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Reconfigurable multi-robot coordination with guaranteed convergence in obstacle cluttered environments under local communication

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Abstract

In this paper, we consider a networked multi-robot system operating in an obstacle populated planar workspace under a single leader-multiple followers architecture. We propose a distributed reconfiguration strategy of the set of connectivity and formation specifications that assures convergence to the desired point, while guaranteeing global connectivity. In particular, we construct a low-level distributed navigation functions based controller that encodes the goals and safety requirements of the system. However, owing to topological obstructions, stable critical points other than the desired one may appear. In such case, we employ a high-level distributed discrete procedure which attempts to solve a distributed constraint satisfaction problem on a local Voronoi partition, providing the necessary reconfiguration for the system to progress towards its goal. Eventually, we show that the system either converges to the desired point or attains a tree configuration with respect to the formation topology, in which case the system switches to a novel controller based on the prescribed performance control technique, that eventually guarantees convergence. Finally, multiple simulation studies clarify and verify the approach.

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Notes

  1. More general types of obstacles can be considered by appropriately transforming them into disks [see Loizou (2014)].

  2. The same approach holds for convex obstacles in general, where \(x_k\) can be any arbitrary point in the interior of the obstacle.

  3. The formation graph \(\mathcal {G}_f\) is considered piecewise constant.

  4. Definitions of switches:

    $$\begin{aligned}&\sigma _\epsilon (z) \triangleq {\left\{ \begin{array}{ll}-\frac{1}{\epsilon ^2}z^2+\frac{2}{\epsilon }z,&{} z<\epsilon \\ 1,&{} z\ge \epsilon \end{array}\right. },\\&\sigma _{\epsilon ,R}(z) \triangleq {\left\{ \begin{array}{ll}1, &{}z\le R-\epsilon \\ \frac{2}{\epsilon ^3}z^3+\frac{-6R+3\epsilon }{\epsilon ^3}z^2 + \frac{6R^2-6R\epsilon }{e^3}z + \frac{-2R^3+3R^2\epsilon }{\epsilon ^3}, &{}R-\epsilon<z<R\\ 0, &{}z\ge R \end{array}\right. }\end{aligned}$$

  5. Agents can agree that the system has reached an equilibrium through a consensus procedure (Olfati-Saber et al. 2007).

  6. This a valid assumption given that both \(\theta _i\) and \(d_i\) are initially known, thus rendering proper initialization trivial.

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Authors and Affiliations

  1. Control Systems Laboratory, School of Mechanical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, 15780, Zografou, Greece

    Constantinos Vrohidis, Panagiotis Vlantis, Charalampos P. Bechlioulis & Kostas J. Kyriakopoulos

Authors
  1. Constantinos Vrohidis
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  2. Panagiotis Vlantis
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  3. Charalampos P. Bechlioulis
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  4. Kostas J. Kyriakopoulos
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Corresponding author

Correspondence to Charalampos P. Bechlioulis.

Additional information

This is one of several papers published in Autonomous Robots comprising the Special Issue on Online Decision Making in Multi-Robot Coordination.

This work was supported by the EU funded project Co4Robots: Achieving Complex Collaborative Missions via Decentralized Control and Coordination of Interacting Rob‘ots, H2020-ICT-731869, 2017–2019.

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Vrohidis, C., Vlantis, P., Bechlioulis, C.P. et al. Reconfigurable multi-robot coordination with guaranteed convergence in obstacle cluttered environments under local communication. Auton Robot 42, 853–873 (2018). https://doi.org/10.1007/s10514-017-9660-y

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  • DOI: https://doi.org/10.1007/s10514-017-9660-y

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