Selective spectral correlation for efﬁcient map merging in multi-robot systems

This letter addresses the problem of grid map merging in multi-robot systems without knowledge of inter-robot observations, common landmarks and initial relative poses. Several map merging methods have been proposed to solve the problem while overcoming the lack of features or local minima. This letter proposes a selective spectral correlation method for more efﬁcient map merging which can reduce computation times while maintaining the accuracy. The performance of the proposed method was tested with experimental datasets and compared with other existing methods.

Introduction: Multi-robot systems (MRS) have received a lot of attention because of their advantages over single robot systems in terms of time efficiency and flexibility. If a MRS is operated in unknown environments, it should build a collective map by merging individual maps of robots using their own sensors. If there is no initial relative pose and no direct observation information between robots, a map merging method should find and align overlapping areas between individual maps without the direct information [1]. Carpin [2] proposed a spectra-based map merging method using geometric spectra extracted from grid maps. Saeedi et al. [3] proposed a map merging method using Hough peak matching. They have shown good performance but sometimes failed due to local minima. In our previous works [4][5][6], we proposed a tomographic feature-based map merging method using tomographic features extracted from grid maps. It has shown improved accuracy but required much computation time, which degenerates the applicability to real-time systems. This letter proposes a selective spectral correlation method for more efficient map merging, which can reduce computation times while maintaining the accuracy. This selective method has two advantages over the conventional method. First, it can reduce the computation time because it can reduce the number of iterations in the loop. Second, it can avoid local minima which can be caused by excessive spectral information on ambiguous areas.
The concept of the proposed method is shown in Figure 1. Individual maps built by a MRS are transformed to Hough images with peaks. Then, rotational spectra are extracted selectively around the peak points, and the rotation angle is estimated by the correlation between the selective Hough spectra. Next, -Y spectra are extracted selectively around the peak points of the rotated Hough image, and translation amounts are estimated by the correlation between selective translational spectra. Finally, particle swarm optimization (PSO) [7] finds the optimal MTM (map transformation matrix), and the merged map is obtained. Given two individual maps M n where n = 1, 2, a selective angle range set s θ,n of M n for −2π ≤ θ < 2π is generated by selectively gathering the angles corresponding to the peak cells p M = {p M,i } i=1,2,...,n . Then, the selective rotational spectrum θ,n is extracted by counting the Hough values for not the whole range but the selective angle range set s θ,n as follows: The difference between the conventional spectrum and θ is shown in Figure 2(a). By the selective strategy, many zero values appears in θ,n . Next, the selective rotational spectral correlation function θ between θ,1 and θ,2 is generated by selectively applying the circular crosscorrelation process to not the whole angle range but the reduced range 0 ≤ θ ≤ |θ 1 −θ 2 | whereθ n is the angle corresponding to the peak of θ,n as follows: where N θ is the maximum angle. The difference between θ and the conventional rotational correlation is shown in Figure 2  Because θ = 0 • , 90 • in H Mn indicates respectively line segments perpendicular to x and y axes, the selective x and y translational spectra X ,n and Y,n are respectively extracted by counting the Hough values for not the whole x and y range but s x,n and s y,n as follows: The difference between the conventional translational spectrum and R is shown in Figure 3(a). Because of the selective strategy, many zero values appears in X ,n . The selective x and y translational spectral correlation function X and Y are generated by selectively applying the circular cross-correlation process to not the whole range but the reduced ranges 0 ≤ x ≤ |x 1 −x 2 | and 0 ≤ y ≤ |ŷ 1 −ŷ 2 | wherex n andŷ n are x and y coordinates corresponding to the peak of X ,n and Y,n as follows: where N X and N Y are the maximum x and y translations. The difference between X and the conventional x-translational correlation is shown in Figure 3(b). Because of the selective strategy, many zero values appears in X . Finally, the x and y translational amounts are respectively estimated as follows: X = arg max x X (x) and Y = arg max y Y (y).

MTM refinement with PSO:
The MTM needs to be refined due to the inevitable errors caused by differently built individual maps, which is commonly applied to all map merging algorithms. Thus, the proposed method includes a MTM refinement process with PSO. The search space are determined based on the estimated MTMT as follows: and σ Y are margin values. Then, particles {p j } j=1,...,Np are sampled from the uniform distribution for the search space, where N p is the number of particles. At every t, the velocity v j (t ) and position p j (t ) of each particle are respectively updated by where p j (t ) = [p j,x , p j,y , p j,θ ] where j = 1, . . . , N p . ω < 1 is a constriction factor which acts like friction, and κ ∼ [0, 1] is a random vector with uniform distribution, and τ 2 is a control factor for relative attraction to p sb and p j,pb . The personal best position p j,pb indicates the best position of p j so far with the maximum similarity between M 1 and to measure the quality of each particle for map merging is defined as follows: After the PSO is converged as shown in Figure 4(a) and Figure 4(b), the MTM T is determined as T = p sb at the final iteration.
Experimental results: The proposed algorithm was tested with datasets obtained by real experiments with a multi-robot system as shown in the top left of Figure 1. Each robot had produced its own grid map by our simultaneous localization and mapping technique [8] with LIDAR. The individually produced grid maps were successfully merged by the proposed method as shown in the bottom right of Figure 1. For more clear evaluation, we define a total performance index indicating both the accuracy and computation times as follows: K =¯ /T where¯ andT are a normalised value of the objective value defined as (9) and a normalized computation time. The maxima of and T were respectively 266.3 and 1.175 s. The total index of the proposed algorithm was quantitatively compared with those of tomographic featurebased map merging (TMM) [5], spectra-based map merging (SMM) [2], mean squared error (MSE)-based image registration method, and oriented FAST and rotated BRIEF (ORB) feature-based method [9]. As shown in Figure 5, the proposed algorithm showed high accuracy, small computation time, and thus the best total index. This improvement has benefited from the selective spectral correlation in the proposed method.
Conclusions: This letter proposes a selective spectral correlation method for more efficient map merging which can reduce computation times while maintaining the accuracy. The evaluation results with experimental datasets showed that the proposed method can reduce the computation time with high similarity. Consequently, map merging can be conducted more reliably in real-time MRS.

© 2021 The Authors. Electronics Letters published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Received: 9 December 2020 Accepted: 20 February 2021 doi: 10.1049/ell2.12139