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 · The Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA · Mechatronics Engineering Department, Isparta University of Applied Sciences, Isparta, Turkiye · Department of Electrical and Computer Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
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.
Figure 2: (a) Velocity alignment: direct use of instantaneous vj−vi and (b) Position-based alignment: inference via [(pj−pi)−(pj(0)−pi(0))]/t .
Figure 3: Time-dependent alignment gain ϕ . The function transitions from a decaying transient regime ( ϕ=∣Ni∣/t ) to a persistent regime ( ϕ=k∣Ni∣ ) 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
vj−vi
[(pj−pi)−(pj(0)−pi(0))]/t
No memory of initial state
Weak memory imprint pj(0)−pi(0)
Constant influence over time
Time-dependent behavioral switch
transient (t≤1/k)→ sustained (t>1/k)
Table 1: Velocity-based and position-based alignment components.
Figure 4: Trajectories of the collective over [0,100]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.
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 γ , (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.
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 .
Multi-agent control coordinates interacting autonomous agents to achieve shared goals while respecting safety, communication, and resource constraints.
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.
Pranav Kedia, Aaron Gan, Hannah J. Williams +2
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
This paper describes an automatic method for adjusting or tuning models of multi-agent motion. Simulating the motion of bird flocks, human crowds, vehicle traffic, and other multi-agent systems is a widely used technique. These simulations model the behavior of a single group member (bird, human, or vehicle). The group behaviors (flock, crowd, traffic) emerge from interactions between group members. These models typically have many numerical control parameters. Even if each parameter is intuitive in isolation, their interaction can be complex and nonlinear. It is challenging to determine which parameters to adjust for the desired change in group behavior. Changing one aspect of group behavior often causes other aspects to change, leading to a tedious process of incremental changes. This work takes an inverse design approach. The desired group behavior is measured with a user-defined objective(/fitness/loss) function and optimized with a genetic algorithm. The objective function used here for basic flocking rewards proper spacing with neighbors, flying near a desired speed, and avoiding obstacles. Interestingly, the vivid alignment seen in bird flocks appears to emerge from maintaining proper spacing between flockmates.
Coordinating many miniature robots in a confined arena, with no leader, central planner, or global map, is a core challenge for swarm robotics. As the swarm grows denser, collision avoidance becomes the limiting factor, and the number of safely coexisting robots depends on the formulation of the inter-robot safety constraint. We present a distributed predictive flocking controller in which each robot solves its own nonlinear model predictive control (NMPC) problem, optimizing swarm cohesion and alignment costs, inter-robot and obstacle safety, and a task objective, while exchanging only predicted trajectories with local neighbors. Within this generalized controller architecture, solved in real time, we compare six barrier and control-barrier-function (CBF) safety formulations on a digital twin of an open-source vibration-driven bristlebot in a 0.64m2 arena. A look-ahead discrete-time CBF performs best overall, with the fewest collisions and the widest inter-robot margins across nearly every swarm size tested. We deploy it on phototaxis, phototactic orbiting, and cohesion without a stimulus tasks, using swarm sizes starting from ten robots and up to the geometric packing limit. The swarm holds well: collisions stay low in small swarms, rising steeply as the packing limit approaches, while coordination and cohesion degrade gently rather than collapsing. The swarm is found not to trade safety for order, keeping both across the confined arena, with local alignment high at every swarm size.
Prajol Shrestha, Siddhant Mohapatra, Filip Novkoski +4
Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany · PULS, Institute for Theoretical Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany · GRASP, Institute of Physics B5a, University of Liège, B4000, Liège, Belgium +1