Methodology of Designing Multi-agent Robot Control Systems Utilising Hierarchical Petri Nets

Cezary Zieli\'nski; Maksym Figat

arxiv: 1906.11614 · v2 · pith:2PLEUQK5new · submitted 2019-06-27 · 💻 cs.RO · cs.MA

Methodology of Designing Multi-agent Robot Control Systems Utilising Hierarchical Petri Nets

Maksym Figat , Cezary Zieli\'nski This is my paper

Pith reviewed 2026-05-25 14:35 UTC · model grok-4.3

classification 💻 cs.RO cs.MA

keywords multi-agent robot systemshierarchical Petri netsrobot control architectureautomatic code generationconcurrent subsystemssystem decompositionembodied agents

0 comments

The pith

Robot systems are designed as five-layer hierarchical Petri nets that organize concurrent subsystems and enable automatic controller code generation.

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

The paper establishes a methodology that models a robot system as a set of embodied agents, each decomposed into cooperating subsystems whose activities are defined using hierarchical Petri nets with conditions. These nets are built layer by layer: first the multi-agent robot system, then the agent, subsystem, behaviour, and finally the communication layer. This replaces an earlier finite state machine approach where communication was handled only at implementation time. A sympathetic reader would care because the method supplies both a systematic organization for development and a complete description of concurrent activities, plus a tool that turns the nets into executable controller code and thereby shortens the implementation phase.

Core claim

Activities of a robot system are represented by hierarchical Petri nets with conditions that are created by specifying five consecutive layers: the multi-agent robot system layer, the agent layer, the subsystem layer, the behaviour layer, and the communication layer. This decomposition organizes the development of a robot system in a systematic manner and introduces a comprehensive description of concurrently acting subsystems. A tool built on these considerations produces the nets and automatically generates the robot controller code, accelerating the implementation phase, as shown by the development of a controller for a rudimentary task.

What carries the argument

Hierarchical Petri nets with conditions built from five successive layers (multi-agent robot system, agent, subsystem, behaviour, communication) that model concurrent subsystem activities and support automatic code generation.

If this is right

Development of robot systems follows a repeatable five-layer decomposition process.
Communication between subsystems receives an explicit model rather than remaining an implementation detail.
Controller code is produced directly from the Petri net description, shortening the coding stage.
The same nets serve both as a design document and as input to automatic code generation.

Where Pith is reading between the lines

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

The approach could be tested on tasks that require dynamic reconfiguration of subsystem interactions to see whether the fixed layer structure still suffices.
Generated controllers might integrate more readily with formal verification tools that operate on Petri nets than controllers written by hand.
The method could be applied to fleets of robots by treating the top layer as a collection of multiple embodied agents rather than a single robot.

Load-bearing premise

Specifying the five layers with hierarchical Petri nets with conditions is sufficient to capture all necessary behavior and to generate correct controller code automatically.

What would settle it

Run the tool on a multi-subsystem robot task with known concurrency requirements and check whether the generated code executes the concurrent behaviors without additional manual fixes or runtime errors.

Figures

Figures reproduced from arXiv: 1906.11614 by Cezary Zieli\'nski, Maksym Figat.

**Figure 1.** Figure 1: Internal structure of an embodied agent aj defining particular behaviours sBj,v,ω of sj,v (ω is the behaviour designator), 4) behaviour layer defining behaviours sBj,v,ω represented by pages sP B j,v,ω, 5) communication layer determining the communication models used by behaviours sBj,v,ω, i.e. defining pages sP B j,v,ω,snd (net describing behaviour of sj,v when data is sent to other subsystems) and sP B… view at source ↗

**Figure 2.** Figure 2: HPN H defining the activities of a robot system one is based on a predicate called an initial condition s f σ j,v,α(α – predicate designator) [21]. Initial conditions of next behaviours are associated with the transitions pointed at by the arcs emerging from the place with which the just terminated behaviour is associated. The communication model must define whether communicating subsystems activities are… view at source ↗

**Figure 4.** Figure 4: Specification of c1 subsystem partial transition function c,ef 1,control, where L ≡ r x c i 1,sensor[left], M ≡ r x c i 1,sensor[middle] and R ≡ r x c i 1,sensor[right] are binary signals produced by the left, middle and right sensor. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: (a) Generated code simulation, (b) Agent layer [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: a, behaviour layer in Fig. 6b and communication layer in Fig. 3a. For the sake of briefness this paper presents only the control subsystem c1 HPN cH1 , which exhibits two behaviours: cB1,init, which initiates the connection with the simulated robot, and cB1,control, which calculates the transition function c,ef 1,control ( [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

read the original abstract

A robot system is designed as a set of embodied agents. An embodied agent is decomposed into cooperating subsystems. In our previous work activities of subsystems were defined by hierarchical finite state machines. With their states, activities were associated. In that approach communication between subsystems was treated as an implementation issue. This paper represents the activities of a robot system using hierarchical Petri nets with conditions. Such net is created by specifying consecutive layers: multi-agent robot system layer, agent layer, subsystem layer, behaviour layer and communication layer. This decomposition not only organizes in a systematic manner the development of a robot system but also introduces a comprehensive description of concurrently acting subsystems. Based on those theoretical considerations, a tool was created for producing hierarchical Petri nets defining the model of a robotic system and enabling automatic generation of the robot controller code, resulting in a significant acceleration of the implementation phase. The capabilities of the tool are presented by the development of a robot controller performing a rudimentary task.

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.

Desk Editor's Note private letter to a colleague

The paper moves their prior FSM work to a five-layer hierarchical Petri net model for multi-agent robots plus a code-generation tool, but supplies no semantics or checks that the generated code preserves the intended concurrency.

read the letter

The core of this paper is the switch to hierarchical Petri nets with conditions, structured in five explicit layers (multi-agent system, agent, subsystem, behaviour, communication) to model concurrent robot subsystems, plus a tool that builds the nets and emits controller code. They demonstrate it on one basic task. This is a direct evolution from their cited earlier finite-state-machine papers, and the layering does give a more systematic handle on concurrency than treating communication as an implementation detail after the fact. The tool claim is concrete enough that it could save time in their own development workflow. That part is useful as far as it goes. The soft spot is the missing bridge from model to code. Nothing in the description supplies operational semantics for the nets-with-conditions, a preservation argument for concurrency properties, or model-checking results on the output. The single rudimentary example does not test inter-subsystem synchronisation or communication-layer transitions, so the central claim that the approach produces correct controllers rests on unverified generation. This is aimed at robotics groups already using structured modeling for multi-agent controllers, especially those who liked the authors' FSM line of work. A reader wanting formal guarantees or substantial empirical validation will not find it here. I would bring it to a reading group as maybe, mainly to talk through whether the layering idea is worth extending. I would not cite it in the next year. It deserves peer review so referees can ask for the semantics or larger examples; the idea is coherent enough on its own terms to warrant that step.

Referee Report

2 major / 1 minor

Summary. The paper proposes a methodology for designing multi-agent robot control systems by representing activities via hierarchical Petri nets with conditions, decomposed into five layers (multi-agent robot system, agent, subsystem, behaviour, communication). This extends prior hierarchical finite state machine work by treating communication as part of the model. A tool is presented that generates the nets and automatically produces controller code, claimed to accelerate implementation; the approach is illustrated on a single rudimentary task.

Significance. If verified, the five-layer decomposition could offer a systematic organization for concurrent robot subsystems and the tool could reduce implementation effort. The explicit creation of a generation tool and its application to even a basic example constitute a concrete contribution toward practical use. However, the lack of any formal semantics or correctness argument for the generated code substantially reduces the assessed significance of the methodology.

major comments (2)

[Abstract] Abstract: the claim that the tool 'enables automatic generation of the robot controller code' is load-bearing yet unsupported; no operational semantics are supplied for the hierarchical Petri nets with conditions, nor any argument that the generated code preserves concurrency or inter-subsystem synchronization properties of the nets.
[tool and example description] The description of the tool and the rudimentary-task demonstration: the single example does not examine whether communication-layer transitions or concurrent subsystem synchronisation are correctly compiled, leaving the central claim that the layering 'introduces a comprehensive description of concurrently acting subsystems' unverified.

minor comments (1)

The manuscript would benefit from an explicit diagram or small worked example showing how a condition is attached to a transition at the communication layer and how that maps to generated code.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback highlighting both the practical aspects of our methodology and the areas needing clarification. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the tool 'enables automatic generation of the robot controller code' is load-bearing yet unsupported; no operational semantics are supplied for the hierarchical Petri nets with conditions, nor any argument that the generated code preserves concurrency or inter-subsystem synchronization properties of the nets.

Authors: The manuscript describes a practical tool that performs code generation via structural translation from the five-layer hierarchical Petri net model to controller code, as implemented and shown in the tool and example sections. We agree that no operational semantics or formal preservation arguments are supplied. In revision we will expand the tool description to detail the generation mapping and its handling of concurrency and communication, while noting that a complete formal treatment lies beyond the current scope. revision: partial
Referee: [tool and example description] The description of the tool and the rudimentary-task demonstration: the single example does not examine whether communication-layer transitions or concurrent subsystem synchronisation are correctly compiled, leaving the central claim that the layering 'introduces a comprehensive description of concurrently acting subsystems' unverified.

Authors: The provided example illustrates the layer-by-layer construction for a basic task and the resulting generated code. We acknowledge that it does not explicitly verify compilation correctness for communication transitions or subsystem synchronisation. We will revise the manuscript to include additional discussion and, where feasible, annotations in the example showing how the tool maps these elements, thereby better supporting the claim of comprehensive concurrent description. revision: yes

standing simulated objections not resolved

Formal operational semantics for the hierarchical Petri nets with conditions and proofs that generated code preserves concurrency and synchronization properties.

Circularity Check

0 steps flagged

Methodology paper introduces layered Petri net representation without circular derivation

full rationale

The paper presents a design methodology decomposing robot systems into five layers (multi-agent, agent, subsystem, behaviour, communication) using hierarchical Petri nets with conditions, extending prior FSM work. No equations, fitted parameters, predictions, or uniqueness theorems appear. The central claims concern organization of development and code generation acceleration via a tool, which are descriptive choices rather than reductions to inputs by construction. Self-citation to previous FSM work is mentioned but not load-bearing for any mathematical result. The derivation chain is self-contained as a representational proposal; no step reduces by definition or self-citation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review based solely on abstract; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5693 in / 1086 out tokens · 35176 ms · 2026-05-25T14:35:15.445030+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Such net is created by specifying consecutive layers: multi-agent robot system layer, agent layer, subsystem layer, behaviour layer and communication layer.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

A tool was created for producing hierarchical Petri nets defining the model of a robotic system and enabling automatic generation of the robot controller code

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

23 extracted references · 23 canonical work pages

[1]

Billington et al

D. Billington et al. Requirements Engineering via Non- monotonic Logics and State Diagrams. Berlin, Heidelberg, Springer Berlin Heidelberg 2011, pp. 121–135

work page 2011
[2]

I. Bluemke. Structural modelling with Petri nets. IFAC Proceedings Volumes, 1997, vol. 30, nr 1, pp. 63 – 68. IFAC Workshop on Manufacturing Systems: Modelling, Manage- ment and Control, Vienna, Austria, 3-5 February

work page 1997
[3]

R. A. Brooks. Intelligence without reason. Artiﬁcial intelli- gence: critical concepts, 1991, vol. 3, pp. 107–163

work page 1991
[4]

E. W. Dijkstra. A discipline of programming. (Prentice-Hall series in automatic computation). Englewood Cliﬀs: Prentice- Hall

work page
[5]

Figat, C

M. Figat, C. Zieliński, R. Hexel. FSM based speciﬁcation of robot control system activities. In: 2017 11th International Workshop on Robot Motion and Control (RoMoCo). Proce- edings, July, 2017, pp. 193–198

work page 2017
[6]

Girault, V

C. Girault, V. Rudiger. Petri Nets for Systems Engineering. Springer-Verlag Berlin Heidelberg New York 2003

work page 2003
[7]

Huber, K

P. Huber, K. Jensen, R. M. Shapiro. Hierarchies in Coloured Petri Nets. Lecture Notes in Computer Science; Advances in Petri Nets 1990, Proceedings Ed. G. Rozenberg, Berlin, Heidelberg, Springer Berlin Heidelberg, 1991, vol. 483, pp. 313–341

work page 1990
[8]

N. R. Jennings, K. Sycara, M. Wooldridge. A roadmap of agent research and development. Autonomous Agents and Multi-Agent Systems, Jan, 1998, vol. 1, nr 1, pp. 7–38

work page 1998
[9]

Kornuta, C

T. Kornuta, C. Zieliński. Robot control system design exem- pliﬁed by multi-camera visual servoing. Journal of Intelligent & Robotic Systems, 2013, Vol. 77, No. 3–4, pp. 499–524

work page 2013
[10]

J. Luo, H. Ni, M. Zhou. Control Program Design for Automated Guided Vehicle Systems via Petri Nets. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 45(1), pp. 44-55, Jan 2015

work page 2015
[11]

Kortenkamp, R

D. Kortenkamp, R. Simmons. Robotic systems architectures and programming. In: Springer Handbook of Robotics Ed. O. Khatib, B. Siciliano, pp. 187–206. Springer 2008

work page 2008
[12]

Montano, F

L. Montano, F. J. Garc´ ıa, J. L. Villarroel. Using the time Petri net formalism for speciﬁcation, validation, and code generation in robot-control applications. The International Journal of Robotics Research, 2000, vol. 19, nr 1, pp. 59–76

work page 2000
[13]

J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall 1981

work page 1981
[14]

R. Valk. Essential Features of Petri Nets. Berlin, Heidelberg, Springer Berlin Heidelberg 2003, pp. 9–28

work page 2003
[15]

W. Vogler. Modular construction and partial order semantics of Petri nets. 1992

work page 1992
[16]

The robot simulator VREP, http://www.coppeliarobotics.com/ accessed: 2018-09-12

work page 2018
[17]

M. C. Zhou, F. Dicesare, D. L. Rudolph. Design and Implementation of a Petri Net Based Supervisor for a Flexible Manufacturing System. Automatica, 28(6), pp. 1199-1208, 1992

work page 1992
[18]

Zieliński, M

C. Zieliński, M. Figat, R. Hexel. Communication Within Multi-FSM Based Robotic Systems. Journal of Intelligent & Robotic Systems, Jun, 2018

work page 2018
[19]

Zieliński, M

C. Zieliński, M. Figat, R. Hexel. Robotic Systems Implemen- tation Based on FSMs. In: Automation 2018. Proceedings Ed. R. Szewczyk, C. Zieliński, M. Kaliczyńska. Springer International Publishing, 2018, pp. 441–452

work page 2018
[20]

Zieliński, T

C. Zieliński, T. Winiarski. General speciﬁcation of multi-robot control system structures. Bulletin of the Polish Academy of Sciences – Technical Sciences, 2010, Vol. 58, No. 1, pp. 15–28

work page 2010
[21]

Zieliński, M

C. Zieliński, M. Figat. Robot System Design Procedure Based on a Formal Speciﬁcation. In: Recent Advances in Automa- tion, Robotics and Measuring Techniques. Proceedings Ed. R. Szewczyk, C. Zieliński, M. Kaliczyńska. Springer, 2016. vol. 440, series Advances in Intelligent Systems and Computing (AISC), pp. 511–522

work page 2016
[22]

Zieliński, T

C. Zieliński, T. Kornuta, T. Winiarski. A systematic method of designing control systems for service and ﬁeld robots. In: 19- th IEEE International Conference on Methods and Models in Automation and Robotics, MMAR. Proceedings. IEEE, 2014, pp. 1–14

work page 2014
[23]

W. M. Zuberek, I. Bluemke. Hierarchies of place/transition reﬁnements in Petri nets. In: Emerging Technologies and Factory Automation, 1996. EFTA ’96. Proceedings., 1996 IEEE Conference on. Proceedings, Nov, 1996. vol. 1, pp. 355– 360

work page 1996

[1] [1]

Billington et al

D. Billington et al. Requirements Engineering via Non- monotonic Logics and State Diagrams. Berlin, Heidelberg, Springer Berlin Heidelberg 2011, pp. 121–135

work page 2011

[2] [2]

I. Bluemke. Structural modelling with Petri nets. IFAC Proceedings Volumes, 1997, vol. 30, nr 1, pp. 63 – 68. IFAC Workshop on Manufacturing Systems: Modelling, Manage- ment and Control, Vienna, Austria, 3-5 February

work page 1997

[3] [3]

R. A. Brooks. Intelligence without reason. Artiﬁcial intelli- gence: critical concepts, 1991, vol. 3, pp. 107–163

work page 1991

[4] [4]

E. W. Dijkstra. A discipline of programming. (Prentice-Hall series in automatic computation). Englewood Cliﬀs: Prentice- Hall

work page

[5] [5]

Figat, C

M. Figat, C. Zieliński, R. Hexel. FSM based speciﬁcation of robot control system activities. In: 2017 11th International Workshop on Robot Motion and Control (RoMoCo). Proce- edings, July, 2017, pp. 193–198

work page 2017

[6] [6]

Girault, V

C. Girault, V. Rudiger. Petri Nets for Systems Engineering. Springer-Verlag Berlin Heidelberg New York 2003

work page 2003

[7] [7]

Huber, K

P. Huber, K. Jensen, R. M. Shapiro. Hierarchies in Coloured Petri Nets. Lecture Notes in Computer Science; Advances in Petri Nets 1990, Proceedings Ed. G. Rozenberg, Berlin, Heidelberg, Springer Berlin Heidelberg, 1991, vol. 483, pp. 313–341

work page 1990

[8] [8]

N. R. Jennings, K. Sycara, M. Wooldridge. A roadmap of agent research and development. Autonomous Agents and Multi-Agent Systems, Jan, 1998, vol. 1, nr 1, pp. 7–38

work page 1998

[9] [9]

Kornuta, C

T. Kornuta, C. Zieliński. Robot control system design exem- pliﬁed by multi-camera visual servoing. Journal of Intelligent & Robotic Systems, 2013, Vol. 77, No. 3–4, pp. 499–524

work page 2013

[10] [10]

J. Luo, H. Ni, M. Zhou. Control Program Design for Automated Guided Vehicle Systems via Petri Nets. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 45(1), pp. 44-55, Jan 2015

work page 2015

[11] [11]

Kortenkamp, R

D. Kortenkamp, R. Simmons. Robotic systems architectures and programming. In: Springer Handbook of Robotics Ed. O. Khatib, B. Siciliano, pp. 187–206. Springer 2008

work page 2008

[12] [12]

Montano, F

L. Montano, F. J. Garc´ ıa, J. L. Villarroel. Using the time Petri net formalism for speciﬁcation, validation, and code generation in robot-control applications. The International Journal of Robotics Research, 2000, vol. 19, nr 1, pp. 59–76

work page 2000

[13] [13]

J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall 1981

work page 1981

[14] [14]

R. Valk. Essential Features of Petri Nets. Berlin, Heidelberg, Springer Berlin Heidelberg 2003, pp. 9–28

work page 2003

[15] [15]

W. Vogler. Modular construction and partial order semantics of Petri nets. 1992

work page 1992

[16] [16]

The robot simulator VREP, http://www.coppeliarobotics.com/ accessed: 2018-09-12

work page 2018

[17] [17]

M. C. Zhou, F. Dicesare, D. L. Rudolph. Design and Implementation of a Petri Net Based Supervisor for a Flexible Manufacturing System. Automatica, 28(6), pp. 1199-1208, 1992

work page 1992

[18] [18]

Zieliński, M

C. Zieliński, M. Figat, R. Hexel. Communication Within Multi-FSM Based Robotic Systems. Journal of Intelligent & Robotic Systems, Jun, 2018

work page 2018

[19] [19]

Zieliński, M

C. Zieliński, M. Figat, R. Hexel. Robotic Systems Implemen- tation Based on FSMs. In: Automation 2018. Proceedings Ed. R. Szewczyk, C. Zieliński, M. Kaliczyńska. Springer International Publishing, 2018, pp. 441–452

work page 2018

[20] [20]

Zieliński, T

C. Zieliński, T. Winiarski. General speciﬁcation of multi-robot control system structures. Bulletin of the Polish Academy of Sciences – Technical Sciences, 2010, Vol. 58, No. 1, pp. 15–28

work page 2010

[21] [21]

Zieliński, M

C. Zieliński, M. Figat. Robot System Design Procedure Based on a Formal Speciﬁcation. In: Recent Advances in Automa- tion, Robotics and Measuring Techniques. Proceedings Ed. R. Szewczyk, C. Zieliński, M. Kaliczyńska. Springer, 2016. vol. 440, series Advances in Intelligent Systems and Computing (AISC), pp. 511–522

work page 2016

[22] [22]

Zieliński, T

C. Zieliński, T. Kornuta, T. Winiarski. A systematic method of designing control systems for service and ﬁeld robots. In: 19- th IEEE International Conference on Methods and Models in Automation and Robotics, MMAR. Proceedings. IEEE, 2014, pp. 1–14

work page 2014

[23] [23]

W. M. Zuberek, I. Bluemke. Hierarchies of place/transition reﬁnements in Petri nets. In: Emerging Technologies and Factory Automation, 1996. EFTA ’96. Proceedings., 1996 IEEE Conference on. Proceedings, Nov, 1996. vol. 1, pp. 355– 360

work page 1996