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Real-time adaptive multi-robot exploration with application to underwater map construction


This paper deals with the problem of autonomous exploration of unknown areas using teams of Autonomous X Vehicles (AXVs)—with X standing for Aerial, Underwater or Sea-surface—where the AXVs have to autonomously navigate themselves so as to construct an accurate map of the unknown area. Such a problem can be transformed into a dynamic optimization problem which, however, is NP-complete and thus infeasible to be solved. A usual attempt is to relax this problem by employing greedy (optimal one-step-ahead) solutions which may end-up quite problematic. In this paper, we first show that optimal one-step-ahead exploration schemes that are based on a transformed optimization criterion can lead to highly efficient solutions to the multi-AXV exploration. Such a transformed optimization criterion is constructed using both theoretical analysis and experimental investigations and attempts to minimize the “disturbing” effect of deadlocks and nonlinearities to the overall exploration scheme. As, however, optimal one-step-ahead solutions to the transformed optimization criterion cannot be practically obtained using conventional optimization schemes, the second step in our approach is to combine the use of the transformed optimization criterion with the cognitive adaptive optimization (CAO): CAO is a practicably feasible computational methodology which adaptively provides an accurate approximation of the optimal one-step-ahead solutions. The combination of the transformed optimization criterion with CAO results in a multi-AXV exploration scheme which is both practically implementable and provides with quite efficient solutions as it is shown both by theoretical analysis and, most importantly, by extensive simulation experiments and real-life underwater sea-floor mapping experiments in the Leixes port, Portugal.

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  1. 1.

    The problem of multi-robot trajectory generation for maximizing SLAM efficiency is also referred in the literature as exploration or optimal motion strategy. In the rest of this paper, these terms will be used interchangeably.

  2. 2.

    For simplicity, we assume that the orientation of the AXVs is fixed and constant all the time. All the results of this paper can be easily extended in the case where the orientation changes by the navigation algorithm.

  3. 3.

    Additionally, it might be useful to set an upper limit (big enough) in the times that a landmark can be estimated by at least one AXV with any accuracy. This limit will serve as deadlock avoidance meachnism in cases of a landmark cannot be accurately estimated, due to the local morphology of the area to be mapped. We would like to thank one of the reviewers who pointed that out.

  4. 4.

    Table 1 presents the performance using the average percentage of the Non-Accurately estimated landmarks, so as to be in-line with the upcoming results.

  5. 5.

    According to Kosmatopoulos (2009) and Kosmatopoulos and Kouvelas (2009) it suffices to choose N to be any positive integer larger or equal to \(2\times \)[the number of variables being optimized by CAO]. In our case the variables optimized are the robot positions \(\mathbf{X}^R_{t_i}\) and thus it suffices for N to satisfy \(N\ge 2N_R\times \dim \left( \mathbf{X}^R_{t_i}\right) \).

  6. 6.

    A video footage of this experiment can be found on

  7. 7.

    Please note that both interpolated versions of usual practice present some ridges along the constructed terrain. These ridges correspond to the areas where the AUVs traversed and therefore the samples’ concentration is greater than the rest of the terrain.

  8. 8.

    In order to implement this, at first we discretize, with a sufficient small step, the areas to be compared and afterwords we apply the \(L^2\)-Norm on the vectorized versions of the sampled areas.


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The research leading to these results has received funding from the European Communities Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 270180 (NOPTILUS).

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Correspondence to Athanasios Ch. Kapoutsis.

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Kapoutsis, A.C., Chatzichristofis, S.A., Doitsidis, L. et al. Real-time adaptive multi-robot exploration with application to underwater map construction. Auton Robot 40, 987–1015 (2016).

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  • Path planning for multiple mobile robot systems
  • Trajectory generation
  • Cognitive robotics
  • Mapping
  • Marine robotics