Position-Based Flocking for Persistent Alignment without Velocity Sensing

Hossein B. Jond; Veli Bakırcıoğlu; Logan E. Beaver; Nejat Tükenmez; Adel Akbarimajd; Martin Saska

cs.ROFeb 25, 2026

Position-Based Flocking for Persistent Alignment without Velocity Sensing

Authors: Hossein B. Jond, Veli Bakırcıoğlu, Logan E. Beaver, Nejat Tükenmez, Adel Akbarimajd, Martin Saska

Organizations: Department of Cybernetics, Czech Technical University in Prague, Prague, Czechia · Aksaray University, 68100, Aksaray, Türkiye · Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA, USA · Mechatronics Engineering Department, Istanbul Technical University, Istanbul, Turkiye ·

Abstract

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.

Figures & tables

Figure 1: Conceptual analogy between motion inference in robotic and biological swarms. Robots reconstruct relative motion from time-integrated position differences, while biological agents infer motion directly from local sensory imprints.

Panel of Figure 2 — Figure 2: (a) Velocity alignment: direct use of instantaneous $\mathbf{v}_{j}-\mathbf{v}_{i}$ and (b) Position-based alignment: inference via $[(\mathbf{p}_{j}-\mathbf{p}_{i})-(\mathbf{p}_{j}(0)-\mathbf{p}_{i}(0))]/t$ .

Figure 3: Time-dependent alignment gain

\phi

. The function transitions from a decaying transient regime (

\phi=|\mathcal{N}_{i}|/t

) to a persistent regime (

\phi=k|\mathcal{N}_{i}|

) at the threshold

t=1/k

. Initial relative positions exert a strong influence (imprinting effect) before the threshold, after which alignment stabilizes (social reinforcement phase).

Velocity-Based	Position-Based Alignment
Direct relative velocity input	Inferred relative velocity via positions
$\mathbf{v}_{j}-\mathbf{v}_{i}$	$[(\mathbf{p}_{j}-\mathbf{p}_{i})-(\mathbf{p}_{j}(0)-\mathbf{p}_{i}(0))]/t$
No memory of initial state	Weak memory imprint $\mathbf{p}_{j}(0)-\mathbf{p}_{i}(0)$
Constant influence over time	Time-dependent behavioral switch
	transient $(t\leq 1/k)\rightarrow$ sustained $(t>1/k)$

Table 1: Velocity-based and position-based alignment components.

Figure 4: Trajectories of the collective over $[0,100]\,\text{s}$ under (a) the velocity-alignment-based model ( 2 ) (V-based), (b) the position-based model ( 5 ) with threshold alignment gain (P-based (thr.)), and (c) the position-based model without threshold (P-based (no thr.)), all starting from identical random initial conditions. The V-based trajectories achieve cohesive and coherent motion with relatively strong alignment, yet exhibit a spatially flexible pattern with varying collective direction over time. The P-based (thr.) trajectories rapidly converge to strong, persistent alignment and form a compact, directionally stable flocking configuration throughout the simulation. The P-based (no thr.) trajectories initially display strong alignment and persistent direction similar to the threshold case but show gradual weakening of alignment over extended time due to the decaying gain, resulting in progressive loss of directional coherence.

Panel of Figure 5 — Figure 5: Time histories for the collective trajectory under the velocity-alignment-based model ( 2 ) (V-based), the position-based model ( 5 ) with the threshold alignment gain (P-based (thr.)) and no threshold alignment gain (P-based (no thr.)): (a) alignment metric $\gamma$ , (b) inter-agent distances, (c) average speeds, and (d) collective radii.

Characteristic	V-based	P-based (thr.)
Alignment strength & persistence	Strong, with minor variation	Very strong & persistent
Formation structure	Flexible, spatially adaptive	Less flexible, directionally stable
Inter-agent separation	Wider	Narrower
Cohesion & directional consensus	Moderate	Superior

Table 2: Qualitative comparison of key flocking characteristics between the velocity-alignment-based model (V-based) and the proposed position-based model with threshold (P-based (thr.)).

Figure 6: Assessment of formation rigidity. Pairwise distance variance increases during the transient phase, showing that the initial formation is not preserved.

Panel of Figure 7 — Figure 7: Snapshots from the real-robot experiment demonstrating cohesive and coherent flocking under the position-based model. A supplementary video showing the full experiment, including real-time data visualization and trajectory evolution, is available at https://youtu.be/g8ClSYKpmQY .

Figure 8: Alignment metric in the experiment.

Multi-Agent Control

Multi-agent control coordinates interacting autonomous agents to achieve shared goals while respecting safety, communication, and resource constraints.

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Speed-Weighted Adaptive Flocking for Sailing Swarms under Dynamic Environmental Forcing

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Centre for the Advanced Study of Collective Behaviour, Konstanz, Germany · Dep. of Computer and Information Science, University of Konstanz, Germany · University of Pittsburgh, Pittsburgh, USA+2

Swarm Robotics Robotics Simulation Robotics Multi-Robot Coordination

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Collective behavior models, such as aggregation and flocking, usually assume self-propelled robots that can directly execute their desired speed and direction of motion without fundamental constraints. However, autonomous sailing robots violate this assumption. Their motion is shaped by wind-dependent propulsion, restricted headings, and spatially varying wind conditions. In particular, maneuverability is coupled to wind speed: in weak wind, sailboats may turn only slowly or not at all, whereas stronger wind enables faster turns. This introduces transient heterogeneity in speed and maneuverability across the flock. We focus on this fast-slow coordination problem in sailing robot flocks. To study this problem, we introduce SailSwarmSwIM, a reduced-order simulator for autonomous sailing robot swarms that captures wind-dependent speed and maneuverability, no-go zones, tacking behavior, and steady or gusty wind fields. To design our novel flocking technique, we start from the Couzin model and introduce a speed-weighted social interaction rule that accounts for each robot's transient motion constraints. A key result is that increasing the social influence of slower robots improves polarization and reduces close encounters. This effect arises from a balance between attraction to fast neighbors, which helps maintain movement, and cohesion around slow neighbors, which prevents the flock from fragmenting. Together, our simulator, SailSwarmSwIM, and the speed-weighted interaction rule provide a modeling framework for studying adaptive collective behavior in robotic fleets whose motion capabilities are continuously shaped by wind.

Abstract

Multi-Agent Control

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