A study on force-based collaboration in swarms


Cooperative manipulation is a basic skill in groups of humans, animals and in many robotic applications. Besides being an interesting challenge, communication-less approaches have been applied to groups of robots in order to achieve higher scalability and simpler hardware and software design. We present a generic model and control law for robots cooperatively manipulating an object, for both ground and floating systems. The control method exploits a leader–follower scheme and is based only on implicit communication (i.e., the sensing of contact forces). The control objective mainly consists of steering the object manipulated by the swarm of robots to a desired position and orientation in a cooperative way. For a system with just one leader, we present analytical results on the equilibrium configurations and their stability that are then validated by numerical simulations. The role of object internal forces (induced by the robots through contact forces) is discussed in terms of convergence of the object position and orientation to the desired values. We also present a discussion on additional properties of the controlled system that were investigated using thorough numerical analysis, namely the robustness of the system when the object is subject to external disturbances in non-ideal conditions, and how the number of leaders in the swarm can affect the aforementioned convergence and robustness.

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  1. 1.

    \(\mathrm{SO}({3}) = \{ \varvec{R}\in {\mathbb {R}}^{3 \times 3} \; | \; \varvec{R}^\top \varvec{R}= \varvec{I}_{3} \}\) where \(\varvec{I}_{i} \in {\mathbb {R}}^{i \times i}\) is the identity matrix of dimension i.

  2. 2.

    The left superscript indicates the reference frame. From now on, \({\mathcal {F}}_W\) is considered as reference frame when the superscript is omitted.

  3. 3.

    \(\varvec{S}(\star ): {\mathbb {R}}^{3} \rightarrow {\mathbb {R}}^{3 \times 3}\) is such that \(\varvec{S}({\varvec{x}}){\varvec{y}}= {\varvec{x}}\times {\varvec{y}}\) for every \({\varvec{x}}\in {\mathbb {R}}^{3}\) and \({\varvec{y}}\in {\mathbb {R}}^{3}\).

  4. 4.

    Forces that do not result in a motion of the object, nor compensate any external wrench. For a more complete description, the reader can refer to Prattichizzo and Trinkle (2008).

  5. 5.

    \(\varvec{R}_{{\varvec{z}}_W}(\star ) \in \mathrm{SO}({3})\) describes a rotation along the axes \({\varvec{z}}_W\) about the angle \(\star \).


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This research was partially supported by the ANR, Project ANR-17-CE33-0007 MuRoPhen.

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Correspondence to Antonio Franchi.

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Gabellieri, C., Tognon, M., Sanalitro, D. et al. A study on force-based collaboration in swarms. Swarm Intell 14, 57–82 (2020). https://doi.org/10.1007/s11721-019-00178-7

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  • Multi-robot manipulation
  • Communication-less coordination
  • Admittance-controlled robots
  • Aerial robotic co-manipulation