Bio-Swarm Modular Architecture for Climbing Robots: Analytical Characterization of Critical-Mass Thresholds and Coordination Constraints

Abstract

Climbing robotic swarms may fail because of insufficient coordination among agents or because adhesion mechanisms lose contact with the operating surface. Existing frameworks generally address these failure modes separately. This study proposes the Bio Swarm Modular Architecture, a five-layer conceptual framework that integrates both constraints through the critical-mass threshold N∗ = max (Nadh, Ncoord). The adhesion-derived bound is obtained from a Bernoulli reliability model, while the coordination-derived bound is formulated as a function of a baseline coordination threshold and a normalized Task Difficulty Index. The model is examined through sensitivity analysis, alternative coordination functions, correlated adhesion-failure scenarios, and a numerical case study. Under the assumptions and parameter ranges evaluated, coordination is the dominant constraint in most nominal operating conditions, whereas adhesion becomes restrictive under low-reliability or common-cause failure scenarios. A multi-criteria decision analysis (MCDA) comparison and a layer-interface specification are also presented to support architectural analysis. The proposed framework should be interpreted as a theoretical and simulation-supported tool for mission-level planning rather than as an experimentally validated robotic architecture.

Received: 8 April 2026 | Revised: 3 August 2026 | Accepted: 7 September 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Edwin Gerardo Acuña Acuña: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration. Sacramento Cruz-Doriano: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing – review & editing, Supervision. María Teresita de Jesús Chi-Chan: Conceptualization, Validation, Investigation, Writing – review & editing, Visualization.