplicates have been removed, and 401 unique records have been screened by title, abstract, and keywords. From these, 247 studies were retained for full-text eligibility assessment (235 eligible and 12 borderline records to be resolved during full-text review). A preliminary analysis of the retained studies suggests strong concentration on coverage-oriented formulations, multi-UAV coordination, and energy-aware optimization, while fewer studies explicitly address weather, uncertainty, or obstacle-rich environments. Most retained studies rely on simulation-based validation, highlighting a potential simulation-to-reality gap, and recent publications show increasing interest in reinforcement learning, hybrid optimization, and geometry-aware planning. These early findings indicate an active but fragmented research landscape and support the need for a structured synthesis to identify mature techniques and unresolved gaps for realistic environmental monitoring missions.

Lunar helium-3 is a highly valuable strategic resource, pivotal to the advancement of both deep-space exploration and space mining. Existing lunar helium-3 exploration methodologies rely primarily on indirect measurements via remote sensing, which are often characterized by limited precision, low reliability, and insufficient spatial resolution. In this paper, we introduce He3-Seeker, an active robotic exploration method for helium-3 distribution mapping. First, we provide a formal definition of the active helium-3 exploration problem. Subsequently, we developed the He3-Seeker framework, which is conceptually based on multi-point drilling, sampling, and in situ analysis. In particular, we use robotic information planning (RIP) to guide autonomous robot navigation and active sensing. Additionally, to thoroughly evaluate the proposed algorithm, we introduce a reliable method for generating reference data of lunar helium-3 distribution based on low-resolution orbital remote sensing measurements. Simulation experiments verify that He3-Seeker achieves both rapid and high-fidelity mapping of helium-3 distribution, providing a reliable solution for resource exploration tasks. Our code and simulation environment will be publicly accessible at https://github.com/OpenSpace-Lab/He3-Seeker.

Autonomous exploration in unknown environments requires unmanned aerial vehicles (UAVs) to efficiently generate informative trajectories while simultaneously constructing accurate maps. Although many existing exploration methods rely on geometric information, they often lack semantic awareness, resulting in suboptimal exploration efficiency and limited environmental understanding. To address this limitation, this paper proposes a semantic-aware exploration framework that adds semantic information to a roadmap-based exploration strategy. The proposed method builds on the Dynamic Exploration Planner (DEP), which incrementally constructs a Probabilistic Roadmap (PRM), and augments this roadmap with a semantic layer. A semantic reward function is introduced to prioritize regions containing meaningful objects and structures, enabling the UAV to focus on areas with higher information value. Furthermore, the roadmap is continuously updated to support efficient frontier selection and path planning during exploration. The proposed framework is implemented in ROS Noetic and Gazebo using an RGB-D sensor for simultaneous acquisition of geometric and semantic information. Experimental results in multiple simulated environments demonstrate that the proposed approach achieves exploration coverage rates between 90% and 94% while reducing exploration time and travel distance compared with conventional geometry-based exploration methods.

We study trajectory optimization in mobile sensing systems that must identify which member of a finite candidate set is the true target, while maintaining reachability to all potential candidate targets, under resource constraints. Deferred-Decision Trajectory Optimization (DDTO) addresses this setting by computing trajectories that reach individual targets but remain coincident for as long as possible before separating toward different targets. We propose Active-Sensing DDTO (AS-DDTO), which extends DDTO by adding a trajectory-dependent information-acquisition term to the planning objective. The resulting planner maintains reachability to candidate targets while biasing the coincident portion of the trajectories toward regions that enable earlier target identification. The framework supports Bayesian updates and conformal candidate-set updates for distance-dependent sensing. We derive a mixed-integer conic reformulation and provide guarantees on recursive feasibility, belief concentration, and fixed-time coverage for the raw conformal candidate set. Numerical simulations show improved target identification compared with standard DDTO under distance-dependent sensing uncertainty and limited sensing budget.

Exploration and object search require robots to perceive their environment, identify regions of interest, and plan trajectories that improve target-detection likelihood or maximize information gain. Many IPP methods, especially in continuous environmental monitoring, rely on Gaussian-process belief models, while object-search settings often produce complex, multimodal belief maps from semantic or open-vocabulary perception. Global trajectory generation directly conditioned on such non-Gaussian belief maps remains comparatively underexplored. Although diffusion-based planners offer strong capabilities for modeling such distributions, their use in informative path planning remains limited. In this work, we propose DIFF-IPPO, a pipeline that integrates an open-vocabulary belief map generator with a diffusion-based planner for global trajectory generation over belief maps. The method generates trajectories that concentrate sensor coverage over high-belief regions, achieving normalized detection scores between 81.49% and 86.55% across different dataset scenarios. We validate the system in a simulated search-and-rescue scenario where the planner searches candidate building regions to locate a burning building. In this setting, a team of five drones using batched belief-map-conditioned trajectory generation achieves first detections in 3.5 minutes.

Safe ground navigation in large, threat-augmented environments requires aerial support that actively reduces the risks that a ground vehicle faces along its route. Existing aerial reconnaissance systems focus on mapping or covering the environment, but do not direct sensing toward regions that are most relevant for ground vehicle safety. In this paper, we address the problem of coordinating a team of unmanned aerial vehicles (UAVs) to improve the safety of an unmanned ground vehicle (UGV) navigating through unknown threat zones. A key aspect of our approach is a shared exposure belief that is updated online from aerial observations and used jointly by the UAV team and the ground vehicle. This enables us to direct aerial sensing towards route-relevant regions while allowing the UGV to replan around newly revealed threats. We coordinate the UAV team through spatial region assignment to avoid redundant sensing. Simulation experiments show that our approach reduces cumulative UGV exposure by 38% compared to a system that does not account for hazard levels, and reduces redundant aerial coverage from 38.8% to 3.7% under our multi-UAV coordination scheme.

Autonomous surface vehicles offer an efficient solution for environmental cleanup as well as search and rescue operations in open waters. Targets in these settings drift continuously, so efficient search must balance exploration of unobserved regions with tracking of known targets. However, most target tracking and pursuit scenarios consider simple guidance behaviours and short-term predictions for decision-making. In this letter, we address the problem of search and capture of multiple drifting targets, such as litter, in dynamic environments, using a hybrid planning framework. A key aspect of our strategy is a spatiotemporal informative planning method based on model predictive path integral (MPPI) control, a sampling-based model predictive control approach. The planner directly generates kinematic-level commands by optimising continuous trajectories over long horizons. A multi-objective cost balances search and tracking objectives while ensuring safe, feasible trajectories. In the interception stage, we switch to a pure pursuit guidance controller for the physical capture of moving targets. Experiments show that our planner outperforms the chosen planning baselines. Finally, we validate our approach in field trials with an ASV.

Unmanned aerial vehicles (UAVs) are increasingly used for active sensing and information gathering in spatially distributed environments. Their performance, however, is constrained by limited flight time, sensing uncertainty, and the trade-off between spatial coverage and observation accuracy. This paper presents a real-world validation of a multi-UAV active sensing framework for probabilistic binary terrain mapping, with precision agriculture used as the application case. The environment is represented as a probabilistic belief map, where spatial dependencies are modeled through a factor-graph formulation. UAV decision making is guided by Information Gain based Informative Path Planning (IGbIPP), and the approach is compared with Random Walk and Sweep coverage path planning baselines using both synthetic terrains and real UAV-derived agricultural imagery. The study also evaluates spatial correlation weights and several probabilistic belief-fusion rules for multi-UAV information sharing. Results show that IGbIPP reduces entropy and mapping error more effectively than the baselines, while a wider field of view improves real-world coverage and map accuracy. The results further show that simple equal or biased spatial weights can be more robust than adaptive weights, and that Bayesian, log-odds, and Dempster--Shafer fusion achieve the best cooperative mapping performance. These findings highlight the importance of uncertainty-driven planning, sensing geometry, spatial modeling, and probabilistic fusion for real-world UAV-based active sensing.

Bearing-only target localization is a fundamental problem in optical measurement and finds extensive applications in unmanned aerial vehicle (UAV) technology. Effective trajectory planning establishes favorable observation geometries, thereby enhancing the target localization accuracy of bearing-only UAV systems. This paper proposes an trajectory optimization method for unmanned aerial vehicles (UAVs) in bearing-only target localization scenarios. By leveraging the Fisher Information Matrix (FIM), the proposed approach dynamically integrates the geometric configuration and vehicle maneuverability into the optimization framework. Specifically, we introduce a spectrally-weighted FIM objective function that provides better gradient dynamics near degenerate configurations, enabling the planner to rapidly escape from poor observation conditions. For dual-UAV scenarios, an intersection angle sine term is introduced to optimize triangulation geometry by improving the sight-line intersection angle, thereby preventing trajectory aggregation. Furthermore, we propose an improved Particle Swarm Optimization (PSO) algorithm with motion model constraints and particle normalization to ensure the physical feasibility of the trajectory and enhance the compatibility with the objective functions. Simulation results demonstrate that the proposed method reduces the median localization error by 99.21% compared to conventional FIM-based approaches in single-UAV scenarios, and achieves a 69.70% improvement for dual-UAV configurations, exhibits superior performance in long-duration bearing-only target localization of maneuverability targets at extended ranges.

Uncrewed aerial vehicles (UAVs) are increasingly used for exploration-driven monitoring in hazardous environments such as disaster zones, contaminated sites, wildfire areas, and damaged infrastructure, where limited flight endurance must be allocated between visiting reported locations and gathering new information. In these settings, prior information regarding hazards is often incomplete, spatially imprecise, and subject to change during execution. For example, initial reports may identify a region where a hazard is likely to exist, but the actual hazard may be displaced, partially observed, or entirely unreported. We present an integrated exploration-aware UAV route optimization and path planning framework for hazard monitoring under uncertain and evolving prior information. The environment is represented as a spatial risk map, where each location has an associated belief of hazardous conditions. Reported hazards are modeled as uncertain regions of interest (ROIs) rather than confirmed target locations, requiring the UAV to inspect reported areas while also using its limited flight endurance to explore informative regions. The proposed method solves a vehicle routing problem over reported ROIs, augments the route with auxiliary pseudo-nodes to improve spatial coverage, allocates the remaining flight distance budget across route segments, and optimizes dynamically feasible B-spline trajectories for local exploration. During execution, UAV measurements update a grid-based belief map, and the remaining trajectory is replanned when new information and the remaining budget justify adaptation. Across 48 scenario configurations, online replanning improves average KL reduction by 15.9% over the offline optimized planner and 48.6% over straight-line traversal.

Collaborative navigation of heterogeneous robots in unknown environments poses significant challenges due to sensing, communication, and computational limitations. In this work, a lead robot navigates toward a target while a mobile sensor robot (e.g., a drone) assists by transmitting information about its locally observed map under bandwidth constraints. We propose a framework that enables the sensor to jointly select its transmitted map points and navigation actions online, while also predicting unexplored regions of the environment. To this end, we present $β$-Sparse Gaussian Processes, a robust variational sparse Gaussian Process model for task-aware inducing point selection under cardinality constraints. Furthermore, we develop an action-selection strategy that balances task relevance with exploration. Simulations on Mars and Earth maps show that the framework can reduce path cost by 18% relative to no communication and decrease transmitted information by 76% compared to raw-data transmission baselines.

Autonomous robot teams navigating partially known environments face costly backtracking when ground robots encounter blocked roads that are only revealed upon physical traversal. We address this with Scout-Assisted Planning, a heterogeneous planning framework in which scouting Unmanned Aerial Vehicles proactively gather environmental information to improve Unmanned Ground Vehicle navigation. To focus scouting on the most consequential edges, we propose Information Gain-based Action Pruning, which scores candidate scouting actions by their expected impact on ground robot behavior. Since exact Information Gain-based Action Pruning computation is prohibitively expensive, we develop a Graph Neural Network based model that predicts information gain values directly from graph structure and belief state, reducing planning time to real-time levels without sacrificing solution quality. Experiments across three environment types show that SAP with Information Gain Action Pruning reduces ground robot travel cost by 31.9--37.7% over the Canadian Traveler Problem baseline, and outperforms proximity-based scouting guidance by an additional 8--14%, confirming that principled information-gain-guided scouting is both more effective and computationally feasible for real-world deployment

A "path-based sensor" produces a single observation along a continuous path. For example, a boolean path-based sensor returns a single "1" if an event of interest is detected at any point along the path and a "0" otherwise. Notably, a "1" provides no direct information about where along the path the event(s) may have occurred. Previous work has demonstrated that observations from multiple path-based sensors can be fused to create a Bayesian belief map over the spatial locations of the underlying event or phenomenon. Moreover, path planning can employ Shannon information theory to accelerate the rate of convergence of the belief map. In this paper, we present a new method to update the belief map based on a path-based sensor observation, and then plan paths to increase information gain. In contrast to prior work that approximates the posterior by averaging over the alternative event histories, we introduce a Bayesian Network (BN) formulation that models the probabilistic relationships between the latent variables and path-based sensor measurements, enabling a more principled Bayesian belief update. We consider static hazard detection in a communication-denied environment as a representative problem setting. The event of a robot returning from its path corresponds to a path-based hazard sensor reading of "0" (hazard not detected), while a robot failing to return corresponds to a reading of "1" (hazard detected). We consider false positives and false negatives. We find that the new method leads to quicker convergence of the belief map than prior work in both single- and multi-robot cases.

Active perception is a fundamental problem in autonomous robotics in which the robot must decide where to move and what to sense in order to obtain the most informative observations for accomplishing its mission. Existing approaches either solve a computationally expensive traveling salesman problem over heuristically selected informative nodes, or adopt a more efficient but overly constrained shortest path tree formulation. To address these limitations, we explore beam search algorithms as scalable alternatives. While the standard beam search provides scalability by preserving the top-B paths at each depth level, it is prone to local optima and exhibits parameter sensitivity. Our first contribution is a node-wise beam search (NBS) algorithm, which maintains top-B candidates per node to enable more effective exploration of the solution space. Systematic benchmarking on graphs shows that NBS consistently outperforms other baselines and maintains strong performance even at low beam widths. As a second contribution, we integrate the concept of frontiers into the path selection criterion, introducing the expected gain metric, which better balances exploration and exploitation compared to existing alternatives. Our third contribution proposes the rapidly-exploring random annulus graph (RRAG), a novel graph construction method that preserves full orientation sampling and ensures connectivity in cluttered environments through a fallback local sampling-based planner. Extensive experiments demonstrate that NBS combined with RRAG achieves the highest performance across all three representative active perception tasks, outperforming state-of-the-art algorithms by at least 20% in one or more tasks. We further validate the approach on real robotic platforms in different scenarios.

Current 3D mapping pipelines generally assume static environments, which limits their ability to accurately capture and reconstruct moving objects. To address this limitation, we introduce the novel task of active mapping of moving objects, in which a mapping agent must plan its trajectory while compensating for the object's motion. Our approach, Paparazzo, provides a learning-free solution that robustly predicts the target's trajectory and identifies the most informative viewpoints from which to observe it, to plan its own path. We also contribute a comprehensive benchmark designed for this new task. Through extensive experiments, we show that Paparazzo significantly improves 3D reconstruction completeness and accuracy compared to several strong baselines, marking an important step toward dynamic scene understanding. Project page: https://davidea97.github.io/paparazzo-page/

Efficient and robust path planning hinges on combining all accessible information sources. In particular, the task of path planning for robotic environmental exploration and monitoring depends highly on the current belief of the world. To capture the uncertainty in the belief, we present a Gaussian process based path planning method that adapts to multi-modal environmental sensing data and incorporates state and input constraints. To solve the path planning problem, we optimize over future waypoints in a receding horizon fashion, and our cost is thus a function of the Gaussian process posterior over all these waypoints. We demonstrate this method, dubbed OLAhGP, on an autonomous surface vessel using oceanic algal bloom data from both a high-fidelity model and in-situ sensing data in a monitoring scenario. Our simulated and experimental results demonstrate significant improvement over existing methods. With the same number of samples, our method generates more informative paths and achieves greater accuracy in identifying algal blooms in chlorophyll a rich waters, measured with respect to total misclassification probability and binary misclassification rate over the domain of interest.

Zero-shot object-goal navigation (ZSON) requires navigating unknown environments to find a target object without task-specific training. Prior hierarchical solutions mainly focus on either scene understanding and representations (belief) or high-level decision-making and planning (policy), yet treat the option, i.e., the subgoal candidate that belief proposes and policy selects, as an interface inherited from adjacent modules rather than a design axis in its own right. In practice, options are predominantly single waypoints scored by destination utility: a lone destination hides the value gathered en route, and a flat list obscures the relationships among candidates. Our insight is that the option space should be a tree of paths. Full paths expose en-route information gain that destination-only scoring systematically neglects; a tree of shared segments enables coarse-to-fine LLM reasoning that dismisses or pursues entire branches before examining individual leaves, compressing the combinatorial path space into an efficient hierarchy. We instantiate this insight in REST (Receding Horizon Explorative Steiner Tree), a training-free framework that (1) builds an explicit open-vocabulary 3D map from online RGB-D streams; (2) grows an agent-centric tree of safe and informative paths as the option space via sampling-based planning; and (3) textualizes each branch into a spatial narrative and selects the next-best path through chain-of-thought LLM reasoning. Across the Gibson, HM3D, and HSSD benchmarks, REST consistently ranks among the top methods in success rate and path efficiency.

In classical Informative Path Planning (C-IPP), robots are typically modeled as mobile sensors that acquire digital measurements such as images or radiation levels. In this model, since making a measurement leaves the robot's physical state unchanged, the cost of traversing an edge remains static regardless of when it is traversed. This is a natural assumption for many missions, but does not extend to settings involving physical sample collection, where each collected sample adds mass and increases the energy cost of all subsequent motion. As a result, IPP formulations that ignore this coupling between information gain and load-dependent traversal cost can produce plans that are distance-efficient but energy-suboptimal, collecting fewer samples and less data than the energy budget would permit. In this paper, we first introduce Load-aware Informative Path Planning (LIPP), a strict generalization of C-IPP that explicitly models this coupling, with C-IPP recovered as the special case of zero sample mass. We then formulate LIPP as a Mixed-Integer Quadratic Program (MIQP) that jointly optimizes visitation location, order, and per-location sampling count under an energy budget. We further derive theoretical bounds on the path-length increase of LIPP relative to C-IPP, characterizing the trade-off for improved energy efficiency. Finally, through extensive simulations across 2,000 diverse mission scenarios, we demonstrate that LIPP progressively achieves higher uncertainty reduction per unit energy as sample mass increases.

Mutual information (MI) is a principled and widely used objective for robotic information gathering (RIG), providing strong theoretical guarantees for sensor placement (SP) and informative path planning (IPP). However, its high computational cost - dominated by repeated log-determinant evaluations - has limited its use in real-time planning. This paper presents Schur-MI, a Gaussian process (GP) MI formulation that (i) leverages the iterative structure of RIG to precompute and reuse expensive intermediate quantities across planning steps, and (ii) uses a Schur-complement factorization to avoid large determinant computations. Together, these methods reduce the per-evaluation cost of MI from $\mathcal{O}(|\mathcal{V}|^3)$ to $\mathcal{O}(|\mathcal{A}|^3)$, where $\mathcal{V}$ and $\mathcal{A}$ denote the candidate and selected sensing locations, respectively. Experiments on real-world bathymetry datasets show that Schur-MI achieves up to a $12.7\times$ speedup over the standard MI formulation. Field trials with an autonomous surface vehicle (ASV) performing adaptive IPP further demonstrate the method's practicality. By making MI computation tractable for online planning, Schur-MI helps bridge the gap between information-theoretic objectives and real-time robotic exploration. Our code is available at: www.sgp-tools.com