An Original Theoretical Investigation into Morphogenetic Algorithms for Self-Reconfiguring Modular Robotic Systems Applicable to Disaster Recovery in Nigerian Urban Contexts

Self-reconfiguring modular robotic systems, composed of large populations of identical robotic modules capable of dynamically changing their interconnection topology to assume different locomotion morphologies and manipulation configurations, offer uniquely adaptive capabilities for disaster recovery operations in collapsed building environments such as those encountered in earthquake and gas explosion incidents in Nigerian urban areas. The fundamental theoretical gap limiting the practical scalability of self-reconfiguring systems is the absence of algorithms that can reliably guide large-scale module populations through complex three-dimensional reconfiguration sequences in cluttered, dynamically changing environments without centralized coordination. This dissertation presents an original theoretical investigation into morphogenetic algorithms, inspired by biological cellular differentiation and positional information theory, as a class of distributed self-reconfiguration algorithms for large-scale modular robots. A formal morphogenetic algorithm framework is developed in which individual modules act as artificial cells executing local gene expression rules that are modulated by chemical gradient signals broadcast from reference modules, enabling emergent formation of target three-dimensional robot morphologies without global planning. Convergence theorems for the proposed morphogenetic algorithm are derived under the assumption of connected module communication graph topology, providing theoretical guarantees on reconfiguration time scaling with module population size. Robustness to module communication failures is characterized through a percolation theory analysis of the module connectivity graph. A simulation study involving 256-module systems validates near-linear scaling of reconfiguration time with population size under the morphogenetic algorithm, compared to exponential scaling for a centralized planning baseline. Physical validation is conducted using a 32-module prototype system developed in collaboration with the University of Maiduguri. Keywords: morphogenetic algorithm, self-reconfiguring robot, modular robotics, disaster recovery, distributed control