Position-Based Flocking for Persistent Alignment without Velocity Sensing

TL;DR

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.

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 (8)

• 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 $\mathbf{v}_j - \mathbf{v}_i$ 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).
• Figure 4: Trajectories of the collective over $[0, 100]\,\text{s}$ under (a) the velocity-alignment-based model \ref{['eq:control-flk']} (V-based), (b) the position-based model \ref{['eq:position-model']} 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 \ref{['eq:control-flk']} (V-based), the position-based model \ref{['eq:position-model']} 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.