pith. sign in

arxiv: 1907.08531 · v1 · pith:K5ZNFOP7new · submitted 2019-07-19 · 📡 eess.SY · cs.SY

An optimization-based cooperative path-following framework for multiple robotic vehicles

Andrea Alessandretti , A. Pedro Aguiar This is my paper

Pith reviewed 2026-05-24 19:09 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords model predictive controlcooperative path followingmulti-agent systemsconsensusoutput regulationrobotic vehiclesdistributed control
0
0 comments X

The pith

Model predictive control embeds an auxiliary consensus law to jointly solve output regulation and coordination for multiple agents.

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

The paper develops a distributed control method for networks of robotic vehicles that must follow paths while agreeing on a common coordination state. It frames the task as a coordinated output regulation problem in which each vehicle steers its output to the origin and its coordination vector to consensus with neighbors. The solution is an MPC scheme whose cost function directly incorporates a pre-existing auxiliary consensus controller, thereby trading off regulation error against coordination error at each step. Convergence guarantees are stated for the closed-loop system under the given network topology. The approach is illustrated on a fleet of three-dimensional nonholonomic vehicles.

Core claim

By augmenting the MPC performance index with the output of a pre-existing auxiliary consensus control law, the resulting optimization problem yields a distributed controller that drives agent outputs to the origin while driving coordination vectors to consensus, with explicit convergence conditions supplied for the coordinated output regulation problem.

What carries the argument

Model predictive control scheme whose quadratic cost combines an output-regulation term with a consensus term taken directly from an auxiliary consensus controller.

If this is right

  • The controller remains distributed: each agent uses only its own state, its coordination vector, and those of its neighbors.
  • The transient balance between path-following error and coordination error is optimized at every time step.
  • The same framework applies to any multi-agent system whose dynamics admit an auxiliary consensus law.
  • Numerical evidence on nonholonomic vehicles confirms that the combined objective produces feasible trajectories.

Where Pith is reading between the lines

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

  • The method could be tested on physical robot platforms to measure communication load and computation time against purely consensus-based or purely path-following baselines.
  • If the auxiliary consensus law is itself optimal for some secondary criterion, the MPC layer may inherit additional performance properties not stated in the paper.
  • The approach suggests a template for other coordinated tasks, such as formation control or synchronized manipulation, whenever an auxiliary consensus module is available.

Load-bearing premise

A suitable auxiliary consensus control law already exists and can be inserted unchanged into the MPC cost function.

What would settle it

A concrete network and auxiliary consensus law for which the closed-loop MPC trajectories fail to reach consensus or output regulation despite satisfying all stated assumptions.

Figures

Figures reproduced from arXiv: 1907.08531 by Andrea Alessandretti, A. Pedro Aguiar.

Figure 1
Figure 1. Figure 1: Block diagram of the proposed control architecture. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The black lines denote the desired paths [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The dashed lines are associated to the case [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Closed-loop signal associated with the simulation of the decoupled [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

This paper addresses the design of an optimization-based cooperative path-following control law for multiple robotic vehicles that optimally balances the transient trade-off between coordination and path-following errors. To this end, we formulate a more general multi-agent framework where each agent is associated with (i) a continuous-time dynamical model, which governs the evolution of its state, and (ii) an output equation that is a function of both the state of the agent and a coordination vector. According to a given network topology, each agent can access its state and coordination vector, as well as the coordination vectors of the neighboring agents. In this setup, the goal is to design a distributed control law that steers the output signals to the origin, while simultaneously driving the coordination vectors of the agents of the network to consensus. To solve this, we propose a model predictive control scheme that builds on a pre-existing auxiliary consensus control law to design a performance index that combines the output regulation objective with the consensus objective. Convergence guarantees under which one can solve this coordinated output regulation problem are provided. Numerical simulations display the effectiveness of the proposed scheme applied to a cooperative path following control problem of a network of 3D nonholonomic robotic vehicles.

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 proposes a model predictive control (MPC) framework for cooperative path-following of multiple robotic vehicles. It formulates a general multi-agent setup with continuous-time dynamics and output maps depending on agent states and coordination vectors. Under a given network topology, the distributed control objective is simultaneous output regulation to the origin and consensus on the coordination vectors. The key construction is an MPC scheme whose performance index is designed by directly incorporating a pre-existing auxiliary consensus control law; convergence guarantees for the resulting coordinated output regulation problem are asserted, and the approach is illustrated on numerical simulations of 3D nonholonomic vehicles.

Significance. If the convergence guarantees hold under the stated assumptions, the framework would offer a systematic optimization-based method to trade off transient coordination and path-following errors in multi-vehicle networks. The explicit use of an auxiliary consensus law to construct the MPC cost is a distinguishing feature that could reduce redesign effort when consensus controllers already exist. No machine-checked proofs or parameter-free derivations are present, but the reproducibility of the numerical example on nonholonomic dynamics is a modest strength.

major comments (2)
  1. [Abstract] Abstract (third paragraph): the central claim that the MPC performance index is built by incorporating a pre-existing auxiliary consensus control law 'without further modification' is load-bearing for both the coordinated output regulation objective and the asserted convergence guarantees, yet no conditions are supplied ensuring existence or direct incorporability of such a law for arbitrary continuous-time dynamics, output maps, or the specific 3D nonholonomic vehicle model.
  2. [Problem formulation / MPC design] Problem formulation and MPC design sections: the weakest assumption—that an auxiliary consensus law exists independently of the MPC design, is compatible with the network topology, and remains unmodified when inserted into the cost—receives no supporting argument or existence result, undermining the generality of the convergence guarantees for the class of systems considered.
minor comments (2)
  1. [Numerical simulations] The abstract states that 'numerical simulations display the effectiveness' but provides no quantitative metrics, error bounds, or comparison baselines; this should be expanded in the simulation section with explicit performance indices.
  2. [Problem statement] Notation for the coordination vector and output map is introduced in the abstract but would benefit from an early dedicated table or diagram in the problem statement to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comments below, clarifying the role of the auxiliary consensus law assumption and indicating revisions to improve precision.

read point-by-point responses

  1. Referee: [Abstract] Abstract (third paragraph): the central claim that the MPC performance index is built by incorporating a pre-existing auxiliary consensus control law 'without further modification' is load-bearing for both the coordinated output regulation objective and the asserted convergence guarantees, yet no conditions are supplied ensuring existence or direct incorporability of such a law for arbitrary continuous-time dynamics, output maps, or the specific 3D nonholonomic vehicle model.

    Authors: We agree that the abstract phrasing could be read as implying broader applicability without explicit caveats. The framework is designed for the class of systems where a compatible auxiliary consensus law already exists (as is standard when leveraging prior consensus results). For the 3D nonholonomic vehicles, the specific consensus law is constructed and used in Section V. We will revise the abstract to state explicitly that the method assumes the availability of such a pre-existing law that is compatible with the network topology and can be inserted unmodified into the cost. revision: yes

  2. Referee: [Problem formulation / MPC design] Problem formulation and MPC design sections: the weakest assumption—that an auxiliary consensus law exists independently of the MPC design, is compatible with the network topology, and remains unmodified when inserted into the cost—receives no supporting argument or existence result, undermining the generality of the convergence guarantees for the class of systems considered.

    Authors: The manuscript treats the existence of a suitable auxiliary consensus law as a standing assumption (see the problem setup in Section II and the MPC cost construction in Section III), rather than deriving an existence result, because consensus controller design is a distinct and well-studied problem. The convergence guarantees in Theorem 1 are conditional on this assumption and on the law being compatible with the given topology. We will add a clarifying remark in Section II stating the assumption explicitly and noting that the guarantees hold whenever such a law is available and unmodified. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation builds on external auxiliary law with independent convergence guarantees

full rationale

The paper formulates a coordinated output regulation problem and proposes an MPC scheme that incorporates a pre-existing auxiliary consensus control law into a performance index combining output regulation and consensus objectives. It then states convergence guarantees under which the problem can be solved. No quoted step reduces a claimed prediction or result to a fitted parameter, self-definition, or self-citation chain by construction. The auxiliary law is treated as an external input whose existence is an assumption, not derived within the paper; the guarantees are presented as conditional on that assumption rather than tautological. This matches the default expectation of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields minimal ledger entries; the central claim rests on standard multi-agent assumptions and the existence of an auxiliary controller.

axioms (2)
  • domain assumption Network topology permits each agent to access its own state, coordination vector, and neighbors' coordination vectors
    Invoked in the problem setup for distributed control.
  • domain assumption Existence of a pre-existing auxiliary consensus control law
    Explicitly used to construct the MPC performance index.

pith-pipeline@v0.9.0 · 5744 in / 1204 out tokens · 25679 ms · 2026-05-24T19:09:13.870457+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Coordinated path-following control for nonlinear systems with logic-based communication,

    A. P. Aguiar and A. M. Pascoal, “Coordinated path-following control for nonlinear systems with logic-based communication,” in IEEE Con- ference on Decision and Control , 2007, pp. 1473–1479

    work page 2007

  2. [2]

    Coordinated path following of multiple UA Vs for time-critical missions in the presence of time-varying communication topologies,

    A. P. Aguiar, I. Kaminer, R. Ghabcheloo, A. M. Pascoal, E. Xargay, N. Hovakimyan, C. Cao, and V . Dobrokhodov, “Coordinated path following of multiple UA Vs for time-critical missions in the presence of time-varying communication topologies,” in Proc of the 17th IFAC World Congress, Seoul, Korea, jul 2008, pp. 16 015–16 020

    work page 2008

  3. [3]

    A coordination architecture for spacecraft formation control,

    R. Beard, J. Lawton, and F. Hadaegh, “A coordination architecture for spacecraft formation control,” IEEE Trans. on Control Systems Technology, vol. 9, pp. 777–790, 2001

    work page 2001

  4. [4]

    Straight line path following for formations of underactuated marine surface vessels,

    E. Børhaug, A. Pavlov, E. Panteley, and K. Y . Pettersen, “Straight line path following for formations of underactuated marine surface vessels,” IEEE Transactions on Control Systems Technology , vol. 19, no. 3, pp. 493–506, 2011

    work page 2011

  5. [5]

    Safe coordi- nated maneuvering of teams of multirotor unmanned aerial vehicles: A cooperative control framework for multivehicle, time-critical missions,

    V . Cichella, R. Choe, S. B. Mehdi, E. Xargay, N. Hovakimyan, V . Do- brokhodov, I. Kaminer, A. M. Pascoal, and A. P. Aguiar, “Safe coordi- nated maneuvering of teams of multirotor unmanned aerial vehicles: A cooperative control framework for multivehicle, time-critical missions,” IEEE Control Systems , vol. 36, no. 4, pp. 59–82, 2016

    work page 2016

  6. [6]

    Formation constrained multi-agent control,

    M. Egerstedt and X. Hu, “Formation constrained multi-agent control,” IEEE Transactions on Robotics and Automation, vol. 17, no. 6, pp. 947– 951, Dec. 2001

    work page 2001

  7. [7]

    Coordinated path-following in the presence of communication losses and time delays,

    R. Ghabcheloo, A. P. Aguiar, A. M. Pascoal, C. Silvestre, I. Kaminer, and J. P. Hespanha, “Coordinated path-following in the presence of communication losses and time delays,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 234–265, 2009

    work page 2009

  8. [8]

    Passivity-based designs for synchronized path-following,

    I.-A. F. Ihle, M. Arcak, and T. I. Fossen, “Passivity-based designs for synchronized path-following,” Automatica, vol. 43, no. 9, pp. 1508– 1518, 2007

    work page 2007

  9. [9]

    Robust output maneuvering for a Class of nonlinear systems,

    R. Skjetne, T. Fossen, and P. Kokotovic, “Robust output maneuvering for a Class of nonlinear systems,” Automatica, vol. 40, no. 3, pp. 373–383, 2004

    work page 2004

  10. [10]

    Synchronized path following control of multiple homogenous underactuated auvs,

    X. Xiang, C. Liu, L. Lapierre, and B. Jouvencel, “Synchronized path following control of multiple homogenous underactuated auvs,” Journal of Systems Science and Complexity , vol. 25, no. 1, pp. 71–89, 2012

    work page 2012

  11. [11]

    Parallel and Distributed Computa- tion: Numerical Methods,

    D. P. Bertsekas and J. N. Tsitsiklis, “Parallel and Distributed Computa- tion: Numerical Methods,” 1989

    work page 1989

  12. [12]

    Consensus problems in networks of agents with switching topology and time-delays,

    R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” Automatic Control, IEEE Trans. on , vol. 49, no. 9, pp. 1520–1533, sep 2004

    work page 2004

  13. [13]

    Consensus and Cooper- ation in Networked Multi-Agent Systems,

    R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and Cooper- ation in Networked Multi-Agent Systems,” Proc. of the IEEE , vol. 95, no. 1, pp. 215–233, jan 2007

    work page 2007

  14. [14]

    Mesbahi and M

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

    work page 2010

  15. [15]

    Nonlinear Model Predictive Control for Constrained Output Path Following,

    T. Faulwasser and R. Findeisen, “Nonlinear Model Predictive Control for Constrained Output Path Following,” IEEE Trans. on Automatic Control, vol. 9286, no. c, pp. 1–1, 2015

    work page 2015

  16. [16]

    Receding horizon tracking control of wheeled mobile robots,

    D. Gu and H. Hu, “Receding horizon tracking control of wheeled mobile robots,” IEEE Trans. on Control Systems Technology, vol. 14, no. 4, pp. 743–749, jul 2006

    work page 2006

  17. [17]

    Trajectory-tracking and path-following controllers for constrained underactuated vehicles using Model Predictive Control,

    A. Alessandretti, A. P. Aguiar, and C. N. Jones, “Trajectory-tracking and path-following controllers for constrained underactuated vehicles using Model Predictive Control,” in Proc. of the 2013 European Control Conference, 2013, pp. 1371–1376

    work page 2013

  18. [18]

    Con- strained model predictive control: Stability and optimality,

    D. Q. Mayne, J. B. Rawlings, C. V . Rao, and P. O. M. Scokaert, “Con- strained model predictive control: Stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, jun 2000

    work page 2000

  19. [19]

    J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design. Nob Hill Pub., 2009

    work page 2009

  20. [20]

    Model predictive control: Recent developments and future promise,

    D. Q. Mayne, “Model predictive control: Recent developments and future promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, nov 2014

    work page 2014

  21. [21]

    Architectures for distributed and hierarchical Model Predictive Control A review,

    R. Scattolini, “Architectures for distributed and hierarchical Model Predictive Control A review,” Journal of Process Control, vol. 19, no. 5, pp. 723–731, may 2009

    work page 2009

  22. [22]

    Distributed receding horizon control for multi-vehicle formation stabilization,

    W. B. Dunbar and R. M. Murray, “Distributed receding horizon control for multi-vehicle formation stabilization,” Automatica, vol. 42, no. 4, pp. 549–558, 2006

    work page 2006

  23. [23]

    Distributed model predictive control of dynamically decoupled systems with coupled cost,

    C. Wang and C.-J. Ong, “Distributed model predictive control of dynamically decoupled systems with coupled cost,” Automatica, vol. 46, no. 12, pp. 2053–2058, 2010

    work page 2053

  24. [24]

    Distributed predictive control: A non- cooperative algorithm with neighbor-to-neighbor communication for linear systems,

    M. Farina and R. Scattolini, “Distributed predictive control: A non- cooperative algorithm with neighbor-to-neighbor communication for linear systems,” Automatica, vol. 48, no. 6, pp. 1088–1096, 2012

    work page 2012

  25. [25]

    Model Predictive Control Schemes for Consensus in Multi-Agent Systems with Single- and Double-Integrator Dynamics,

    G. Ferrari-Trecate, L. Galbusera, M. P. E. Marciandi, and R. Scattolini, “Model Predictive Control Schemes for Consensus in Multi-Agent Systems with Single- and Double-Integrator Dynamics,” IEEE Trans. on Automatic Control , vol. 54, no. 11, pp. 2560–2572, 2009

    work page 2009

  26. [26]

    Stability of multiagent systems with time-dependent com- munication links,

    L. Moreau, “Stability of multiagent systems with time-dependent com- munication links,” IEEE Trans. on Automatic Control , vol. 50, no. 2, pp. 169–182, 2005

    work page 2005

  27. [27]

    A distributed model predictive control scheme for coordinated output regulation,

    A. Alessandretti and A. P. Aguiar, “A distributed model predictive control scheme for coordinated output regulation,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 8692–8697, 2017

    work page 2017

  28. [28]

    On Convergence and Performance Certification of a Continuous-Time Economic Model Pre- 13 dictive Control Scheme with Time-Varying Performance Index,

    A. Alessandretti, P. A. Aguiar, and C. Jones, “On Convergence and Performance Certification of a Continuous-Time Economic Model Pre- 13 dictive Control Scheme with Time-Varying Performance Index,” Auto- matica, vol. 68, pp. 305 – 313, 2016

    work page 2016

  29. [29]

    Notions of input to output stability,

    E. D. Sontag and Y . Wang, “Notions of input to output stability,” Systems & Control Letters , vol. 38, pp. 235–248, 1999

    work page 1999

  30. [30]

    Input-output-to-state sta- bility,

    M. Krichman, E. D. Sontag, and Y . Wang, “Input-output-to-state sta- bility,” SIAM Journal on Control and Optimization , vol. 39, no. 6, pp. 1874–1928, 2001

    work page 1928

  31. [31]

    Uniting Local and Global Output Feedback Controllers,

    C. Prieur and A. R. Teel, “Uniting Local and Global Output Feedback Controllers,” IEEE Trans. Autom. Control, vol. 56, no. 7, pp. 1636–1649, 2011

    work page 2011

  32. [32]

    Input to state stability: Basic concepts and results,

    E. D. Sontag, “Input to state stability: Basic concepts and results,” in Nonlinear and Optimal Control Theory . Springer, 2006, pp. 163–220

    work page 2006

  33. [33]

    A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability,

    H. Chen and F. Allg ¨ower, “A Quasi-Infinite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability,” Automatica, vol. 34, no. 10, pp. 1205–1217, 1998

    work page 1998

  34. [34]

    A general framework to design stabilizing nonlinear model predictive controllers,

    F. A. C. C. Fontes, “A general framework to design stabilizing nonlinear model predictive controllers,” Systems & Control Letters, vol. 42, no. 2, pp. 127–143, 2001

    work page 2001

  35. [35]

    Findeisen and F

    R. Findeisen and F. Allg ¨ower, The quasi-infinite horizon approach to nonlinear model predictive control . Springer Berlin Heidelberg, 2003

    work page 2003

  36. [36]

    H. K. Khalil, Nonlinear Systems. Prentice Hall PTR, 2002

    work page 2002

  37. [37]

    Input-to-state stability for discrete-time nonlinear systems,

    Z. P. Jiang and Y . Wang, “Input-to-state stability for discrete-time nonlinear systems,” Automatica, 2001

    work page 2001