Highly Efficient Observation Process based on FFT Filtering for Robot Swarm Collaborative Navigation in Unknown Environments

TL;DR

This work tackles collaborative swarm navigation in unknown environments lacking external localization by introducing an FFT-based filtering pipeline to (i) rapidly extract safe forward directions from sensor data and (ii) compress observations for low-bandwidth fusion within the swarm. A protective distance model couples robot geometry with a pair of FFT-based filters to produce real-time safety directions and compact feature representations, while a probabilistic fusion framework combines self and neighbor observations to drive planning decisions. The approach achieves microsecond-level processing, enables bit-level data transmission, and supports 2D and 3D scenarios, with validation in real-world sensor tests and extensive Gazebo simulations showing improved arrival rates and path efficiency over baseline Bug planners. Overall, the method offers a scalable, low-cost solution for real-time swarm navigation in complex unknown environments, with demonstrated potential for 3D deployment and future refinements in filter designs and 3D performance.

Abstract

Collaborative path planning for robot swarms in complex, unknown environments without external positioning is a challenging problem. This requires robots to find safe directions based on real-time environmental observations, and to efficiently transfer and fuse these observations within the swarm. This study presents a filtering method based on Fast Fourier Transform (FFT) to address these two issues. We treat sensors' environmental observations as a digital sampling process. Then, we design two different types of filters for safe direction extraction, as well as for the compression and reconstruction of environmental data. The reconstructed data is mapped to probabilistic domain, achieving efficient fusion of swarm observations and planning decision. The computation time is only on the order of microseconds, and the transmission data in communication systems is in bit-level. The performance of our algorithm in sensor data processing was validated in real world experiments, and the effectiveness in swarm path optimization was demonstrated through extensive simulations.

Figures (8)

• Figure 1: Architecture of our proposed method, which comprises sensors, filters, and 3 modules. (A) Dimension reduction and reconstruction. (B) Safety directions extraction from sensor data. (C) Probabilistic fusion decision and planning. The filter parameters correspond to the robot dimensions, so the filter sequences can be pre-stored in the robots' ROM. The outputs of the algorithm, consisting of safe directions and probabilistic fusion decisions, serve as inputs for the planner, where the Bug planner is used as an example.
• Figure 2: Protective Distance Model. (a) Geometric relationship between the robot collision radius $r_0$, protection radius $r$ and planning distance $l_{th}$. (b) The observation of the robot is divided into 4 quadrants based on left and right, as well as whether it is within the safety sector.
• Figure 3: Illustrative example of extracting safety directions from sensor data. Simulation parameters are presented in Section \ref{['subsec:resultes-planning']}. (a) Filter $h_1$ in the time domain. The width of the rectangular window $T_c$ corresponds to the robot's safe sector angle $\alpha$. (b) Filter $H_1$ in the frequency domain. The FFT points $N_0=1024$. The digital cutoff frequency is $f_c=0.013$, at which the filter gain is -3dB. (c) The robot's sensor data points overlaid on the picture of the working environment. The two arrows in the figure represent the optional forward directions towards the target direction. (d) Truncated observation data using the planning distance of $l_{th}=0.6m$. (e) The data after filtering in normalized scale. (f) The safe direction determined using condition (\ref{['eq:y1 for safe']}). The two arrows in the figure correspond to those in (c).
• Figure 4: Filter design for dimension reduction and reconstruction of sensor data. The environment and the robot observations are the same as those in Figure \ref{['fig:h1']}c. (a) Filter $h_2$ in the time domain. The main lobe width of the filter corresponds to the robot's safe sector angle $\alpha$, and the sidelobe decays rapidly. (b) Filter $H_2$ in the frequency domain. The filter gain is -3dB at digital cutoff frequency $f_c=0.013$. (c) Filtered sensor data. Dimension reduction can be achieved by finding the extrema, as described in (\ref{['eq:extrema']}). The compressed data for transmission in normalized scale is $\Sigma_0=$ {(26, 0.42), (67, 0.074), (125, 0.598), (183, 0.208), (229, 0.606), (267, 0.358), (294, 0.542), (342, 0.08)}. (d) The reconstructed observation based on $\Sigma_0$.
• Figure 5: Our algorithm processes 3D observations. (a) Depth observation of the forest. The color bar represents the depth value in meters. (b) Safe direction domain extracted by filtering.