Coal mine tunnels present harsh conditions, making manual inspection inefficient and risky. Mobile robots offer a promising alternative, but existing research has its limitations.
Task allocation studies typically rely on simple distance or time measures, overlooking road-environment factors like slopes, obstacles, and slippery surfaces. Path-planning research rarely couples road conditions with energy consumption and charging feasibility. Moreover, charging decisions are often reduced to fixed battery thresholds rather than predictive assessments.
To address these gaps, this paper proposes a charging-aware two-stage framework that integrates underground road modeling, energy-aware task allocation, charging feasibility, and path planning for continuous multi-robot inspection.
Environmental Model Construction
The environment model represents underground tunnels as a two-dimensional space containing task points (inspection equipment), irregular obstacles (coal seams), and fixed charging stations.
While two-dimensional, the model is not purely geometric, as factors like dust, poor illumination, uneven road surfaces, and slope variations are quantified as road-environment weights, speed correction terms, and energy consumption costs, which are then incorporated into task allocation and path planning.
Multi-Robot Task Allocation with Charging Constraints
The task-allocation stage treats the problem as a single-depot, multiple-traveling-salesman scenario, where multiple robots depart from a common starting point, visit their assigned inspection points exactly once, and return to the start. The objective is to minimize total travel cost while respecting each robot's constraints.
What distinguishes this model from prior work is its predictive charging mechanism. Rather than triggering a recharge when battery levels fall below a fixed threshold, each robot evaluates whether it can complete the next task segment and still reach an available charging station while maintaining a safety margin of 20% battery.
If the answer is negative, a charging stop is inserted before the next task. When selecting a charging station, the model considers travel time to the pile, estimated queue time under a first-come, first-served rule, and the required charging duration, rather than simply choosing the nearest pile.
The cost function combines distance and time, both of which are adjusted by road-environment factors such as dust, dim lighting, and uneven surfaces. Additionally, a piecewise correction factor accounts for reduced battery discharge efficiency at lower charge levels, reflecting the engineering reality that effective range shrinks as the battery depletes.
To solve this allocation problem, the paper uses an improved bidirectional ant colony optimization (IBACO) algorithm. Two strategies are introduced: a dynamic evaporation factor that adjusts pheromone decay based on iteration progress to enhance solution diversity, and a ranking factor in which only top-performing ants deposit pheromone with rank-based weighting, accelerating convergence toward the global optimum.
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Multi-Robot Path Planning with Charging Constraints
Given the task sequences from the first stage, the path-planning stage generates safe, collision-free routes for each robot. The paper acknowledges that this two-stage decoupling may sacrifice strict global optimality, but it significantly reduces computational complexity compared to a fully joint optimization.
Initial paths are created through linear interpolation between consecutive task points. Each newly generated point undergoes a rationality check. If it falls inside an obstacle or creates a line segment that intersects one, the point is repositioned until a valid path emerges.
The cost function for path planning incorporates three indicators, which are distance, time, and physical work. Distance and time costs are adjusted by road-environment weights, consistent with the task-allocation stage.
The work cost is more elaborate, accounting for the energy a robot expends overcoming gravity on inclined slopes, rolling resistance from ground conditions, slope resistance, air resistance within the tunnel, and acceleration resistance. Slope-changing sections are treated as low-speed traversable areas, capturing their influence through speed correction and resistance terms rather than tracking every instantaneous change.
To optimize these paths, the paper employs an improved honey-badger-fly optimization algorithm (IHBAFOA). The key modification is a density factor with random perturbation, which introduces controlled randomness into the search process.
This fluctuation is larger in early iterations and stabilizes over time, helping the algorithm escape local optima more effectively than the original smoothly decreasing factor. When the honey badger stage generates an invalid point, the fly algorithm cancels it and produces a corrected position.
Simulation Experiments and Benchmark Results
Simulations were conducted in MATLAB using a two-dimensional (2D) underground tunnel model with 30 task points, four robots, and two charging stations. Three experiment sets were performed.
First, comparing scenarios with and without charging piles showed that without piles, robots had to interrupt inspection and return to the starting point to recharge, breaking task continuity. With charging piles, robots recharged mid-route and completed their task sequences smoothly, enabling continuous inspection.
Second, a self-comparison confirmed that the full IBACO^IHBAFOA framework outperformed partial-improvement variants, including BACO^IHBAFOA and IBACO^HBAFOA, in convergence speed and final cost.
Third, against six other algorithm combinations, IBACO^IHBAFOA achieved the lowest average cost function value of 6800.3 with a standard deviation of 6.50, indicating strong stability. However, its average running time of 120 seconds was not the shortest, highlighting computational efficiency as a remaining concern.
A Promising Step Forward
This study presents a charging-aware, two-stage planning method for continuous multi-robot inspection in underground coal mines. The first stage allocates tasks using an IBACO algorithm with road-environment factors and predictive charging decisions. The second stage generates collision-free paths using an IHBAFOA that accounts for distance, time, and work costs.
Simulations showed lower path costs and relatively good stability versus six comparison algorithms, though computational efficiency remains a limitation. The method has not yet been validated using physical robots or high-fidelity underground simulations, and the authors note that real-world factors such as sensor noise, wheel slip, communication delays, localization errors, and dynamic obstacles require further study.
Journal Reference
Xu, J., et al. (2026). Task allocation and path planning for multi-robot inspection in mines considering charging. Scientific Reports. DOI:10.1038/s41598-026-65759-z. https://www.nature.com/articles/s41598-026-65759-z.
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