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arxiv: 2509.12390 · v2 · submitted 2025-09-15 · 💻 cs.RO

Distributed Event-Triggered Distance-Based Formation Control for Multi-Agent Systems

Evangelos Psomiadis , Panagiotis Tsiotras This is my paper

Pith reviewed 2026-05-18 15:52 UTC · model grok-4.3

classification 💻 cs.RO
keywords multi-agent systemsevent-triggered controlformation controldistance-based controlcollision avoidancedistributed controlnonlinear controlrobot teams
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The pith

A distributed event-triggered controller lets multi-agent teams reach distance-based formations from any start while updating controls only on error thresholds and avoiding collisions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a nonlinear controller for robot teams to form a prescribed shape using only local distance measurements between neighbors. Updates occur only when the difference between actual and last-used distances exceeds a fixed threshold, which the analysis shows preserves closed-loop stability and cuts total actuation compared with continuous feedback. A separate distributed barrier function modifies the input to keep inter-agent distances above a safety margin at all times. Experiments on both simulated and physical platforms confirm that the formation error converges while the number of control transmissions drops sharply relative to periodic or continuous baselines. A reader would care because many real robot teams operate under tight power and bandwidth limits, so infrequent yet safe updates directly extend mission duration.

Core claim

The authors prove that a distributed, distance-based, nonlinear law combined with an event condition on measurement error drives the team to the desired formation asymptotically for arbitrary initial positions and time-varying communication graphs, while a distributed control barrier function enforces collision-free motion; the closed-loop trajectories remain bounded and the formation error vanishes provided the triggering threshold satisfies a stability-derived bound.

What carries the argument

The event-triggering condition that fires when the norm of the distance measurement error exceeds a fixed positive threshold, together with the nonlinear distance-based control law and the distributed control barrier function that overrides the nominal input near collision boundaries.

If this is right

  • Agents reach the target formation asymptotically without continuous communication or actuation.
  • Inter-agent collisions are prevented even when the event condition is active.
  • Performance remains comparable to periodic triggering while the total control effort decreases.
  • The same threshold works across different formation shapes and network topologies.
  • The method scales to larger teams without redesign of the triggering rule.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The fixed-threshold design could be relaxed to an adaptive threshold that grows with formation size to further reduce updates in very large teams.
  • Because only distances are used, the controller might combine with vision-based distance estimators in GPS-denied settings without changing the stability proof.
  • If agents have bounded velocity constraints, the barrier function would need an additional velocity term to remain valid.
  • The same event logic might apply to time-varying target formations by feeding a slowly changing reference distance into the error signal.

Load-bearing premise

A single fixed threshold on measurement error can be chosen in advance so that the resulting event condition keeps the closed-loop system stable for every possible initial configuration and every possible sequence of communication graphs.

What would settle it

Run the controller on hardware with deliberately varying initial positions and intermittently dropping communication links; if any agent pair violates the minimum distance or the formation error fails to converge to zero while the number of updates remains lower than a periodic controller, the claim is false.

Figures

Figures reproduced from arXiv: 2509.12390 by Evangelos Psomiadis, Panagiotis Tsiotras.

Figure 1
Figure 1. Figure 1: Six GRITSBot X robots, initially arranged in a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Distributed, event-triggered, distance-based formation [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Final position of agents along with their corre [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Control inputs and (b) measurement errors for six [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Initial arrangement of 200 agents on a sphere (a) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Average formation error ∆ and (b) Colormap of agent control inputs for a 200-agent simulation. in distances primarily occur among agents near the equator, with minimal direct impact on agents further away in the communication graph. VI. CONCLUSIONS In this paper, we proposed a distributed, event-triggered, distance-based formation controller for multi-agent systems with limited resources. We establishe… view at source ↗
read the original abstract

This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from an arbitrary initial configuration. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller. Unlike the well-studied linear formation control strategies, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability while minimizing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a distributed event-triggered nonlinear controller for distance-based formation control of multi-agent systems. The controller triggers updates when the measurement error exceeds a fixed threshold, aiming to reduce actuation effort while ensuring stability and incorporating a distributed control barrier function for inter-agent collision avoidance. The approach is validated via simulations and real-world robot experiments across various formations, communication graphs, and parameter settings, with comparisons to periodic control.

Significance. If the stability guarantees hold, the work offers a practical method for resource-efficient formation control in robotic teams, with empirical evidence from hardware tests supporting reduced control effort without compromising performance. The combination of event-triggering and CBF is a notable contribution for safety-critical multi-agent applications.

major comments (2)
  1. [§V, Theorem 1] §V, Theorem 1: The stability analysis claims asymptotic stability under the event-triggered law with fixed threshold ε; however, no explicit lower bound on ε is derived that is independent of the initial inter-agent distance error norm or the minimum eigenvalue of the rigidity matrix, so the negative-definiteness of V̇ cannot be guaranteed for arbitrary initial configurations.
  2. [§IV, Eq. (12)] §IV, Eq. (12): The distributed event condition uses a constant threshold that is assumed to preserve closed-loop stability under switching graphs, yet the Lyapunov analysis appears to be carried out only for fixed connected graphs; temporary loss of edges can allow measurement errors large enough to violate the ultimate boundedness claim.
minor comments (2)
  1. [Figure 4] Figure 4: The plots of inter-agent distances would be clearer if the desired formation distances were overlaid as dashed lines for direct visual comparison.
  2. [§III] Notation for the measurement error e_i(t) is introduced in §III but its relation to the distance-based error vector is not restated in the stability section, which slightly reduces readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We address each major comment point by point below, providing clarifications and indicating where revisions will be made to improve the rigor of the theoretical results.

read point-by-point responses

  1. Referee: [§V, Theorem 1] §V, Theorem 1: The stability analysis claims asymptotic stability under the event-triggered law with fixed threshold ε; however, no explicit lower bound on ε is derived that is independent of the initial inter-agent distance error norm or the minimum eigenvalue of the rigidity matrix, so the negative-definiteness of V̇ cannot be guaranteed for arbitrary initial configurations.

    Authors: We acknowledge this observation on the stability analysis. Upon closer inspection of the proof of Theorem 1, the Lyapunov derivative yields ultimate boundedness of the formation error (rather than asymptotic convergence to the origin) when ε > 0, with the size of the ultimate bound depending on ε, the initial inter-agent distance error, and the minimum eigenvalue of the rigidity matrix. The manuscript does not claim asymptotic stability for positive fixed thresholds; we will revise the theorem statement, proof, and surrounding text in §V to explicitly state ultimate boundedness and derive the explicit ultimate error bound in terms of these quantities. This makes the dependence on initial conditions and the rigidity matrix transparent for arbitrary configurations. revision: yes

  2. Referee: [§IV, Eq. (12)] §IV, Eq. (12): The distributed event condition uses a constant threshold that is assumed to preserve closed-loop stability under switching graphs, yet the Lyapunov analysis appears to be carried out only for fixed connected graphs; temporary loss of edges can allow measurement errors large enough to violate the ultimate boundedness claim.

    Authors: We agree that the main Lyapunov analysis supporting the ultimate boundedness result is developed under the assumption of a fixed, connected communication graph, which ensures the rigidity matrix properties remain constant. The event condition in Eq. (12) keeps the measurement error below the threshold to preserve this boundedness when the graph is connected. Simulations and experiments do explore varying topologies, but the theory does not fully cover arbitrary switching. We will revise §IV to explicitly state the fixed connected graph assumption, add a remark on the potential violation under temporary edge loss, and include a brief discussion of how the result extends to switching graphs under persistent connectivity (e.g., joint connectivity over bounded intervals). This will be noted as a limitation and direction for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; controller design and stability analysis are independent of fitted inputs

full rationale

The paper formulates a new nonlinear distance-based event-triggered controller and invokes a distributed CBF for collision avoidance. Stability is established via a Lyapunov analysis that incorporates the event-triggering condition directly into the derivative bound, with the threshold treated as a design parameter chosen to satisfy the inequality. No step reduces a claimed prediction or uniqueness result to a quantity fitted from the same data or to a self-citation chain; the derivation remains self-contained against the stated assumptions on the rigidity matrix and graph connectivity.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The design depends on user-chosen thresholds and gains whose selection is not derived from first principles but tuned for performance; stability analysis assumes standard continuous-time multi-agent dynamics under event conditions.

free parameters (2)
  • event-triggering threshold
    Predefined constant that decides when a control update occurs based on distance measurement error.
  • controller gains
    Tunable parameters in the nonlinear distance-based control law required for convergence and stability.
axioms (1)
  • domain assumption The multi-agent system can be modeled with continuous dynamics and discrete event updates that admit Lyapunov stability analysis.
    Invoked to guarantee formation stability under the proposed triggering rule.

pith-pipeline@v0.9.0 · 5671 in / 1377 out tokens · 76381 ms · 2026-05-18T15:52:44.381025+00:00 · methodology

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Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

  1. [1]

    Consensus and cooperation in networked multi-agent systems,

    R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,”Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007

    work page 2007

  2. [2]

    Information flow and cooperative control of vehicle formations,

    J. Fax and R. Murray, “Information flow and cooperative control of vehicle formations,”IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465–1476, 2004

    work page 2004

  3. [3]

    Flocking for multi-agent dynamic systems: algo- rithms and theory,

    R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algo- rithms and theory,”IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006

    work page 2006

  4. [4]

    Mesbahi and M

    M. Mesbahi and M. Egerstedt,Graph Theoretic Methods in Multiagent Networks. Princeton University Press, 2010

    work page 2010

  5. [5]

    Comparison of periodic and event based sampling for first-order stochastic systems,

    K. Johan Astrom and B. Bernhardsson, “Comparison of periodic and event based sampling for first-order stochastic systems,” inIF AC World Congress, vol. 32, no. 2, Beijing, China, July 5-9, 1999, pp. 5006– 5011

    work page 1999

  6. [6]

    Event-triggered real-time scheduling of stabilizing control tasks,

    P. Tabuada, “Event-triggered real-time scheduling of stabilizing control tasks,”IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1680–1685, 2007

    work page 2007

  7. [7]

    Optimal event-triggered control of nonde- terministic linear systems,

    D. Maity and J. S. Baras, “Optimal event-triggered control of nonde- terministic linear systems,”IEEE Transactions on Automatic Control, vol. 65, no. 2, pp. 604–619, 2020

    work page 2020

  8. [8]

    Event-triggered control from data,

    C. De Persis, R. Postoyan, and P. Tesi, “Event-triggered control from data,”IEEE Transactions on Automatic Control, vol. 69, no. 6, 2024

    work page 2024

  9. [9]

    The robotarium: Globally impactful opportunities, challenges, and lessons learned in remote-access, distributed control of multirobot systems,

    S. Wilson, P. Glotfelter, L. Wang, S. Mayya, G. Notomista, M. Mote, and M. Egerstedt, “The robotarium: Globally impactful opportunities, challenges, and lessons learned in remote-access, distributed control of multirobot systems,”IEEE Control Systems Magazine, vol. 40, no. 1, pp. 26–44, Feb 2020

    work page 2020

  10. [10]

    Event-triggered communication and control of networked systems for multi-agent consensus,

    C. Nowzari, E. Garcia, and J. Cort ´es, “Event-triggered communication and control of networked systems for multi-agent consensus,”Auto- matica, vol. 105, pp. 1–27, 2019

    work page 2019

  11. [11]

    Event-triggered optimal formation tracking control using reinforcement learning for large- scale uav systems,

    Z. Yan, L. Han, X. Li, J. Li, and Z. Ren, “Event-triggered optimal formation tracking control using reinforcement learning for large- scale uav systems,” inIEEE International Conference on Robotics and Automation (ICRA), London, United Kingdom, May 29 - June 02, 2023, pp. 3233–3239

    work page 2023

  12. [12]

    Distributed event-triggered control for multi-agent systems,

    D. V . Dimarogonas, E. Frazzoli, and K. H. Johansson, “Distributed event-triggered control for multi-agent systems,”IEEE Transactions on Automatic Control, vol. 57, no. 5, pp. 1291–1297, 2012

    work page 2012

  13. [13]

    Event-based broadcasting for multi-agent average consensus,

    G. S. Seyboth, D. V . Dimarogonas, and K. H. Johansson, “Event-based broadcasting for multi-agent average consensus,”Automatica, vol. 49, no. 1, pp. 245–252, 2013

    work page 2013

  14. [14]

    Decentralized event-triggered formation of linear multi-agent system,

    X. Li, X. Dong, Q. Li, and Z. Ren, “Decentralized event-triggered formation of linear multi-agent system,” inIEEE International Con- ference on Control and Automation (ICCA), Ohrid, North Macedonia, July 3-6, 2017, pp. 988–993

    work page 2017

  15. [15]

    An iterative learning approach to formation control of multi-agent systems,

    Y . Liu and Y . Jia, “An iterative learning approach to formation control of multi-agent systems,”Systems and Control Letters, vol. 61, no. 1, pp. 148–154, 2012

    work page 2012

  16. [16]

    Event-triggered formation control of a generalized multi-agent system,

    R. Toyota and T. Namerikawa, “Event-triggered formation control of a generalized multi-agent system,” inAnnual Conference of the Society of Instrument and Control Engineers of Japan (SICE), Nara, Japan, Sep. 11-14, 2018, pp. 940–945

    work page 2018

  17. [17]

    Event-triggered connectivity- preserving formation control of heterogeneous multiple USVs,

    C. Chen, W. Zou, and Z. Xiang, “Event-triggered connectivity- preserving formation control of heterogeneous multiple USVs,”IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 54, no. 12, pp. 7746–7755, 2024

    work page 2024

  18. [18]

    Distributed event-triggered collision avoidance formation control for QUA Vs with disturbances based on virtual tubes,

    H. Guo, M. Chen, Y . Shen, and M. Lungu, “Distributed event-triggered collision avoidance formation control for QUA Vs with disturbances based on virtual tubes,”IEEE Transactions on Industrial Electronics, vol. 72, no. 2, pp. 1892–1903, 2025

    work page 1903

  19. [19]

    Distance-based formation shape stabilisation via event-triggered control,

    Q. Liu, Z. Sun, J. Qin, and C. Yu, “Distance-based formation shape stabilisation via event-triggered control,” inChinese Control Confer- ence (CCC), Hangzhou, China, July 28 - 30 2015, pp. 6948–6953

    work page 2015

  20. [20]

    Formation control of multi-agent systems with connectivity preservation by using both event-driven and time- driven communication,

    H. Yu and P. J. Antsaklis, “Formation control of multi-agent systems with connectivity preservation by using both event-driven and time- driven communication,” inIEEE Conference on Decision and Control, Maui, HI, USA, Feb. 10-13, 2012, pp. 7218–7223

    work page 2012

  21. [21]

    The GRITSBot in its natural habitat - a multi-robot testbed,

    D. Pickem, M. Lee, and M. Egerstedt, “The GRITSBot in its natural habitat - a multi-robot testbed,” inIEEE International Conference on Robotics and Automation (ICRA), Seattle, W A, USA, May 26-30, 2015, pp. 4062–4067

    work page 2015

  22. [22]

    Control barrier functions: Theory and applications,

    A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in18th European Control Conference (ECC), Naples, Italy, June 25- 28, 2019, pp. 3420–3431

    work page 2019

  23. [23]

    Near-identity diffeomorphisms and exponential epsilon-tracking and epsilon-stabilization of first-order nonholonomic SE(2) vehicles,

    R. Olfati-Saber, “Near-identity diffeomorphisms and exponential epsilon-tracking and epsilon-stabilization of first-order nonholonomic SE(2) vehicles,” inIEEE American Control Conference, vol. 6, An- chorage, AK, USA, May 8-10, 2002, pp. 4690–4695

    work page 2002