From Forecast to Action: Uncertainty-Aware UAV Deployment for Ocean Drifter Recovery

We present a novel predict-then-optimize framework for maritime search operations that integrates trajectory forecasting with UAV deployment optimization-an end-to-end approach not addressed in prior work. A large language model predicts the drifter’s trajectory, and spatial uncertainty is modeled using Gaussian-based particle sampling. Unlike traditional static deployment methods, we dynamically adapt UAV detection radii based on distance and optimize their placement using meta-heuristic algorithms. Experiments on real-world data from the Korean coastline demonstrate that our method, particularly the repair mechanism designed for this problem, significantly outperforms the random search baselines. This work introduces a practical and robust integration of trajectory prediction and spatial optimization for intelligent maritime rescue.

💡 Research Summary

The paper introduces a comprehensive “predict‑then‑optimize” framework for maritime search‑and‑rescue (SAR) that tightly couples ocean drifter trajectory forecasting with the strategic deployment of unmanned aerial vehicles (UAVs). The authors argue that, while prior work has treated trajectory prediction and UAV placement as separate problems, real‑time SAR demands an end‑to‑end solution that can react to uncertain drift paths and operational constraints.

Trajectory Prediction
The forecasting component uses Chronos, a pretrained large language model (LLM) that treats time‑series forecasting as a language‑modeling task. Historical latitude‑longitude pairs are fed to Chronos, which generates one‑step‑ahead predictions in an iterative (recursive) fashion. To mitigate error accumulation, the authors do not rely on a single point estimate. Instead, they construct a bivariate Gaussian distribution centered at the predicted coordinate, with covariance Σ = σ²I where σ is set to four times the Haversine error observed at the previous time step. From this distribution they draw k particles (e.g., 200), each representing a plausible drifter location. This particle cloud captures spatial uncertainty and serves as the basis for the downstream optimization.

Uncertainty‑Aware Search Area
The feasible UAV deployment region A_u is defined as a circle around the LLM‑predicted center. Its radius R is four times the previous prediction error, a conservative heuristic that ensures the true drifter location is likely inside A_u.

Dynamic UAV Detection Radius
The UAV model (DJI Matrice 300 RTK) has a base detection radius of 100 m. The authors augment this with a spiral search pattern that can expand the effective radius up to 600 m when the UAV operates close to the center. Because flight time is limited (55 min total, 1.38 km/min cruise speed), the farther a UAV must travel to its assigned coordinate, the less time remains for the spiral search. This trade‑off is modeled linearly:

 D_r_i(x_i, y_i) = –200·d + 600

where d is the haversine distance (km) from the UAV’s assigned point to the center. Consequently, detection radii shrink from 600 m (near the center) to 200 m (at the edge of the feasible region).

Optimization Problem
Given n UAVs, the decision variables are the 2‑D coordinates (x_i, y_i) for each UAV. The objective is to maximize the number of straight‑line drifter trajectories (from the accident origin to each Gaussian particle) intersecting the UAV detection circles. For computational tractability during the meta‑heuristic search, the authors use geometric coverage as the fitness function; final performance is evaluated with a probabilistic detection model:

 P_oD = 1 – e^{‑c}

where c is the ratio of the UAV’s effective detection radius to the maximum (600 m). Constraints enforce (1) no UAV overlap, (2) adherence to flight‑time and speed limits, and (3) detection radii within the 200‑600 m band.

Meta‑Heuristic Algorithms and Repair Mechanism
Three population‑based meta‑heuristics are employed:

1. Genetic Algorithm (GA) – individuals encode all UAV coordinates; initialization samples angles and distances uniformly within A_u. Blend crossover (BLX‑α) and random mutation (re‑sampling positions) generate offspring.
2. Particle Swarm Optimization (PSO) – each particle represents a full UAV layout; velocities are updated using inertia, cognitive, and social components.
3. Simulated Annealing (SA) – a temperature schedule controls the acceptance of neighbor solutions.

All three algorithms incorporate a custom “repair mechanism” after each generation or move. The repair step (Algorithm 1) checks for (a) overlapping detection circles, (b) violation of the maximum travel distance (derived from flight‑time constraints), and (c) detection radius bounds. If any violation is detected, the offending UAV’s position is re‑sampled or its radius is adjusted to the nearest feasible value. This ensures every candidate solution respects operational limits, dramatically improving convergence speed and solution quality.

Experimental Evaluation
The framework is tested on real‑world drifter data collected along the Korean coastline (both West and East seas). Experimental settings include: n = 5–10 UAVs, k = 200 Gaussian particles, and a search‑area radius R set to four times the previous prediction error. Baselines consist of random UAV placement (Random Search) and static‑radius heuristics.

Key results:

• GA with repair achieved the highest detection success rate, improving over Random Search by 27 percentage points.
• PSO‑repair and SA‑repair also outperformed the baseline, delivering 12 % and 9 % gains respectively.
• Average Euclidean distance error between the true drifter location and the nearest UAV detection circle decreased by 35 % relative to the baseline.
• Computational overhead remained modest; the GA‑repair solution converged within a few hundred generations, compatible with the time‑critical nature of SAR missions.

Contributions

1. First end‑to‑end predict‑then‑optimize pipeline for maritime SAR that integrates LLM‑based trajectory forecasting with UAV deployment.
2. Novel uncertainty modeling via Gaussian particle sampling anchored on LLM predictions.
3. Dynamic detection‑radius model reflecting realistic UAV flight constraints.
4. A robust repair mechanism that enforces feasibility across multiple meta‑heuristics, markedly improving solution quality.
5. Empirical validation on authentic Korean coastal data, demonstrating practical superiority over random baselines.

Implications
The proposed framework showcases how foundation models can be repurposed for high‑stakes, real‑time decision making in uncertain environments. By explicitly modeling prediction uncertainty and embedding it into a constrained optimization problem, the approach yields UAV deployment plans that are both operationally realistic and statistically robust. The methodology is readily extensible to other domains such as wildfire monitoring, oil‑spill containment, or wildlife tracking, where uncertain target motion and limited sensor platforms coexist.