Modified Fire Hawk Optimizer Sharpens Direction Finding for Humanoid Robots

Humanoid robots working in homes, hospitals, and service centers face a deceptively simple question every time a signal reaches their sensors: where did it come from? Answering that question — known as direction-of-arrival (DOA) estimation — is central to how a robot orients its head toward a speaking person, tracks warning signals, or localizes wireless devices around it. A new simulation study published in Discover Robotics reports a modified version of a nature-inspired optimization algorithm that, according to its authors, improves the accuracy of this direction-finding task in cluttered, reverberant indoor wireless environments.

The work, carried out by Vaibhav Kumar Kamal, Geetha P, and Satyasai Jagannath Nanda, integrates a head-mounted Uniform Circular Antenna Array (UCAA) into a humanoid robot model and treats DOA estimation as an optimization problem rather than a classical signal-processing task. Their proposed algorithm, called the Modified Fire Hawk Optimizer (MFHO), builds on the Fire Hawk Optimizer introduced in 2022, a metaheuristic inspired by raptors such as whistling kites, black kites, and brown falcons that deliberately spread fire to flush out hidden prey. The algorithm translates that behavior into search mechanics: candidate solutions act as fire hawks and prey, and the best solution so far serves as the main fire guiding the hunt through the search space.

The modification lies in how positions are updated. Instead of fixed update rules, the researchers introduced time-varying control parameters: an attraction strength that decays linearly from 0.85 to 0.5, an attraction decay rate falling from 1 to 0.7, an adaptive step size shrinking from 0.8 to 0.2, a Gaussian random perturbation with zero mean and unit standard deviation, and a Euclidean-distance-based interaction factor. According to the authors, these choices widen exploration early in the search, shift gradually toward local exploitation, and help the population escape local optima — a persistent risk in multimodal problems such as DOA estimation under multipath propagation.

Before applying the algorithm to the robotics problem, the team benchmarked it on 24 unconstrained, multi-dimensional test functions drawn from a public benchmark repository. Over thirty independent runs with 1500 iterations, MFHO achieved the best average fitness values in most functions, outperforming the original Fire Hawk Optimizer in 21 of the 24 cases. The exceptions were the Banana Shape, Downhill Step, and Giunta functions. The comparison set also included the Grey Wolf Optimizer, Particle Swarm Optimization, and the Spatial Spectrum Fusion Estimation and Localization (SSFEAL) algorithm, with average fitness values generally decreasing from SSFEAL toward MFHO across the benchmark suite.

The robotics scenario models a moving humanoid robot whose head carries a circular array, with an embedded processing unit in the torso handling snapshot acquisition, covariance estimation, and optimization-based DOA computation. The circular geometry was chosen for practical reasons: it provides full 360-degree azimuthal coverage and rotational symmetry without mechanical rotation, in a compact configuration suited to a robot’s head. In the simulations, the array elements are spaced at half the carrier wavelength, and the received signal model accounts for direct paths from user devices, multiple reflected paths from walls and furniture, and additive white Gaussian noise. Robot motion is assumed slow relative to the estimation frame, allowing quasi-static, snapshot-based processing.

The DOA estimate itself is obtained by minimizing a cost function derived from the sample covariance matrix of the received signals, following a maximum-likelihood formulation. Because the objective function becomes nonlinear and multimodal in reverberant indoor conditions — precisely where classical subspace methods such as MUSIC and ESPRIT tend to degrade at low signal-to-noise ratios and limited snapshots — the authors argue that a metaheuristic search is better suited to finding the global optimum. The simulations used an OFDM system with 64-QAM modulation, a 30 MHz subcarrier channel bandwidth, and 312 kHz subcarrier spacing, with a 64-element UCAA at the base stations.

Performance was tested across SNR values from -20 dB to 30 dB, snapshot sizes of 50, 100, 150, and 200, and scenarios with 10 and 20 active user devices. The reported results show MFHO consistently producing lower root-mean-square error (RMSE) than the comparison methods across all SNR levels and snapshot settings, with the largest advantages in the low-SNR regime between -10 dB and 0 dB, where classical and unmodified metaheuristic methods showed higher errors. Box plots over thirty independent runs indicated that MFHO’s RMSE distributions were more tightly confined, with minimized medians at each SNR condition. Fitness values for all algorithms rose as the number of user devices increased from 10 to 20, reflecting greater multipath interference, but MFHO maintained the lowest values throughout.

The authors also report that estimated DOA angles closely matched true source directions, and that angle accuracy degraded both with falling SNR and with more user devices, as expected. In a localization comparison at 5 dB SNR against true angles of 30.35, 60.07, 120.82, and 150.07 degrees, all tested methods clustered near the ideal identity line, with MFHO showing the closest alignment. The method also achieved a higher probability of resolving closely spaced sources than the alternatives, and its performance compared favorably against the theoretical Cramér–Rao lower bound, with normalized RMSE comparable to or slightly below other methods as SNR increased.

Statistical validation supported these comparisons. A non-parametric Kruskal–Wallis test conducted over thirty independent runs and 800 iterations rejected the null hypothesis of no significant difference between the methods in most cases for both 10 and 20 user devices, with p-values below the 0.05 significance level. On computational cost, the modified algorithm retains the same order of complexity as the original Fire Hawk Optimizer — proportional to population size, problem dimension, and iteration count — because the adaptive parameters require only simple per-iteration computations. Runtime measurements averaged over 100 Monte Carlo runs showed MUSIC, with its closed-form eigenanalysis, as the fastest method, while MFHO’s runtime remained comparable to other metaheuristics and, the authors argue, within practical limits for real-time robot audition.

The study is entirely simulation-based: no physical robot or over-the-air experiments are reported, and all data were generated from the equations in the manuscript. The authors position the framework as a step toward reliable multi-source localization for humanoid robot audition systems in smart homes, healthcare facilities, and service environments, where multipath propagation, noise, and many simultaneously active devices complicate perception. Within those simulated indoor wireless scenarios, the modified fire hawk search demonstrated lower estimation error, tighter variability, stronger statistical significance, and higher resolution probability than the compared classical and metaheuristic methods, suggesting that adaptive versions of nature-inspired optimizers may earn a place in the signal-processing stack of future socially interactive robots.

Subject of Research: Optimization-based direction-of-arrival estimation for a humanoid robot with a head-mounted uniform circular antenna array in indoor wireless environments

Article Title: Direction of arrival estimation on a humanoid robot using uniform circular array with Modified Fire Hawk Optimizer

Article References: Kamal, V. K., P, G., & Nanda, S. J. (2026). Direction of arrival estimation on a humanoid robot using uniform circular array with Modified Fire Hawk Optimizer. Discover Robotics, 2(1), Article 24. https://doi.org/10.1007/s44430-026-00038-0

Image Credits: AI Generated

DOI: 10.1007/s44430-026-00038-0

Keywords: humanoid robots, direction-of-arrival estimation, uniform circular antenna array, Fire Hawk Optimizer, metaheuristic optimization, indoor wireless localization, multipath propagation, signal processing, RMSE, Kruskal-Wallis test, robot audition, simulation study