Vel-v4.3: A Decentralized Swarm Protocol for Autonomous Volume Dominance

This paper presents the comprehensive empirical validation of the Vel-v4.3 protocol, a decentralized swarm coordination system for autonomous robotic navigation, introducing a critical architectural upgrade: the replacement of center-outward bloom repulsion with Map-Aware Gradient Repulsion (MAGR). Validated across five systematic parameter sweeps comprising $105{,}000$ simulation trials, this architecture is characterized across four independent protocol dimensions: agent population ($N$), repulsion factor ($G$), momentum coefficient ($\mu$), and MAGR scan radius ($r$). The Population Sweep ($N \in \{50, 150, 300\}$) confirms that MAGR successfully restores the monotonic efficiency scaling previously eliminated by the original center-bloom architecture. The integer $G$ Sweep ($G \in \{0, 2, 4, 6, 8\}$) establishes $G = 2$ as the coarse optimum and reveals that repulsion mechanics account for over 97% of total protocol efficiency, a configuration further refined by the Fine $G$ Sweep ($G \in [1.0, 3.0], \Delta G = 0.25$) to $G = 1.5$ at $N = 300$, yielding an average efficiency of $\bar{\eta} = 1.796$. Additionally, the Momentum Sweep ($\mu \in [0.70, 0.99]$) identifies $\mu = 0.99$ as the empirical optimum, delivering an average efficiency of $\bar{\eta} = 2.696$, which marks a 49.6% performance gain over the original baseline assumption of $\mu = 0.88$. Finally, the Scan Radius Sweep ($r \in [2, 10]$) demonstrates that while MAGR efficiency is fundamentally radius-invariant ($\Delta\eta = 0.006$ across all tested values), the computational overhead scales by $17.6\times$ from $r = 2$ to $r = 10$, thereby establishing $r = 2$ as the optimal deployment radius. Ultimately, the global operational efficiency optimum is achieved at $N = 300$, $G = 1.5$, $\mu = 0.99$, and $r = 2$, delivering a performance profile of $\bar{\eta} = 2.696$, a low rolling variance of $\sigma = 0.089$, and an average convergence time of $\bar{T} = 35$ steps. This represents a 78.7% improvement over the initial baseline, effectively superseding the original operational benchmark of $\eta > 0.105$ with an expected target of $\eta > 2.0$ for fully-optimized MAGR configurations.