Utility-Aware Path Search (UAPS)

• UAPS is a planning formulation where paths are evaluated not only by geometric cost but also by the utility gained from sensing and information acquisition along the route.
• These methods augment the search state with belief, energy, or safety metrics, employing techniques like value iteration, augmented A*, and gradient-free optimization for trajectory refinement.
• Empirical results indicate that UAPS can reduce travel distance and improve mission performance, though challenges remain in scaling and providing theoretical guarantees.

to=shell ＿色 code=json {"command":["bash","-lc","python - <<'PY'\nimport urllib.request, textwrap\nids=['(Santejudean et al., 2023)','(Meera et al., 2019)','(Mugford et al., 13 Nov 2025)','(Gasche et al., 4 Apr 2025)','(Yang et al., 2019)','(González-Gudiño et al., 16 Oct 2025)','(Xiang et al., 2024)','(Hague et al., 11 Nov 2025)','(Essen et al., 3 Apr 2025)','(Granadeno et al., 12 May 2025)']\nfor aid in ids:\n url=f'http://export.arxiv.org/api/query?id_list={aid}'\n data=urllib.request.urlopen(url, timeout=20).read().decode('utf-8')\n line=[l.strip() for l in data.splitlines() if '<title>' in l] [1]\n print(aid, line.replace('<title>','').replace('</title>','').strip())\nPY"]} code=0 {"output":"(Santejudean et al., 2023) Path-aware optimistic optimization for a mobile robot\n(Meera et al., 2019) Obstacle-aware Adaptive Informative Path Planning for UAV-based Target Search\n(Mugford et al., 13 Nov 2025) A^SAR: ε-Optimal Graph Search for Minimum Expected-Detection-Time Paths with Path Budget Constraints for Search and Rescue\n(Gasche et al., 4 Apr 2025) Energy Aware and Safe Path Planning for Unmanned Aircraft Systems\n(Yang et al., 2019) Connectivity-Aware UAV Path Planning with Aerial Coverage Maps\n(González-Gudiño et al., 16 Oct 2025) Active Jammer Localization via Acquisition-Aware Path Planning\n(Xiang et al., 2024) Learning-accelerated A* Search for Risk-aware Path Planning\n(Hague et al., 11 Nov 2025) Occlusion-Aware Ground Target Search by a UAV in an Urban Environment\n(Essen et al., 3 Apr 2025) Adaptive path planning for efficient object search by UAVs in agricultural fields\n(Granadeno et al., 12 May 2025) Land-Coverage Aware Path-Planning for Multi-UAV Swarms in Search and Rescue Scenarios\n"}

Editor’s term: “Utility-Aware Path Search” (UAPS) denotes a family of search and planning formulations in which a feasible path is evaluated not only by geometric travel cost, but by the value of what the path is expected to reveal, detect, confirm, avoid, or preserve. Across the literature grouped under this label, utility has been instantiated as optimistic bound reduction during global optimization, information gain or acquisition value over a Gaussian-process map, reduction of cumulative undetected probability, connectivity quality, energy- and safety-aware mission progress, and discounted probability of viewing a moving target. The unifying shift is from selecting isolated destinations or samples to selecting trajectories whose intermediate states matter because sensing, belief update, and resource consumption occur along the route (Santejudean et al., 2023, Meera et al., 2019, Mugford et al., 13 Nov 2025).

1. Scope and problem setting

UAPS arises when the path itself is part of the sensing or decision process. In path-unaware black-box optimization, one may select the next sample directly from an acquisition function or an optimistic bound. In the mobile-robot setting studied by path-aware optimistic optimization, this assumption fails because the robot cannot teleport to arbitrary query locations, samples $f$ along a single trajectory, and incurs time or energy costs through motion (Santejudean et al., 2023). A similar structural issue appears in informative UAV search: trajectories must satisfy collision constraints, sensor geometry, and flight-time limits, while measurements are accumulated continuously along the path rather than only at a terminal viewpoint (Meera et al., 2019).

This broad formulation includes several distinct problem classes. One class treats path choice as informative motion planning under belief uncertainty, as in Gaussian-process occupancy mapping for UAV target search, acquisition-aware jammer localization, and occlusion-aware search with a probabilistic visibility volume (Meera et al., 2019, González-Gudiño et al., 16 Oct 2025, Hague et al., 11 Nov 2025). A second class treats path choice as constrained graph search with path-dependent utility, as in minimum expected-detection-time search under a fixed mission horizon, connectivity-aware shortest path under outage constraints, and shortest path under a cumulative safety threshold (Mugford et al., 13 Nov 2025, Yang et al., 2019, Xiang et al., 2024). A third class encodes utility implicitly through mission-efficiency objectives such as energy-aware coverage, terrain-prioritized multi-UAV deployment, or adaptive altitude switching for object confirmation (Gasche et al., 4 Apr 2025, Granadeno et al., 12 May 2025, Essen et al., 3 Apr 2025).

A key consequence is that the relevant state is often augmented beyond geometry. In some formulations it includes current position and a sample-induced upper bound; in others it includes a Gaussian-process posterior, a target-location belief, a residual “unobserved probability” vector, a safety budget, or mission-completion binaries. This suggests that UAPS is less a single algorithm than a modeling pattern: augment the search state until future path value becomes computable from current state and feasible continuations.

2. Utility models

The most direct UAPS formulations define utility as a scalar function accumulated along a path. In path-aware optimistic optimization, the unknown field is $f:X\to\mathbb{R}$, the goal is $x^*\in\arg\max_{x\in X}f(x)$, and classical deterministic optimistic optimization uses the saw-tooth upper bound

$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$

The path-aware extension defines reward

$\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$

where $r(x,u)$ is the predicted volume by which the upper bound will be reduced when moving from $x$ to $x_+=g(x,u)$. Utility is therefore cumulative optimistic bound reduction, weighted toward regions with either high optimistic bound $B(x)$ or high estimated function value $\widehat f(x)$ (Santejudean et al., 2023).

In adaptive informative path planning for UAV target search, the utility is explicit at trajectory level: $f:X\to\mathbb{R}$0 Here $f:X\to\mathbb{R}$1 is either total GP variance reduction,

$f:X\to\mathbb{R}$2

or an adaptive acquisition reward built from

$f:X\to\mathbb{R}$3

combined with altitude-dependent sensor performance. This is a clear utility-per-budget objective: information reward minus collision penalty, normalized by flight time (Meera et al., 2019).

In budgeted search-and-rescue graph search, the paper uses a cost-minimization form that is utility-equivalent. With belief $f:X\to\mathbb{R}$4 over target location under path $f:X\to\mathbb{R}$5, the truncated minimum-time-to-detection objective is

$f:X\to\mathbb{R}$6

Minimizing $f:X\to\mathbb{R}$7 is equivalent to minimizing cumulative undetected probability mass over time, so the utility interpretation is “reduce survival/non-detection mass as early as possible” (Mugford et al., 13 Nov 2025).

Other papers instantiate utility through constraints or cost shaping rather than a direct reward. Connectivity-aware UAV path planning minimizes path length subject to

$f:X\to\mathbb{R}$8

where $f:X\to\mathbb{R}$9 is the connectivity outage ratio and $x^*\in\arg\max_{x\in X}f(x)$0 is the distance of each consecutive outage segment (Yang et al., 2019). Risk-aware planning minimizes path length subject to cumulative safety

$x^*\in\arg\max_{x\in X}f(x)$1

which can be read as a hard utility floor (Xiang et al., 2024). Acquisition-aware jammer localization modifies edge cost directly: $x^*\in\arg\max_{x\in X}f(x)$2 thereby rewarding paths that traverse high-acquisition regions en route to a candidate goal (González-Gudiño et al., 16 Oct 2025).

These formulations show that “utility” in UAPS is not synonymous with entropy reduction. It may be search progress, expected detection, path feasibility under mission-quality constraints, or a cost proxy reflecting energy, safety, or terrain priority. This suggests that UAPS is best defined by where utility is attached—namely to trajectories and path histories—rather than by any single reward family.

3. Search states and algorithmic mechanisms

The algorithmic core of UAPS is the conversion of path utility into a tractable search procedure. In path-aware optimistic optimization, the control problem is written with value function

$x^*\in\arg\max_{x\in X}f(x)$3

optimal $x^*\in\arg\max_{x\in X}f(x)$4-function

$x^*\in\arg\max_{x\in X}f(x)$5

and greedy law

$x^*\in\arg\max_{x\in X}f(x)$6

Because rewards are approximate and time-varying, the method uses online value iteration over a discretized grid, carrying the previous $x^*\in\arg\max_{x\in X}f(x)$7 estimate forward as initialization (Santejudean et al., 2023).

OA-IPP uses a different decomposition. The environment is represented by a GP target occupancy model with isotropic Matérn $x^*\in\arg\max_{x\in X}f(x)$8 kernel, the path is parameterized by spline control points $x^*\in\arg\max_{x\in X}f(x)$9, and planning proceeds in repeated chunks: CoarseGreedySearch proposes a waypoint sequence, then CMA-ES performs gradient-free global optimization of the continuous trajectory objective, with ESDF-based collision checking and FoV-occlusion-aware map updates during execution (Meera et al., 2019).

A$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$0 makes the augmented-state structure explicit. A search state is

$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$1

with accrued objective

$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$2

priority

$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$3

and admissible heuristic $$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$4 derived from a relaxed reachable-set problem in which future path continuity is ignored but per-step best reachable detection action is chosen greedily. This yields an $$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$5-optimal Weighted-A* style search with incumbent-based pruning (Mugford et al., 13 Nov 2025).

Several other methods follow the same pattern of state augmentation for path-dependent utility. Connectivity-aware path planning augments A* with a resettable outage-streak variable $$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$6, updating it as

$$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$7

so that COD becomes a hard search resource (Yang et al., 2019). Risk-aware ASD A* augments a grid state with cumulative safety $$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$8, using update $$f(x)\le B(x)=\min_{(x_s,f(x_s))\in S}[f(x_s)+l(x,x_s)].$$9, and retains multiple nondominated labels per location because different remaining safety budgets imply different future feasibility (Xiang et al., 2024). Occlusion-aware ground-target search uses nodes $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$0, where $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$1 is an “unobserved probability vector,” and performs iterative deepening $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$2 over a path-dependent utility field induced by a probabilistic visibility volume (Hague et al., 11 Nov 2025).

Across these methods, two design motifs recur. First, utility is usually non-Markovian in raw geometric state, so search state is expanded to include a belief, budget, or residual-value representation. Second, tractability depends on optimistic surrogates: heuristic relaxations, pooled maps, coarse grids, or receding-horizon approximations.

4. Representative formulations

The papers below illustrate the main UAPS variants. The table compresses the formulation; the substantive distinctions lie in how utility is estimated and how path dependence enters the search state.

Formulation	Utility definition	Search mechanism
OOPA (Santejudean et al., 2023)	Weighted optimistic bound reduction $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$3	Online value iteration on discretized state-action grid
OA-IPP (Meera et al., 2019)	$\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$4	Greedy initialization + CMA-ES over spline trajectories
A$\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$5 (Mugford et al., 13 Nov 2025)	Minimize cumulative undetected probability $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$6	$\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$7-optimal augmented-state A*/Weighted A*
Connectivity-aware planning (Yang et al., 2019)	Path-length minimization under COR/COD thresholds	Modified A* + penalty search over outage cost
Risk-aware ASD A* (Xiang et al., 2024)	Shortest feasible path under safety threshold $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$8	A* with additional safety dimension and learned heuristic
A-UCB* (González-Gudiño et al., 16 Oct 2025)	Travel cost minus acquisition-weighted edge utility	A* with acquisition-modified edge costs
Occlusion-aware target search (Hague et al., 11 Nov 2025)	Discounted cumulative viewing probability	Iterative deepening A* with probabilistic VV heuristic

Three distinctions are especially important. First, some formulations optimize an explicit reward-minus-cost objective, while others impose utility as a hard feasibility constraint. Second, some utilities are myopic over measurements or viewpoints, whereas others are explicitly long-horizon through dynamic programming or discounted path sums. Third, “path awareness” may enter through endpoint selection, through edge costs, or through belief-dependent state updates caused by intermediate observations.

This clarifies a common misconception: UAPS is not reducible to “A* with an extra heuristic term.” In several representative cases, the utility is path-history-dependent, belief-dependent, or non-additive in raw geometric space, so standard shortest-path abstractions fail unless the state is augmented or the problem is relaxed.

5. Empirical behavior and trade-offs

The empirical literature consistently reports gains when utility is attached to the path rather than only to destinations or static coverage. In path-aware optimistic optimization, when the optimum is found, OOPA uses on average $\rho(x,u)=\frac{\widehat f(x)+B(x)}{2}\,r(x,u),$9 less distance than the path-unaware CDOO baseline, while still usually finding the global optimum within one grid step in the reported 2D experiments (Santejudean et al., 2023). In OA-IPP, adaptive informative planning reduces map error faster than lawnmower and random baselines, outperforms non-adaptive variance-reduction planning later in the mission, and correctly finds all 7 human victims in the realistic urban simulation (Meera et al., 2019).

For graph-search-style UAPS, the advantage is often in bounded optimality or budget efficiency. A$r(x,u)$0 reports that exact search achieves truncated MTTD values $r(x,u)$1 lower on average than the median ACO solutions and $r(x,u)$2 lower on average than parallel track baselines; the $r(x,u)$3 version remains within $r(x,u)$4 of optimal on average while reducing runtimes to $r(x,u)$5–$r(x,u)$6 s in the four reported maritime scenarios (Mugford et al., 13 Nov 2025). Connectivity-aware planning shows that a moderate path-length increase can drastically improve communication quality: in the Virginia case study, the proposed path reduces $r(x,u)$7 by $r(x,u)$8 and maximum $r(x,u)$9 by $x$0 relative to the naive shortest path, with only an $x$1 increase in path length (Yang et al., 2019).

When utility is encoded as a constrained side objective, search efficiency remains a major issue. Learning-accelerated ASD A* reduces explored nodes by $x$2 and time by $x$3 on random maps, and by $x$4 and $x$5 on wind-flow maps, while maintaining identical average path length to Manhattan-heuristic ASD A* in the reported tests (Xiang et al., 2024). Acquisition-aware jammer localization shows the advantage of embedding utility directly in edge costs: in Chicago Downtown and Boston Common, A-UCB* markedly outperforms random motion and random i.i.d. sampling in surrogate-model and BO localization error, with finite path budget $x$6 remaining close to the $x$7 upper-bound variant (González-Gudiño et al., 16 Oct 2025).

Adaptive two-stage search exhibits a different trade-off. In agricultural object search, the adaptive planner yields a $x$8 shorter flight path than low-altitude coverage for non-uniformly distributed objects at only $x$9 lower F1-score, but only a $x_+=g(x,u)$0 shorter path for uniformly distributed objects at the same $x_+=g(x,u)$1 F1 loss; the method loses its advantage as target density becomes high and spatially uniform (Essen et al., 3 Apr 2025). This suggests that utility-aware inspection is especially valuable when uncertain or high-value targets are clustered. Terrain-aware pre-flight planning for multi-UAV SAR shows the same pattern at mission scale: terrain-prioritized coverage improves search and dispatch time over multiple meta-heuristic techniques, and the proposed planner is reported as up to $x_+=g(x,u)$2 faster than the second-best benchmark on the polygon-coverage tests (Granadeno et al., 12 May 2025).

The most general empirical lesson is that UAPS tends to help when intermediate observations materially change the value of future actions. It helps less when the environment is so dense, uniform, or weakly structured that selective path shaping collapses toward exhaustive coverage anyway.

6. Limitations, misconceptions, and broader extensions

UAPS methods inherit several recurring limitations. Many are low-dimensional or grid-based; OOPA is evaluated only in 2D and its runtime grows roughly quadratically with grid resolution, OA-IPP uses a discretized field and repeated global optimization without asymptotic analysis, and risk-aware ASD A* is demonstrated on $x_+=g(x,u)$3 maps despite substantial training cost for the learned heuristic (Santejudean et al., 2023, Meera et al., 2019, Xiang et al., 2024). Many assume known static geometry, known or estimated utility maps, and simplified sensing. OA-IPP assumes a known cluttered 3D environment and a static target occupancy field, occlusion-aware ground-target search assumes a known urban map and a 360° sensor at constant altitude, and connectivity-aware planning assumes a precomputed binary aerial coverage map at fixed altitude (Meera et al., 2019, Hague et al., 11 Nov 2025, Yang et al., 2019).

Theoretical guarantees are uneven. A$x_+=g(x,u)$4 provides an $x_+=g(x,u)$5-optimality guarantee via an admissible heuristic on an augmented state space (Mugford et al., 13 Nov 2025). By contrast, OOPA explicitly states that the reward is time-varying and approximate, so standard convergence guarantees of classical value iteration are unavailable (Santejudean et al., 2023). OA-IPP provides no convergence or regret guarantee, and A-UCB* does not analyze the conditions under which acquisition-modified edge costs preserve standard A* assumptions such as nonnegative costs and admissible heuristics (Meera et al., 2019, González-Gudiño et al., 16 Oct 2025).

A second misconception is that UAPS always uses explicit utility-minus-cost scalarization. Several influential examples do not. OOPA makes path cost matter operationally through motion constraints and finite-horizon execution, but its published reward has no explicit $x_+=g(x,u)$6 term (Santejudean et al., 2023). Connectivity-aware and risk-aware planners treat utility-like criteria as hard constraints rather than as additive rewards (Yang et al., 2019, Xiang et al., 2024). This suggests that UAPS should encompass both utility-maximizing and utility-constrained path search.

Finally, the underlying idea extends beyond physical robot motion. SEARCH-R treats multi-hop reasoning as a sequential path over sub-questions and uses a dependency-tree-based document informativeness score,

$x_+=g(x,u)$7

to retrieve evidence by informational contribution rather than only by similarity (Fu et al., 27 Apr 2026). In healthcare causal analysis, path-specific fairness and utility are evaluated through decompositions such as

$x_+=g(x,u)$8

with the causal fairness utility ratio used to judge whether blocking a pathway improves fairness at acceptable predictive cost (Nagesh et al., 16 Mar 2026). These are not motion-planning papers, but they suggest a broader interpretation: UAPS is a general design pattern for sequential search problems in which the value of a path depends on what the path reveals and on how those revelations alter the quality of subsequent actions.