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A distributed control and parameter estimation protocol with prescribed performance for homogeneous lagrangian multi-agent systems

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Abstract

In this paper, we consider the formation control problem for uncertain homogeneous Lagrangian nonlinear multi-agent systems in a leader-follower scheme under a directed communication protocol. A distributed adaptive control protocol of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate formation establishment as well as synchronization of the parameter estimates of all followers. The estimation and control laws are distributed in the sense that the control signal and the update laws are calculated based solely on local relative state information. Moreover, provided that the communication graph is strongly connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: (i) the underlying graph topology, (ii) the control gains selection and (iii) the agents’ model uncertainties. Finally, extensive simulation studies on the attitude control of flying spacecrafts clarify and verify the approach.

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Notes

  1. Several other works have been proposed for the coordinated tracking control problem in multi-agent systems, that however have assumed that all followers have access to the leader state, leading inevitably in centralized approaches.

  2. Our recent results (Bechlioulis et al. 2016) on the distributed control and parameter estimation of unknown Lagrangian multi-agent systems are extended here by considering a significantly more generic directed communication protocol as well as by verifying the theoretical findings via extensive comparative simulation studies.

  3. Apparently, when no relative offsets are required (i.e., all \(c_{ij}=0\), \(i=1,\dots ,N\)), we consider the synchronization/consensus problem, where a common response, dictated by the leader node, is required for all following agents.

  4. An \(\mathcal {M}\)-matrix is a square matrix having its off-diagonal entries non-positive and all principle minors non-negative.

  5. The desired command/reference trajectory information \(x_{0}\) is only pinned to a subgroup of the N following agents.

  6. Notice that the right product of a matrix \(\mathcal {A}\) with a positive definite and diagonal matrix \(\mathcal {D}\) corresponds to the multiplication of each column of \(\mathcal {A}\) with the corresponding diagonal element of \(\mathcal {D}\). Thus, if \(\mathcal {A}\) is an \(\mathcal {M}\)-matrix, which is equivalent to all its principal minors being positive, then \(\mathcal {AD}\) is also an \(\mathcal {M} \)-matrix since the signs of its principal minors are the same with those of \(\mathcal {A}\), owing to the positive definiteness of \(\mathcal {D}\).

  7. The symmetric part of the Laplacian matrix of a strongly connected and balanced graph is a positive semi-definite matrix (Wu 2005).

  8. Notice that from the proposed control scheme (7a)–(7d), we can select the control gains \(K_{p_{i}}\), \(K_{v_{i}}\) such that \(\tau _{i}\) are retained within certain bounds.

  9. Notice that the proposed methodology does not explicitly take into account any specifications in the input (magnitude or slew rate). Such research direction is an open issue for future investigation and would increase significantly the applicability of the proposed scheme.

  10. The attitude synchronization of multiple spacecrafts plays an important role in aerospace engineering since it increases the coverage of the earth surface during such missions. Apparently, the synchronization control problem is a subclass of generic formation control problems where no relative offsets are required (i.e., all \(c_{ij}=0\), \(i=1,\ldots ,N\)).

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Authors and Affiliations

  1. Control Systems Lab, School of Mechanical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Str, 15780, Athens, Greece

    Charalampos P. Bechlioulis & Kostas J. Kyriakopoulos

  2. Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Michael A. Demetriou

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  1. Charalampos P. Bechlioulis
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  2. Michael A. Demetriou
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  3. Kostas J. Kyriakopoulos
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Correspondence to Charalampos P. Bechlioulis.

Additional information

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

This is one of several papers published in Autonomous Robots comprising the “Special Issue on Distributed Robotics: From Fundamentals to Applications”.

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Bechlioulis, C.P., Demetriou, M.A. & Kyriakopoulos, K.J. A distributed control and parameter estimation protocol with prescribed performance for homogeneous lagrangian multi-agent systems. Auton Robot 42, 1525–1541 (2018). https://doi.org/10.1007/s10514-018-9700-2

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