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A Mechanistic Model for Collective Motion from Sensorimotor Regularities
Vito Mengers, Bao Duc Cao, Oliver Brock
Intelligence
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Summary
The paper introduces a mechanistic model for collective motion based on the AICON robotics framework, which generates behavior through local sensorimotor regularities rather than abstract interaction forces. By simulating agents that perceive neighbors via bearing and apparent-size cues, maintain uncertain state estimates, and act via gradient descent on social distance, the model reproduces diverse collective behaviors like polarized motion, milling, rings, and fragmentation. A global sensitivity analysis demonstrates that behavioral transitions are governed by measurable biological parametersāfield of view, sensory noise, turning agility, and memoryārather than fitted constants, offering a biologically grounded alternative to classical self-propelled particle models.
Entities (11)
Relation Signals (11)
Polarized motion ā emergesfrom ā Sensorimotor parameters
confidence 95% Ā· This simple model produces diverse collective behaviors including polarized motion...
AICON ā extendsto ā Collective motion
confidence 95% Ā· We present such a mechanistic model for collective behavior based on Active InterCONnect (AICON) [11,12], a framework from robotics, extended here to collective motion.
Field of view ā governs ā Behavioral transitions
confidence 95% Ā· A global sensitivity analysis shows that behavioral transitions are governed by sensorimotor parameters corresponding to measurable biological quantities: field of view geometry...
Locusts ā interactvia ā Sensory and cognitive mechanisms
confidence 95% Ā· Recent empirical work makes this concrete: Sayin et al. [18] showed that locusts do not align with neighbors at all; sensory and cognitive mechanisms mediate interaction instead.
Self-propelled particle models ā criticizedfor ā Descriptive nature
confidence 90% Ā· Yet these models are fundamentally descriptive: they leave open the question of how collective behavior is actually produced.
Sensory noise ā degrades ā Collective structure
confidence 90% Ā· Bearing and apparent size noise degrade collective structure through qualitatively different mechanisms.
Ring formations ā emergeat ā Low uncertainty
confidence 90% Ā· Stable rings emerge at low uncertainty, where agents maintain reliable neighbor estimates and accurate distance control...
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Abstract
Abstract:Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open the question of how collective behavior is actually produced. Recent empirical work makes this gap concrete: locusts do not align with neighbors, sensory and cognitive mechanisms mediate interaction instead. A mechanistic model must therefore operate at the sensorimotor level, grounded in what individual organisms can actually perceive, estimate, and physically execute. We present such a model based on a modeling framework from robotics, extended here to collective motion. Each agent perceives neighbors through bearing and apparent-size cues within a limited field of view, maintains uncertain internal state estimates, and selects actions through gradient descent on a desired social distance -- without any prescribed interaction forces. This simple model produces diverse collective behaviors including polarized motion, milling, ring formations, and subgroup fragmentation. A global sensitivity analysis shows that behavioral transitions are governed by sensorimotor parameters corresponding to measurable biological quantities: field of view geometry, sensory noise, turning agility, and memory. Collective behavior can therefore be understood as the emergent outcome of interacting sensorimotor regularities, and differences across species as the emergent outcome of differences in embodiment and environment.
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A Mechanistic Model for Collective Motion from Sensorimotor Regularities Vito Mengers 1,2 , Bao Duc Cao 1 , and Oliver Brock 1,2,3 1 Robotics and Biology Laboratory, Technische UniversitƤt Berlin, Germany 2 Science of Intelligence, Research Cluster of Excellence, Berlin, Germany 3 Robotics Institute Germany v.mengers,oliver.brock@tu-berlin.de Abstract. Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phe- nomena through abstract interaction forces. Yet these models are fun- damentally descriptive: they leave open the question of how collective behavior is actually produced. Recent empirical work makes this gap con- crete: locusts do not align with neighbors, sensory and cognitive mecha- nisms mediate interaction instead. A mechanistic model must therefore operate at the sensorimotor level, grounded in what individual organisms can actually perceive, estimate, and physically execute. We present such a model based on a modeling framework from robotics, extended here to collective motion. Each agent perceives neighbors through bearing and apparent-size cues within a limited field of view, maintains uncertain in- ternal state estimates, and selects actions through gradient descent on a desired social distanceāwithout any prescribed interaction forces. This simple model produces diverse collective behaviors including polarized motion, milling, ring formations, and subgroup fragmentation. A global sensitivity analysis shows that behavioral transitions are governed by sensorimotor parameters corresponding to measurable biological quanti- ties: field of view geometry, sensory noise, turning agility, and memory. Collective behavior can therefore be understood as the emergent outcome of interacting sensorimotor regularities, and differences across species as the emergent outcome of differences in embodiment and environment. Keywords: collective motionĀ· sensorimotor regularitiesĀ· mechanistic modelĀ· emergent behaviorĀ· uncertaintyĀ· embodimentĀ· field of viewĀ· flockingĀ· active sensing 1 Introduction Collective behavior is one of the most striking phenomena in the natural world. Flocks of birds [2,5], schools of fish [9,16], and swarms of insects [1,4] produce coherent group-level patterns from purely local interactions, without centralized control or global information. The mystery is not just that groups coordinate, but that they do so with so little: each individual sees only a handful of neighbors, arXiv:2605.16522v1 [cs.RO] 15 May 2026 2V. Mengers et al. yet the group behaves as if guided by something more. It is this questionā how so much order arises from so littleāthat has driven a rich tradition of computational modeling in biology, physics, and robotics [23,25]. Self-propelled particle models [6,24] have been the dominant modeling frame- work for collective behavior. Agents align with neighbors within a fixed radius, subject to noise, and the result is polarization, milling, cohesion, and phase transitions [7]āestablishing collective behavior as a field of rigorous quantita- tive inquiry with broad influence [10]. These models are compelling precisely be- cause of their simplicity, but that simplicity comes at a cost. Their parametersā interaction radii, alignment strengths, noise levelsāare fit to observed patterns and carry no necessary correspondence to biological quantities. They character- ize what collective behavior looks like rather than how it is produced. Particle models also assume agents have direct access to neighborsā positions and head- ings, quantities that may simply not be available under realistic sensory con- straints [22]. Recent empirical work makes this concrete: Sayin et al. [18] showed that locusts do not align with neighbors at all; sensory and cognitive mecha- nisms mediate interaction instead. This calls for a different level of modeling: one grounded in what organisms can actually perceive and physically execute, with parameters corresponding to measurable biological quantities, so that pre- dictions transfer to new species without refitting. We present such a mechanistic model for collective behavior based on Active InterCONnect (AICON) [11,12], a framework from robotics that generates be- havior by composing sensorimotor regularities without directly encoding behav- ior itself. This makes it a natural substrate for a mechanistic model of collective behavior. The components that determine how an agent perceives, estimates, and acts are precisely the quantities that vary across species and environments. AICON has been applied to biological information processing [14], including col- lective opinion dynamics [13]. Here we extend it to collective motion. Each agent perceives neighbors through bearing and apparent-size cues within a limited field of view, maintains uncertain internal state estimates, and selects actions through gradient descent on a desired social distanceāwithout any prescribed interac- tion forces. Unlike models grounded in instantaneous visual responses [3, 15], abstract Bayesian objectives [8], or specific neural implementations [17], AICON maintains persistent uncertain representations and operates at the sensorimotor level without prescribing how perception translates into social response. The model recovers the behavioral diversity that particle models reproduceā polarized motion, milling, ring formations, and subgroup fragmentationābut from sensorimotor parameters alone: field of view geometry, sensory noise, and turning agility. These are not fitted constants but measurable biological quanti- ties. The same parameters that govern coordination also govern its breakdown, and varying them generates predictions about how collective behavior should differ across species with different sensory systems, motor capabilities, and envi- ronments. Differences in collective behavior across species may reflect differences in sensorimotor properties rather than differences in interaction rules. A Mechanistic Model for Collective Motion from Sensorimotor Regularities3 Ļ j Ī³ j a i Motion Constraints x i Ī£ i Field of View Projective Geometry Bearing Geometry x j Ī£ j p vis j for each neighbor j for each agent i g i Fig. 1. Collective behavior emerges from the composition of local sensorimotor reg- ularities, with no interaction forces prescribed at the collective level. Each agent i maintains recursive estimators for its own pose (x i ,Ī£ i ) and, for each neighbor j, for position (x j ,Ī£ j ) and visibility p vis j . Active interconnections couple these states: Bear- ing Geometry and Projective Geometry update neighbor position from observations Ļ j and Ī³ j , modulated by visibility and own pose; Field of View computes visibility from own and neighbor states; Motion Constraints propagate pose from actions a i . The goal g i , minimizing expected deviation from a desired social distance d 0 , drives action selection through gradient descent along three emergent paths: position adjust- ment toward d 0 , active sensing to reduce estimation uncertainty, and reorientation to maintain neighbors within the field of viewānone of which are explicitly encoded. 2 A Sensorimotor Model of Collective Motion AICON generates behavior through the dynamic composition of sensorimotor regularities, without directly encoding behavior itself. It provides two struc- tural elements: recursive estimators that maintain probabilistic beliefs about task-relevant quantities over time, and active interconnections that encode reg- ularities in the relationships between those quantities as differentiable functional dependencies. By composing these elements, AICON builds a network through which gradients can be propagated from goals back to actions. Behavior emerges from following these gradients, not from a predefined set of rules or a policy, but from the structure of the sensorimotor regularities themselves and the current state of the world. We instantiate this architecture for collective motion as shown in Figure 1. Each agent maintains estimators for its own pose and, for each neighbor, for posi- tion and visibility. Neighbors are perceived through two angular cues: bearing Ļ, the direction to the neighbor relative to the agentās heading, and apparent size Ī³, the angular size of the neighbor as seen by the agent. Together these encode direc- tional and distance-related information without requiring explicit depth sensing, grounding interaction in what the agent can actually observe. Perception is con- strained by a limited field of view Ļ: the visibility state p vis is computed from ego and neighbor position estimates and modulates how strongly observations up- date the neighbor belief. When a neighbor leaves the field of view, its estimator 4V. Mengers et al. continues propagating the last belief forward, accumulating uncertainty. The flow of social information is therefore explicitly state- and uncertainty-dependentāa structural consequence of composing these regularities, not a prescribed rule. Goal-directed behavior arises from a single differentiable cost function: each agent i minimizes the expected deviation from a desired social distance d 0 across all estimated neighbors V i , g i = X jāV i E h ā„x j ā„ā d 0 i ,(1) where the expectation over the belief implicitly couples the cost to estimation uncertainty over the neighborās relative position x j . This is the only objective, yet when pursued with simple gradient descent through the model it gives rise to three distinct gradient paths without any of them being explicitly programmed. The first adjusts position to reduce deviation from d 0 . The second flows through uncertainty: since uncertainty enters the expected cost, there is a gradient to reduce itāproducing active sensing and triangulating motions without this be- ing encoded anywhere. The third flows further still: because the uncertainty is modulated by p vis , there is a gradient to reorient toward neighbors near the field of view boundary. This gradient ensures visibility and thus group cohesion even under narrow fields of view, without implicit encoding. Of these gradients for different neighbors each agent selects the steepest at each time step [12], while angular velocity is bounded by Ļ max , enforcing a physical turning constraint that, as we will show, has a dominant influence on emergent collective structure. No interaction forces are prescribed at the collective level. Coordination emerges entirely from agents following local gradients through their own sen- sorimotor regularities, interacting through shared space and mutual perception, yielding a simple mechanistic model that, as we show, produces a diverse range of collective behaviors governed by sensorimotor parameters. 3 Experimental Setup We simulate groups of N = 250 agents in a two-dimensional continuous environ- ment. Each agent is modeled as a circular body of unit radius with unicycle kine- matics, controlled by linear velocity v and angular velocity Ļ, with |Ļ|ā¤ Ļ max . All simulations use a fixed timestep of āt = 0.1 and are initialized from iden- tical spatial configurations with a fixed random seed to ensure reproducibility. The desired social distance is fixed at d 0 = 50 throughout. We vary sensing, estimation, and motor parameters as summarized in Table 1, running each con- figuration both with memory (neighbor estimates propagated during invisibility) and without (estimates discarded and re-initialized on re-entry). Metrics and Quantitative Analysis We evaluate emergent collective behavior using five complementary metrics that together capture the behavioral diversity the model aims to produce. Polarization P [24] measures directional alignment as the magnitude of the mean unit velocity vector across all agents, averaged over time; values near 1 indicate coherent directed motion, while values A Mechanistic Model for Collective Motion from Sensorimotor Regularities5 Parameter DescriptionValues ĻField of view Ļ 2 , Ļ, 3Ļ 2 , 2Ļ Ļ max Maximum angular velocity0.1, 0.3, 0.6, 0.9 Ļ Ļ Assumed bearing noise std.0.001, 0.01, 1, 10, 100 Ļ Ī³ Assumed apparent size noise std.0.001, 0.01, 1, 10, 100 QAssumed process noise for other agents0.01, 0.1, 1, 10 Table 1. Varied parameters and their ranges. near 0 indicate dispersed or rotational motion. Relative Circular Area (RCA) [15] quantifies spatial compactness by measuring how closely the convex hull of agent positions resembles a circle; high RCA indicates compact circular formations, low RCA elongated or fragmented ones. Maximum mean displacement D cap- tures global translation as the maximum displacement of the group center of mass over the simulation. Center Distance C measures spatial cohesion as the time-averaged minimum distance from any agent to the group center of mass. Directional fragmentation is quantified by applying DBSCAN [19] to agent head- ings in circular space, yielding the average number of heading clusters K and clustered fraction F, capturing whether the population persistently splits into subgroups moving in distinct directions. To quantify parameter influence we compute Sobol first-order (S 1 ) and total-order (S T ) sensitivity indices [21]; the gap between them indicates the degree to which a parameter acts through in- teractions rather than in isolation. 4 Behavioral Diversity from Sensorimotor Parameters 4.1 Emergent Collective Behaviors Starting from identical initial conditions, variation of sensorimotor parameters alone produces qualitatively distinct collective behaviors without any change to the underlying interaction architectureāexactly what a mechanistic model grounded in sensorimotor regularities should produce. Stable rings emerge at low uncertainty, where agents maintain reliable neighbor estimates and accurate distance control; high turning agility keeps agents on circular orbits at d 0 (Fig- ure 2, p), while lower agility produces the same pattern with larger, smoother or- bits (Figure 2, a). Milling emerges under increased uncertainty, where degraded distance estimation prevents stable orbit maintenance; moderate uncertainty produces loose irregular rings (Figure 2, m) while high uncertainty collapses agents into dense rotating clusters (Figure 2, j). Fragmentation into groups moving along a line occurs under narrow field of view with high noise and no memory: without predictive belief propagation, agents preferentially follow whoever is directly ahead, producing elongated drift- ing groups (Figure 3, d). Fragmentation into parallel streams occurs under sim- ilar conditions but lower noise: reliable estimates allow lateral spacing mainte- 6V. Mengers et al. Ļ max = 0 . 1 (a)(b)(c)(d)(e) Ļ max = 0 . 3 (f)(g)(h)(i)(j) Ļ max = 0 . 6 (k)(l)(m)(n)(o) Very Low Ļ Ļ = 0.001Ļ Ī³ = 0.001 Q= 0.01 Ļ max = 0 . 9 (p) Low Ļ Ļ = 0.01Ļ Ī³ = 0.01 Q= 0.1 (q) Medium Ļ Ļ = 1Ļ Ī³ = 1 Q= 0.1 (r) High Ļ Ļ = 10Ļ Ī³ = 10 Q= 1 (s) Very High Ļ Ļ = 100Ļ Ī³ = 100 Q= 10 (t) Uncertainty Maximum Angular Velocity Ļ max Fig. 2. Turning agility and sensory uncertainty jointly determine collective structure, with high uncertainty collapsing all formations into dense clusters regardless of mo- tor capability. At low-to-medium uncertainty (cols. 1ā3), increasing Ļ max produces a graded transition from large smooth rings to tighter compact orbits. This breaks down at higher uncertainty (cols. 4ā5): estimation error overwhelms the gradient signal sus- taining rotational motion, collapsing all configurations into dense milling clusters whose tightness increases with Ļ max . nance, but absent memory causes the group to split into side-by-side streams (Figure 3, b). The same model, the same cost function, the same architectureā only the sensorimotor parameters change, and each regime emerges without pre- scribing rules for it. 4.2 Sensorimotor Parameters Govern Behavioral Transitions We now examine how three biologically interpretable parameter groups shape the behavioral regimes described above. Motor constraints Ļ max governs formation geometry when estimation is reliable but becomes less relevant at high uncertainty. Low angular velocity pro- duces smooth large-radius rings; higher values produce tighter orbits (Figure 2). Beyond a threshold uncertainty, Ļ max instead determines only the tightness of A Mechanistic Model for Collective Motion from Sensorimotor Regularities7 Ļ = 90 (a)(b)(c)(d) Ļ = 180 (e)(f)(g)(h) With Memory Medium Uncertainty Ļ Ļ = 1Ļ Ī³ = 1Q= 0.1 Ļ = 270 (i) No Memory Medium Uncertainty Ļ Ļ = 1Ļ Ī³ = 1Q= 0.1 (j) With Memory High Uncertainty Ļ Ļ = 10Ļ Ī³ = 10Q= 1 (k) No Memory High Uncertainty Ļ Ļ = 10Ļ Ī³ = 10Q= 1 (l) Field of View Ļ Fig. 3. Memory is critical for cohesion under narrow fields of view, while its absence can produce qualitatively different but stable structures under wider fields. At Ļ = 90, memory yields a ring (a, c) while its absence causes complete fragmentation (b, d). As field of view widens, cohesion is preserved even without memory, though structures differācompare the loose ring in (e) with the tight milling ring in (h). the resulting milling cluster (Figure 2, last two rows). This parameter has no counterpart in classical particle models, where heading changes are instantaneous and unconstrained. Crucially, it is not a fitted constant but a measurable prop- erty of the organismāthe kind of biologically grounded parameter a mechanistic model should be governed by. Perceptual uncertainty Bearing and apparent size noise degrade collec- tive structure through qualitatively different mechanisms. High bearing noise disrupts directional localization, driving a transition toward disordered aggre- gation (Figure 4, aāb). High apparent size noise instead degrades distance esti- mation while leaving directional coordination intact, producing inward-spiraling formations as agents triangulate to recover distance information (Figure 4, eāf). Where process noise is low, agents partially compensate through temporal inte- gration and active sensing. That bearing and apparent size noise produce distinct behavioral signatures reflects the distinct roles of these two sensory channelsāa distinction invisible to models that treat noise as a scalar perturbation. Memory Memory determines whether gradient continuity is preserved across periods of visual occlusion, and its effect is qualitative rather than graded. Un- der narrow fields of view, removing memory causes complete fragmentation de- spite identical parameters and initial conditions (Figure 3, first row). Under 8V. Mengers et al. High Bearing Noise Ļ Ļ = 100 Ļ Ī³ = 0 . 01 (a)(b)(c)(d) Ļ= 360Q= 1 High Apparent Size Noise Ļ Ļ = 0 . 01 Ļ Ī³ = 100 (e) Ļ= 360Q= 10 (f) Ļ= 90Q= 0.1 With Memory (g) Ļ= 90Q= 0.1 No Memory (h) Fig. 4. Bearing and apparent size noise degrade collective structure differently, reflect- ing distinct emergent compensation strategies. High bearing noise (top row) disrupts directional estimation, producing disordered clusters (aāb), though low process noise enables recovery through temporal integration and active triangulation (a, c). High apparent size noise (bottom row) leaves directional information intact but degrades distance estimation, producing inward-spiraling rings via distance-reducing triangula- tion (eāf). Without memory, both regimes lose coherence and fragment into aligned subgroups (d, h). Bearing and apparent size noise are thus not interchangeableāa distinction no scalar noise model could capture. wider fields, memory loss shifts the attractor toward qualitatively different sta- ble formations (Figure 3, b). Whether an organism retains estimates of occluded neighbors is a property of its cognitive architectureāand here it determines qualitatively different collective regimes, not just quantitative variation. 4.3 Global Sensitivity of Collective Behavior The qualitative patterns above are confirmed and quantified by a global variance- based sensitivity analysis (Figure 5). Field of view Ļ and process noise Q are the strongest direct drivers across nearly all metrics and both memory condi- tions, consistent with Ļās role as the primary gating factor for neighbor visibility and gradient continuity, and with Qās role in shaping spatial cohesion through overall estimation uncertainty. Sensory noise parameters Ļ Ļ and Ļ Ī³ show simi- larly modest first-order contributions but elevated total-order indices, indicating they act primarily through interactions. The angular velocity limit Ļ max con- tributes consistently but modestly in isolation, in line with its role as a shaping rather than gating parameter. Memory substantially flattens the sensitivity land- scape: first- and total-order indices become more evenly distributed, indicating that predictive belief propagation reduces the systemās dependence on any single sensorimotor quantity and distributes sensitivity more evenly across the full pa- rameter space. Taken together, these results confirm that behavioral transitions are governed by sensorimotor quantitiesāfield of view, noise, turning agility, A Mechanistic Model for Collective Motion from Sensorimotor Regularities9 PolarizationP Rel. Circular Area RCA Max.Avg. DisplacementD Center DistanceC Avg. Num. ClustersK Avg. Clustered FractionF 0.0540.340.0410.0280.15 0.0130.083-0.0015-0.0120.52 0.0890.280.0370.00980.036 0.0064-0.00340.0170.000410.88 -0.070.053-0.018-0.0190.054 -0.000820.20.04-0.00610.24 (a) No Memory āS 1 0.320.710.230.120.61 0.180.290.0560.0380.93 0.370.770.170.0710.73 0.0380.0410.0480.0190.95 0.630.580.290.250.76 0.40.930.140.120.71 (b) No Memory āS T Max. Ang. Velocity Ļ max Field of View Ļ Bearing Noise std. Ļ Ļ App. Size Noise std. Ļ Ī³ Process Noise Q PolarizationP Rel. Circular Area RCA Max.Avg. DisplacementD Center DistanceC Avg. Num. ClustersK Avg. Clustered FractionF 0.0250.19-0.007-0.00360.17 0.0280.22-0.0160.0330.26 0.010.17-0.017-0.00280.25 -0.0170.084-0.00210.00590.44 -0.0560.0870.0160.0150.017 0.0620.270.004-0.00880.16 (c) With Memory āS 1 Max. Ang. Velocity Ļ max Field of View Ļ Bearing Noise std. Ļ Ļ App. Size Noise std. Ļ Ī³ Process Noise Q 0.330.620.170.140.74 0.330.60.220.0950.59 0.280.550.130.140.76 0.0980.440.170.0460.77 0.530.740.240.150.68 0.320.580.190.140.54 (d) With Memory āS T 0.0 0.2 0.4 0.6 0.8 1.0 Sobol index ( S 1 , S T ) Fig. 5. Field of view and overall uncertainty are the dominant direct drivers of collec- tive behavior, while memory redistributes sensitivity away from individual parameters. Only Ļ and Q show substantial first-order contributions (S 1 ); Ļ Ļ , Ļ Ī³ , and Ļ max in- stead act primarily through interactions (low S 1 , elevated S T ). With memory (cād), sensitivity is more evenly distributed, suggesting predictive belief propagation absorbs variance that would otherwise concentrate on Ļ and Q. memoryārather than abstract tuning parameters, and that their influence op- erates through the coupled structure of perception, estimation, and action rather than in isolation. 5 Discussion This work presents collective behavior as the emergent outcome of interacting sensorimotor loops, grounded in what individual agents can actually perceive, es- timate, and physically execute. A diverse range of behaviors arises from variation of sensorimotor parameters alone. Behavioral transitions and coordination break- downs alike are governed by parameters with direct biological interpretations, connecting cross-species variation and failure modes within a single explanatory framework. Comparison to Particle Models The core limitation of classical particle models is not that they are wrong about collective phenomenaāthey are notā but that they are descriptive rather than mechanistic. Their parameters are free constants with no necessary correspondence to biological quantities, meaning they cannot transfer predictions to new species or environments without refit- ting, and cannot explain why coordination breaks down under specific sensory 10V. Mengers et al. or motor conditions. As Sayin et al. [18] recently demonstrated, the mechanistic assumptions underlying these models are not empirically supported even for a paradigmatic species: locusts do not align with neighbors, sensory mechanisms mediate interaction instead. Our results demonstrate a constructive alternative: behavioral diversity is a prediction of the sensorimotor architecture, and the parameters governing transitions correspond to quantities measurable indepen- dently of collective behavior experiments. Comparison to Perceptual Models Several recent models move beyond particle models by incorporating perceptual mechanisms. Vision-based response models [3,15] ground sensory input in visual geometry, but their response param- eters remain phenomenological and the models are stateless and memorylessā there is no estimation, no uncertainty, and no mechanism for behavior to de- pend on prior observations. Active inference models [8] ground coordination in Bayesian belief updating, a genuine advance, but the generative model uses ab- stract sector-wise representations and hyperparameters with no biological refer- ent; motor constraints are absent and field of view is approximated rather than geometrically grounded. Ring attractor models [17] connect collective behavior to neural architecture, but the empirical evidence for ring attractor dynamics applies specifically to heading direction encoding in Drosophila [20]; whether so- cial bearing to neighbors is encoded through the same architecture remains open for virtually all collective behavior species. Our model differs from all three: it operates at the sensorimotor level with parameters corresponding to measurable biological quantities, maintains persistent uncertain internal representations, and couples perception to action through sensorimotor geometry rather than abstract rules or neural commitments. The active sensing behavior that emergesāagents triangulating to reduce bearing uncertainty and reorienting to maintain neigh- bors within the field of viewācannot arise from memoryless response laws or abstract belief updating, and the Sobol analysis demonstrates that behavioral transitions are governed by a sensitivity landscape defined by biological quanti- ties rather than fitted constants. Limitations The cross-species prediction claim remains a hypothesis: pa- rameter regimes corresponding to plausible biological values produce qualita- tively distinct collective behaviors, but these predictions have not yet been val- idated against empirical data from specific organisms. In the current instanti- ation, neighbor interactions are also not geometrically localized: all estimated neighbors contribute to the cost regardless of occlusion or spatial configuration, which likely constrains observable structures toward ring-like formations. Empir- ical work suggests that visual neighborhoods based on ray-casting better account for individual responses than metric or topological alternatives [16], motivating geometrically localized interaction as a natural next extension alongside neigh- bor velocity estimation, validation against species-specific behavioral data, and structured environmental perturbations such as attraction points or external flow fields. The present model also treats all agents as identical; incorporating indi- vidual variation in sensorimotor parameters would bring it closer to biological reality and may reveal additional collective phenomena. A Mechanistic Model for Collective Motion from Sensorimotor Regularities11 6 Conclusion We have shown that a diverse range of collective behaviorsāpolarized motion, milling, line formation, and subgroup formationāemerges from the composition of individual sensorimotor regularities, without prescribing interaction forces or fitting descriptive parameters to observed group patterns. Behavioral transitions are governed by parameters corresponding to measurable biological quantitiesā turning agility, field of view geometry, sensory noise, and memoryāthe same parameters that determine both successful coordination and its breakdown. This demonstrates that collective behavior is not a phenomenon requiring special interaction mechanisms, but a consequence of embodied agents pursuing simple goals under sensorimotor constraints, and that differences across species can productively be understood as differences in embodiment and environment. Acknowledgments. We thank Pawel Romanczuk for valuable discussions and feed- back on this work. We gratefully acknowledge funding by the Deutsche Forschungsge- meinschaft (DFG, German Research Foundation) under Germanyās Excellence Strat- egy ā EXC 2002/1 āScience of Intelligenceā ā project number 390523135. This work has been partially supported by the German Federal Ministry of Research, Technology and Space (BMFTR) under the Robotics Institute Germany (RIG). We used Claude Sonnet 4.6 (Anthropic) to suggest textual improvements, particularly to ensure conciseness. Disclosure of Interests. The authors declare no competing interests. References 1. Attanasi, A., Cavagna, A., Del Castello, L., Giardina, I., Melillo, S., Parisi, L., Pohl, O., Rossaro, B., Shen, E., Silvestri, E., et al.: Collective behaviour without collective order in wild swarms of midges. PLoS Computational Biology 10(7), e1003697 (2014) 2. Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., et al.: Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences 105(4), 1232ā 1237 (2008) 3. Bastien, R., Romanczuk, P.: A model of collective behavior based purely on vision. Science Advances 6(6), eaay0792 (2020) 4. Buhl, C., Sumpter, D.J., Couzin, I.D., Hale, J.J., Despland, E., Miller, E.R., Simp- son, S.J.: From disorder to order in marching locusts. Science 312(5778), 1402ā1406 (2006) 5. Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., Viale, M.: Scale-free correlations in starling flocks. Proceedings of the National Academy of Sciences 107(26), 11865ā11870 (2010) 6. Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision-making in animal groups on the move. Nature 433(7025), 513ā516 (2005) 7. Ginelli, F.: The physics of the vicsek model. The European Physical Journal Special Topics 225(11), 2099ā2117 (2016) 12V. Mengers et al. 8. Heins, C., Millidge, B., Da Costa, L., Mann, R.P., Friston, K.J., Couzin, I.D.: Col- lective behavior from surprise minimization. Proceedings of the National Academy of Sciences 121(17), e2320239121 (2024) 9. Katz, Y., TunstrĆøm, K., Ioannou, C.C., Huepe, C., Couzin, I.D.: Inferring the struc- ture and dynamics of interactions in schooling fish. Proceedings of the National Academy of Sciences 108(46), 18720ā18725 (2011) 10. Marchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M., Simha, R.A.: Hydrodynamics of soft active matter. Reviews of Modern Physics 85(3), 1143ā1189 (2013) 11. MartĆn-MartĆn, R., Brock, O.: Coupled recursive estimation for online interactive perception of articulated objects. The International Journal of Robotics Research 41(8), 741ā777 (2022) 12. Mengers, V., Brock, O.: No plan but everything under control: Robustly solving se- quential tasks with dynamically composed gradient descent. In: IEEE International Conference on Robotics and Automation. p. 90ā96 (2025) 13. Mengers, V., Raoufi, M., Brock, O., Hamann, H., Romanczuk, P.: Leveraging un- certainty in collective opinion dynamics with heterogeneity. Scientific Reports 14, 27314 (2024) 14. Mengers, V., Roth, N., Brock, O., Obermayer, K., Rolfs, M.: A robotics-inspired scanpath model reveals the importance of uncertainty and semantic object cues for gaze guidance in dynamic scenes. Journal of Vision 25(2), 6 (2025) 15. Mezey, D., Deffner, D., Kurvers, R.H., Romanczuk, P.: Visual social information use in collective foraging. PLoS Computational Biology 20(5), e1012087 (2024) 16. Rosenthal, S.B., Twomey, C.R., Hartnett, A.T., Wu, H.S., Couzin, I.D.: Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion. Proceedings of the National Academy of Sciences 112(15), 4690ā4695 (2015) 17. Salahshour, M., Couzin, I.D.: Allocentric flocking. Nature Communications 16(1), 9051 (2025) 18. Sayin, S., Couzin-Fuchs, E., Petelski, I., GĆ¼nzel, Y., Salahshour, M., Lee, C.Y., Graving, J.M., Li, L., Deussen, O., Sword, G.A., et al.: The behavioral mecha- nisms governing collective motion in swarming locusts. Science 387(6737), 995ā 1000 (2025) 19. Schubert, E., Sander, J., Ester, M., Kriegel, H.P., Xu, X.: DBSCAN revisited, revisited: why and how you should (still) use DBSCAN. ACM Transactions on Database Systems 42(3), 19 (2017) 20. Seelig, J.D., Jayaraman, V.: Neural dynamics for landmark orientation and angular path integration. Nature 521(7551), 186ā191 (2015) 21. Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55(1-3), 271ā 280 (2001) 22. Strandburg-Peshkin, A., Twomey, C.R., Bode, N.W., Kao, A.B., Katz, Y., Ioan- nou, C.C., Rosenthal, S.B., Torney, C.J., Wu, H.S., Levin, S.A., et al.: Visual sen- sory networks and effective information transfer in animal groups. Current Biology 23(17), R709āR711 (2013) 23. Sumpter, D.J.: Collective Animal Behavior. Princeton University Press (2010) 24. Vicsek, T., CzirĆ³k, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Physical Review Letters 75(6), 1226 (1995) 25. Vicsek, T., Zafeiris, A.: Collective motion. Physics Reports 517(3-4), 71ā140 (2012)