Timed abstractions for distributed cooperative manipulation

Abstract

This paper addresses the problem of deriving well-defined timed abstractions for the decentralized cooperative manipulation of a single object by N robotic agents. In particular, we propose a distributed model-free control protocol for the trajectory tracking of the cooperatively manipulated object without necessitating feedback of the contact forces/torques or inter-agent communication. Certain prespecified performance functions determine the transient and steady state of the coupled object-agents system. The latter, along with a region partition of the workspace that depends on the physical volume of the object and the agents, allows us to define timed transitions for the coupled system among the derived workspace regions. Therefore, we abstract its motion as a finite transition system and, by employing standard automata-based methodologies, we define high level complex tasks for the object that can be encoded by timed temporal logics. In addition, we use load sharing coefficients to represent potential differences in power capabilities among the agents. Finally, realistic simulation studies verify the validity of the proposed scheme.

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Notes

  1. 1.

    We focus on robotic structures where such a function exists, which constitute the majority of cases.

  2. 2.

    It can be proven that if such a run exists, then there also exists a run that can be always represented as a finite prefix followed by infinite repetitions of a finite suffix (Baier et al. 2008).

  3. 3.

    Note that the nature of the quadrotors makes the whole system underactuated and values \(\phi _{r_j,r_{j'}}(t),\theta _{r_j,r_{j'}}(t) \ne 0\) are not possible to be achieved without interfering with \(p_{\scriptscriptstyle O}(t)\).

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Correspondence to Christos K. Verginis.

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

This work was supported by funding from the Knut and Alice Wallenberg Foundation, the Swedish Resekarch Council (VR), the European Union’s Horizon 2020 Research and Innovation Programme under the Grant Agreement No. 644128 (AEROWORKS), the H2020 ERC Starting Grant BUCOPHSYS and the EU H2020 Research and Innovation Programme under GA No. 731869 (Co4Robots)

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Verginis, C.K., Dimarogonas, D.V. Timed abstractions for distributed cooperative manipulation. Auton Robot 42, 781–799 (2018). https://doi.org/10.1007/s10514-017-9672-7

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Keywords

  • Timed abstractions
  • Cooperative manipulation
  • Formal verification
  • Robotics
  • Multi-agent systems
  • Robust control