Multi-Robot Formation Control

Overview

The field studies how teams of robots can hold a desired shape, move together, and reconfigure around obstacles or changing tasks. Common approaches include leader-follower and distance- or bearing-based control, graph Laplacians and rigidity methods, and predictive controllers paired with control barrier functions for collision avoidance. Systems increasingly combine these controllers with onboard vision or range sensing, cooperative localization, and learned policies, with evaluations spanning UAVs, ground robots, and boats in simulation and hardware trials. A central challenge is achieving reliable coordination with limited sensing and communication while scaling to larger teams and adapting safely to uncertainty, failures, and dynamic environments.

Latest papers

49 papers4 papers in the last four weeks, down 60% on the four weeks before. 0.0% of all new papers.

May 28, 2026

Distributed Non-Uniform Scaling Control of Multi-Agent Formation with Dynamic Agent Joining

Non-uniform scaling control of formation enables multi-agent systems to adjust their shape by scaling with different ratios along different coordinate axes, offering enhanced flexibility in complex environments. However, like most existing formation maneuver strategies, it typically assumes a fixed set of agents, limiting its applicability in scenarios requiring dynamic team expansion. This paper introduces a distributed control framework that enables a formation to incorporate new agents during non-uniform scaling maneuvers in arbitrary dimensions while preserving the spectral properties of the graph Laplacian. Simulation examples validate the effectiveness of the theoretical results.
May 18, 2026

Orchestrating Wheeled Mobile Robots Online without Conflicts

Formation control of wheeled mobile robots (WMRs) has been widely studied due to its broad applications. However, existing studies primarily focus on tracking predefined formations, with limited adaptability to varying environments. To address this limitation, we propose CFOO, a Conflict-Free Online Orchestration framework for continuous formation navigation of WMRs that integrates centralized formation generation with distributed formation maintenance. The upper layer monitors the environment in real time and generates adaptive formations as needed, using the proposed TCF-R2T (Trajectory-Conflict-Free Robot-to-Target assignment) algorithm to compute optimal assignments in polynomial time for timely, conflict-free formation transitions. At the lower layer, each WMR continuously employs JSTP (Joint Spatio-Temporal trajectory Planning) to maintain the given formation by jointly optimizing spatial positions and segment durations, improving coordination over spatial-only optimization with fixed durations. By coordinating these two layers, CFOO orchestrates WMRs to adapt their formations to varying environments and thus enable continuous navigation. Moreover, we design a Time-Varying Formation Reference (TVFR) mechanism to facilitate smooth transitions between successive desired formations. Both simulation and real-world experiments validate the effectiveness and adaptability of CFOO. Experimental videos are available on our project website: https://github.com/dongjh20/CFOO.
May 17, 2026

Distributed 3D Leader-Follower Formation Control with Field-of-View Safety via Control Barrier Functions

This letter proposes a distributed 3D leader-follower formation (3D-LFF) control framework for multi-UAV systems that achieves formation tracking while enforcing perception safety constraints. Maintaining safe, vision-based 3D-LFF is challenging because onboard cameras impose strict Field-of-View (FOV) limitations, and demanding formation commands can drive the leader outside the follower's camera frustum, resulting in loss of visibility. To address this issue, we develop a perception-aware safe control architecture that guarantees visibility by construction. First, we derive a relative kinematic model in a line-of-sight coordinate representation and design a distributed 3D-LFF tracking controller using only locally available relative states. Next, we embed the nominal formation controller within a Control Barrier Function-based Quadratic Program (CBF-QP) safety filter that minimally modifies the commanded velocities to maintain the leader inside the follower's camera frustum while preserving formation tracking whenever feasible. Gazebo simulations and Crazyflie hardware experiments validate the proposed approach, demonstrating accurate formation tracking and effective FOV enforcement, including scenarios in which the nominal desired formation conflicts with visibility constraints.
Apr 20, 2026

Multi-UAV Path Following using Vector-Field Guidance

This paper presents a decentralized, collision-free framework for path following guidance of multiple uncrewed aerial vehicles (UAVs), while maintaining uniform spacing along a reference path. A vector field-based guidance law is employed to drive each UAV toward the reference path. A rotational repulsion mechanism, utilizing relative distance and bearing between UAVs, is proposed to avoid collisions during convergence to the path, and an inter-UAV spacing error-based velocity control law is presented to achieve uniform separation along the path. Analytical guarantees are established for collision avoidance and convergence of the inter-UAV spacing errors to zero, ensuring uniform separation along the path. Numerical simulations demonstrate the efficacy of the proposed method.
Apr 10, 2026

On Feedback Speed Control for a Planar Tracking

This paper investigates a planar tracking problem between a leader and follower agent. We propose a novel feedback speed control law, paired with a constant bearing steering strategy, to maintain an abreast formation between the two agents. We prove that the proposed control yields asymptotic stability of the closed-loop system when the steering of the leader is known. For the case when the leader's steering is unavailable to the follower, we show that the system is still input-to-state stable with respect to the leader's steering viewed as an input. Furthermore, we demonstrate that if the leader's steering is periodic, the follower will asymptotically converge to a periodic orbit with the same period. We validate these results through numerical simulations and experimental implementations on mobile robots. Finally, we demonstrate the scalability of the proposed approach by extending the two-agent control law to an N-agent chain network, illustrating its implications for directional information propagation in biological and engineered flocks.
Apr 7, 2026

Leaderless Collective Motion in Affine Formation Control over the Complex Plane

We propose a method for the collective maneuvering of affine formations in the plane by modifying the original weights of the Laplacian matrix used to achieve static formations of robot swarms. Specifically, the resulting collective motion is characterized as a time-varying affine transformation of a reference configuration, or shape. Unlike the traditional leader-follower strategy, our leaderless scheme allows agents to maintain distinct and possibly time-varying velocities, enabling a broader range of collective motions, including all the linear combinations of translations, rotations, scaling and shearing of a reference shape. Our analysis provides the analytic solution governing the resulting collective motion, explicitly designing the eigenvectors and eigenvalues that define this motion as a function of the modified weights in the new Laplacian matrix. To facilitate a more tractable analysis and design of affine formations in 2D, we propose the use of complex numbers to represent all relevant information. Simulations with up to 20 agents validate the theoretical results.
Apr 6, 2026

FORMULA: FORmation MPC with neUral barrier Learning for safety Assurance

Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.
Apr 5, 2026

Element-based Formation Control: a Unified Perspective from Continuum Mechanics

This paper establishes a unified element-based framework for formation control by introducing the concept of the deformation gradient from continuum mechanics. Unlike traditional methods that rely on geometric constraints defined on graph edges, we model the formation as a discrete elastic body composed of simplicial elements. By defining a generalized distortion energy based on the local deformation gradient tensor, we derive a family of distributed control laws that can enforce various geometric invariances, including translation, rotation, scaling, and affine transformations. The convergence properties and the features of the proposed controllers are analyzed in detail. Theoretically, we show that the proposed framework serves as a bridge between existing rigidity-based and Laplacian-based approaches. Specifically, we show that rigidity-based controllers are mathematically equivalent to minimizing specific projections of the deformation energy tensor. Furthermore, we establish a rigorous link between the proposed energy minimization and Laplacian-based formation control. Numerical simulations in 2D and 3D validate the effectiveness and the unified nature of the proposed framework.
Mar 25, 2026

Enhancing Drone Light Shows Performances: Optimal Allocation and Trajectories for Swarm Drone Formations

Drone light shows (DLShows) represent a rapidly growing application of swarm robotics, creating captivating aerial displays through the synchronized flight of hundreds or thousands of unmanned aerial vehicles (UAVs) as environmentally friendly and reusable alternatives to traditional pyrotechnics. This domain presents unique challenges in optimally assigning drones to visual waypoints and generating smooth, collision-free trajectories at a very large scale. This article introduces the Unified Assignment and Trajectory Generation (UATG) framework. The proposed approach concurrently solves two core problems: the optimal assignment of drones to designated goal locations and the generation of dynamically feasible, collision-free, time-parameterized trajectories. The UATG framework is specifically designed for DLShows, ensuring minimal transition times between formations and guaranteeing inter-drone collision avoidance. A key innovation is its exceptional computational efficiency, enabling the coordination of large-scale in real-time; for instance, it computes the optimal assignment and trajectories for 1008 drones in approximately one second on a standard laptop. Extensive simulations in realistic environments validate the framework's performance, demonstrating its capability to orchestrate complex formations, from alphanumeric characters to intricate 3D shapes, with precision and visual smoothness. This work provides a critical advancement for the DLShow industry, offering a practical and scalable solution for generating complex aerial choreography and establishing a valuable benchmark for ground control station software designed for the efficient coordination of multiple UAVs. A supplemental animated simulation of this work is available at https://youtu.be/-Fjrhw03594.
Mar 18, 2026

Huddle: Parallel Shape Assembly using Decentralized, Minimalistic Robots

We propose a novel algorithm for forming arbitrarily shaped assemblies using decentralized robots. By relying on local interactions, the algorithm ensures there are no unreachable states or gaps in the assembly, which are global properties. The in-assembly robots attract passing-by robots into expanding the assembly via a simple implementation of signaling and alignment. Our approach is minimalistic, requiring only communication between attached, immediate neighbors. It is motion-agnostic and requires no pose localization, enabling asynchronous and order-independent assembly. We prove the algorithm's correctness and demonstrate its effectiveness in forming a 107-robot assembly.
Mar 16, 2026

The Geometry of Transmission Zeros in Distance-Based Formations

This letter presents a geometric input-output analysis of distance-based formation control, focusing on the phenomenon of steady-state signal blocking between actuator and sensor pairs. We characterize steady-state multivariable transmission zeros, where fully excited rigid-body and deformational modes destructively interfere at the measured output. By analyzing the DC gain transfer matrix of the linearized closed-loop dynamics, we prove that for connected, flexible frameworks, structural transmission zeros are strictly non-generic; the configuration-dependent cross-coupling required to induce them occupies a proper algebraic set of measure zero. However, because extracting actionable sensor-placement rules from these complex algebraic varieties is analytically intractable, we restrict our focus to infinitesimally rigid formations. For these baselines, we prove that the absence of internal flexes forces the zero-transmission condition to collapse into an explicit affine hyperplane defined by the actuator and the global formation geometry, which we term the spatial locus of transmission zeros. Finally, we introduce the global transmission polygon--a convex polytope constructed from the intersection of these loci. This construct provides a direct geometric synthesis rule for robust sensor allocation, guaranteeing full-rank steady-state transmission against arbitrary single-node excitations.
Mar 9, 2026

Formation-Aware Adaptive Conformalized Perception for Safe Leader-Follower Multi-Robot Systems

This paper considers the perception safety problem in distributed vision-based leader-follower formations, where each robot uses onboard perception to estimate relative states, track desired setpoints, and keep the leader within its camera field of view (FOV). Safety is challenging due to heteroscedastic perception errors and the coupling between formation maneuvers and visibility constraints. We propose a distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles. The resulting bounds tighten in high-risk configurations (near FOV limits) and relax in safer regions. We integrate these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance. Gazebo simulations show improved formation success rates and tracking accuracy over non-adaptive (global) CP baselines that ignore formation-dependent visibility risk, while preserving finite-sample probabilistic safety guarantees. The experimental videos are available on the project website\footnote{Project Website: https://nail-uh.github.io/iros2026.github.io/}.
Feb 25, 2026

Position-Based Flocking for Persistent Alignment without Velocity Sensing

Coordinated collective motion in bird flocks and fish schools inspires algorithms for cohesive swarm robotics. This paper presents a position-based flocking model that achieves persistent velocity alignment without velocity sensing. By approximating relative velocity differences from changes between current and initial relative positions and incorporating a time- and density-dependent alignment gain with a non-zero minimum threshold to maintain persistent alignment, the model sustains coherent collective motion over extended periods. Simulations with a collective of 50 agents demonstrate that the position-based flocking model attains faster and more sustained directional alignment and results in more compact formations than a velocity-alignment-based baseline. This position-based flocking model is particularly well-suited for real-world robotic swarms, where velocity measurements are unreliable, noisy, or unavailable. Experimental results using a team of nine real wheeled mobile robots are also presented.
Feb 20, 2026

Role-Adaptive Collaborative Formation Planning for Team of Quadruped Robots in Cluttered Environments

This paper presents a role-adaptive Leader-Follower-based formation planning and control framework for teams of quadruped robots operating in cluttered environments. Unlike conventional methods with fixed leaders or rigid formation roles, the proposed approach integrates dynamic role assignment and partial goal planning, enabling flexible, collision-free navigation in complex scenarios. Formation stability and inter-robot safety are ensured through a virtual spring-damper system coupled with a novel obstacle avoidance layer that adaptively adjusts each agent's velocity. A dynamic look-ahead reference generator further enhances flexibility, allowing temporary formation deformation to maneuver around obstacles while maintaining goal-directed motion. The Fast Marching Square (FM2) algorithm provides the global path for the leader and local paths for the followers as the planning backbone. The framework is validated through extensive simulations and real-world experiments with teams of quadruped robots. Results demonstrate smooth coordination, adaptive role switching, and robust formation maintenance in complex, unstructured environments. A video featuring the simulation and physical experiments along with their associated visualizations can be found at https://youtu.be/scq37Tua9W4.
Feb 18, 2026

Decentralized and Fully Onboard: Range-Aided Cooperative Localization and Navigation on Micro Aerial Vehicles

Controlling a team of robots in a coordinated manner is challenging because centralized approaches (where all computation is performed on a central machine) scale poorly, and globally referenced external localization systems may not always be available. In this work, we consider the problem of range-aided decentralized localization and formation control. In such a setting, each robot estimates its relative pose by combining data only from onboard odometry sensors and distance measurements to other robots in the team. Additionally, each robot calculates the control inputs necessary to collaboratively navigate an environment to accomplish a specific task, for example, moving in a desired formation while monitoring an area. We present a block coordinate descent approach to localization that does not require strict coordination between the robots. We present a novel formulation for formation control as inference on factor graphs that takes into account the state estimation uncertainty and can be solved efficiently. Our approach to range-aided localization and formation-based navigation is completely decentralized, does not require specialized trajectories to maintain formation, and achieves decimeter-level positioning and formation control accuracy. We demonstrate our approach through multiple real experiments involving formation flights in diverse indoor and outdoor environments.
Sep 15, 2025

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

This paper addresses 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 controllers, the proposed controller is nonlinear and relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a state-dependent threshold, ensuring system stability while reducing actuation effort. We also employ a distributed control barrier function to guarantee inter-agent collision avoidance. The proposed controller is validated through simulations and real-world experiments involving different communication topologies, scalability tests, and variations in design parameters, and is also compared to periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control effort while preserving formation performance.
May 10, 2025

LLM-Flock: LLM-Driven Decentralized Multi-Robot Flocking via Influence-Based Consensus with Collision Avoidance

Large Language Models (LLMs) have shown strong capabilities in reasoning and planning, prompting researchers to explore their use as decentralized decision-makers for multi-robot formation control. However, directly applying LLMs to such tasks often leads to unstable behavior, in which robots may collapse to the centroid of their positions or diverge entirely, due to hallucinated reasoning and limited coordination awareness. We propose LLM-Flock, a decentralized multi-robot flocking framework that addresses these challenges through two key mechanisms: (1) an influence-based consensus protocol, where robots iteratively refine individually generated formation plans by adopting those of more connected neighbors, driving the team toward a unified plan without centralized control, and (2) a two-layer collision avoidance strategy that pairs LLM-based urgency reasoning with a programmatic collision checker and re-prompting mechanism. We evaluate LLM-Flock across five state-of-the-art LLMs, including both closed-source (GPT-5, Claude 4.5) and open-source (Llama3.1-405b, Qwen-Max, DeepSeek-R1) models, demonstrating notable improvements in formation stability and convergence over prior LLM-based methods. Real-world experiments with Crazyflie drones further validate the framework's applicability to physical multi-robot systems.
Nov 6, 2024

Observability-Aware Control for Quadrotor Formation Flight with Range-only Measurement

Cooperative Localization is a promising approach to achieving safe quadrotor formation flight through precise positioning via low-cost inter-drone sensors. This paper develops an observability-aware control principle tailored to quadrotor formation flight with range-only inter-drone measurements. The control principle is based on a novel approximation of the local observability Gramian (LOG), which we name the Short-Term Local Observability Gramian (STLOG). The validity of STLOG is established by proving its link to directional estimation precision in nonlinear systems. We propose the Observability Predictive Controller (OPC), a receding-horizon controller that generates optimal inputs to enhance information gain in weakly observable state directions by maximizing the minimum eigenvalue of the STLOG. This reduces the risk of estimator divergence due to the unbounded growth of uncertainty in weakly observed state components. Monte Carlo simulations and flight experiments are conducted with quadrotors in a GNSS-denied ferrying mission, showing that the OPC improves positioning confidence and estimator robustness.
Dec 1, 2017

An Optimal Algorithm for Changing from Latitudinal to Longitudinal Formation of Autonomous Aircraft Squadrons

This work presents an algorithm for changing from latitudinal to longitudinal formation of autonomous aircraft squadrons. The maneuvers are defined dynamically by using a predefined set of 3D basic maneuvers. This formation change is necessary when the squadron has to perform tasks which demand both formations, such as lift off, georeferencing, obstacle avoidance and landing. Simulations show that the formation change is done without collision. The time complexity analysis of the transformation algorithm reveals that its efficiency is optimal, and the proof of correctness ensures its longitudinal formation features.