Review sketch

Control Lyapunov and Control Barrier Functions for Safe Coordination in Swarms and Multi-Agent Systems

Angela Cortecchia

Motivation

Research context

  • Swarm and multi-agent systems coordinate through local interactions;
  • Typical tasks include movement, formation, coverage, and flocking;
  • In safety-critical settings, coordination alone is not enough.

Safety concerns

  • Avoid inter-agent collisions;
  • Avoid obstacles and unsafe regions;
  • Preserve constraints such as connectivity or formation structure.
Motivating gap. Safety-aware control methods exist, but it is not clear how they are used across swarm and multi-agent coordination tasks, nor how they connect to high-level swarm programming.

Review objective, scope rationale, and RQs

The planned review investigates how Control Lyapunov Functions and Control Barrier Functions are used to support safe coordination in swarm and multi-agent systems.

PICOC framing

  • Population: swarm and multi-agent robotic systems;
  • Intervention: CLF, CBF, CLF-CBF-QP, barrier certificates;
  • Comparison: swarm programming languages and macro-programming abstractions as an abstraction reference;
  • Outcome: safety, convergence, scalability, and composability;
  • Context: swarm/MAS coordination across centralized, decentralized, distributed, and local implementations.

Guiding questions

  • Which coordination tasks and safety properties are addressed?
  • Which control and coordination architectures are adopted?
  • How are approaches evaluated, and at what scale?
  • What gaps emerge with respect to swarm programming languages?
Rationale. The technical object is CLF/CBF-based safe coordination. Swarm programming is not a competing intervention, but the comparison lens used to ask whether these guarantees can become reusable and composable swarm-level constructs.

Background: CLF and CBF

Two complementary control certificates
Control Lyapunov Functions
  • Encode progress toward a goal;
  • Support convergence and stabilization;
  • Useful for reaching a target, tracking, and formation objectives.
Control Barrier Functions
  • Encode safety constraints;
  • Keep the system inside a safe set;
  • Useful for collision avoidance and obstacle avoidance.
CLF-CBF-QP
Follow a nominal objective while minimally modifying the control input to satisfy safety constraints [1].

[1] A. D. Ames, X. Xu, J. W. Grizzle and P. Tabuada, “Control Barrier Function Based Quadratic Programs for Safety Critical Systems,” 2017.

Review type and tertiary-survey check

Method choice and positioning check
Review type
  • Systematic mapping / SLR-oriented review sketch [2];
  • Content-based classification of primary studies;
  • No meta-analysis: expected evidence is heterogeneous;
  • Structured protocol needed because terminology is fragmented across control, robotics, swarm intelligence, and distributed systems [3].
Mini tertiary-survey protocol
  • Target: secondary studies only: surveys, SLRs, and SMSs;
  • Search mode: preliminary secondary-study scan using CLF/CBF + survey/review/mapping terms;
  • Adjacent areas checked: multi-UAV collision avoidance, aerial swarm robotics, swarm programming;
  • Extraction: coverage, overlap with this review, and remaining gap.
Purpose
The tertiary check verifies whether the planned review is already covered and justifies the scope before screening primary studies.

[2] K. Petersen, S. Vakkalanka and L. Kuzniarz, “Guidelines for conducting systematic mapping studies in software engineering: An update,” 2015.
[3] B. Kitchenham and S. Charters, “Guidelines for performing Systematic Literature Reviews in Software Engineering,” 2007.

Tertiary survey: coverage and gap

What existing surveys cover

  • CLF/CBF theory: nonlinear-affine systems, QP formulations, applications [4];
  • Safe learning: learned or uncertain dynamics with CLF/CBF guarantees [5];
  • Collision avoidance: multi-UAV planning, conflict resolution, guidance [6];
  • Aerial swarms: trajectory generation, task allocation, sensing, mapping [7].

Remaining gap

  • Coverage gap: no retained secondary study maps CLF/CBF methods specifically in swarm/MAS coordination;
  • Evidence gap: limited synthesis of task type, architecture, validation scale, and scalability;
  • Abstraction gap: little attention to the distance between control-level guarantees and swarm-programming abstractions.
Differentiation. The planned review targets the intersection: CLF/CBF-based safe coordination in swarm/MAS, with explicit attention to scalability and swarm-programming abstractions.

[4] B. Li, S. Wen, Z. Yan, G. Wen and T. Huang, “A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems,” 2023.
[5] A. Anand, K. Seel, V. Gjærum, A. Håkansson, H. Robinson and A. Saad, “Safe Learning for Control using Control Lyapunov Functions and Control Barrier Functions: A Review,” 2021.
[6] S. Huang, R. S. H. Teo and K. K. Tan, “Collision avoidance of multi unmanned aerial vehicles: A review,” 2019.
[7] S. J. Chung, A. A. Paranjape, P. Dames, S. Shen and V. Kumar, “A Survey on Aerial Swarm Robotics,” 2018.

Methodological anchors

SLR/SMS basis + tertiary survey

Methodological stance
SLR/SMS guidelines provide the methodological basis for reproducible search, selection, extraction, and synthesis [2,3]. Related secondary studies are used only to position the topic scope, identify overlap, and motivate the gap before screening primary studies [4-7].

Protocol-level choices

  • Use SLR/SMS guidelines as the methodological reference;
  • Use the tertiary survey to position related secondary studies before screening primary studies;
  • Use the aerial-swarm survey to refine task and architecture terminology;
  • Treat the review protocol as the main exam artefact.

Protocol-design rationale

  • Fragmentation is part of the research problem;
  • Control-side dimensions capture what CLF/CBF papers actually prove;
  • Swarm-side dimensions capture task, scale, and distribution assumptions;
  • Programming-side dimensions are used only to expose the abstraction gap.

Search and selection protocol

Query blocks

("control barrier function" OR "control Lyapunov function" OR "CLF-CBF" OR "barrier certificate")
AND
("multi-agent" OR "multi-robot" OR swarm OR "robot swarm")
AND
("collision avoidance" OR "formation control" OR coverage OR flocking OR coordination)
Sources
  • Scopus;
  • IEEE Xplore.
Pilot volume
  • Scopus: 230 raw hits;
  • IEEE Xplore: 149 raw hits;
  • before screening and deduplication.
Selection
  • Deduplicate;
  • Screen title/abstract;
  • Full-text check for borderline studies;
  • Snowball from seed papers [8].
Search-design note
Architecture is not used as a hard filter: centralized, decentralized, distributed, and local implementations are compared during extraction.

[8] C. Wohlin, “Guidelines for snowballing in systematic literature studies and a replication in software engineering,” 2014.

Inclusion, exclusion, and quality checks

Screening rules and evidence sanity checks
Include
Multi-agent, multi-robot, or swarm systems with explicit CLF, CBF, or barrier certificates addressing safety constraints and/or convergence objectives.
Exclude
Single-agent studies, pure path planning without safety certificates, no explicit coordination or safety task, non-English papers.
Quality checks
  • Is the safety property explicitly defined?
  • Are assumptions and system model clear?
  • Is the evaluation scenario described?
  • Is the level of distribution/decentralization explicit?

Extraction and classification framework

Coding scheme for extraction and synthesis
Coordination scope
  • Task: collision avoidance, formation, coverage, flocking;
  • System: ground robots, UAVs, generic nonlinear MAS, simulated swarm.
Control structure
  • Architecture: centralized, decentralized, distributed;
  • Mechanism: CBF, CLF-CBF-QP, barrier certificates, hybrid methods.
Evidence and abstraction
  • Validation: theory only, simulation, hardware experiments;
  • Scalability: number of agents, simulation scale, hardware scale, computational burden;
  • Programming abstraction: none, controller-level API, behavior block, macro-programming language.
Framework derivation. The dimensions map each RQ to extraction needs: tasks and safety mechanisms come from the CLF/CBF seed papers; architecture, validation, and scalability come from the swarm/MAS scope; programming abstraction comes from the PICOC comparison lens.

From safe control to swarm programming

Intervention: CLF/CBF literature

  • Strong formal guarantees;
  • Precise control-level formulations;
  • Often expressed as optimization problems;
  • Usually close to the controller or dynamics model.

Comparison: swarm programming

  • Macro-programming for distributed collective systems [9];
  • Devices compute local values and exchange them with neighbors;
  • Global behavior emerges as a computational field over the network;
  • Emphasis on reusable, composable behavior abstractions.
Comparison rationale. In PICOC, comparison means “abstraction lens”: CLF/CBF papers are checked for evidence of properties associated with swarm-programming abstractions, namely composability, reuse, and expression of collective behavior above controller level.

[9] J. Beal, D. Pianini and M. Viroli, “Aggregate Programming for the Internet of Things,” 2015.

MacroSwarm as a possible bridge

MacroSwarm instantiates aggregate computing in the swarm robotics setting [10]:
collective behaviors are expressed as composable high-level blocks, rather than only as low-level controllers.

  • Collective movement;
  • Flocking and leader-follower behavior;
  • Shape formation and morphogenesis;
  • Team formation and collective planning.
Opportunity
Candidate bridge to assess: safety filters for aggregate-programming behavior blocks.

[10] G. Aguzzi, R. Casadei and M. Viroli, “MacroSwarm: A Field-based Compositional Framework for Swarm Programming,” 2025.

Gap to be assessed

From safe controllers to safe swarm abstractions
Review gap
CLF/CBF methods provide formal safety and convergence guarantees, but the review will assess whether these guarantees become reusable, composable abstractions in swarm-programming frameworks.
Question to assess
Are CLF/CBF-style safety filters already supported, partially explored, or still missing for aggregate-programming behavior blocks?
Conceptual bridge to assess
Aggregate behavior block
collective intent
→
Nominal movement field
desired dynamics
→
CBF/QP safety filter
constraint enforcement
→
Safe distributed actuation
local correction
The mapping checks whether this bridge is supported, partially explored, or still missing in the literature.

Expected outputs

Deliverable chain
Reproducible protocol
RQs, query, sources, criteria
→
Tertiary positioning
related surveys and differentiation
→
Classification taxonomy
tasks, architectures, safety mechanisms
→
Gap analysis
scalability and abstraction
Synthesis focus
The final synthesis will compare evidence across coordination tasks, safety properties, validation type, scale, and the distance from controller-level guarantees to swarm-programming abstractions.

Takeaways

01
A focused technical lens
CLF and CBF provide a concrete way to review formal safety and convergence guarantees in swarm/MAS coordination.
02
A reproducible review protocol
The protocol makes scope, search, selection, extraction, and synthesis explicit before the full screening phase.
03
From control guarantees to swarm abstractions
The review maps how far the literature moves from controller-level safety filters toward reusable, composable swarm-programming constructs.

References

  • [1] A. D. Ames, X. Xu, J. W. Grizzle and P. Tabuada, “Control Barrier Function Based Quadratic Programs for Safety Critical Systems,” 2017.
  • [2] K. Petersen, S. Vakkalanka and L. Kuzniarz, “Guidelines for conducting systematic mapping studies in software engineering: An update,” 2015.
  • [3] B. Kitchenham and S. Charters, “Guidelines for performing Systematic Literature Reviews in Software Engineering,” 2007.
  • [4] B. Li, S. Wen, Z. Yan, G. Wen and T. Huang, “A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems,” 2023.
  • [5] A. Anand, K. Seel, V. Gjærum, A. Håkansson, H. Robinson and A. Saad, “Safe Learning for Control using Control Lyapunov Functions and Control Barrier Functions: A Review,” 2021.
  • [6] S. Huang, R. S. H. Teo and K. K. Tan, “Collision avoidance of multi unmanned aerial vehicles: A review,” 2019.
  • [7] S. J. Chung, A. A. Paranjape, P. Dames, S. Shen and V. Kumar, “A Survey on Aerial Swarm Robotics,” 2018.
  • [8] C. Wohlin, “Guidelines for snowballing in systematic literature studies and a replication in software engineering,” 2014.
  • [9] J. Beal, D. Pianini and M. Viroli, “Aggregate Programming for the Internet of Things,” 2015.
  • [10] G. Aguzzi, R. Casadei and M. Viroli, “MacroSwarm: A Field-based Compositional Framework for Swarm Programming,” 2025.