Topological and Software-Driven Advances in Robotics: Leveraging MATLAB-Simulink and Semiconductor Innovation for Adaptive Autonomous Systems

Abstract: This study investigates how topological representations, model-based software engineering, and semiconductor acceleration can be combined to strengthen adaptive autonomy in robotics. Concept analysis establishes the role of persistent homology and related topological descriptors as stable, noise-robust summaries for perception and planning, while framework analysis formulates a theory-to-silicon pipeline that integrates these descriptors into MATLAB–Simulink components, supports automatic code generation, and targets heterogeneous edge system-on-chips. The central problem addressed is the fragmentation between global guarantees, verifiable software artifacts, and resource-constrained deployment, which limits reliability and traceability in real-time operation. A co-design methodology is proposed: topology-aware perception and planning blocks are implemented in Simulink with runtime contracts; online TDA signals condition motion generation; and hardware-in-the-loop experiments validate timing and schedulability on CPUs/GPUs/NPUs and event-driven sensors. Representative mobile manipulation and aerial tasks are used for evaluation across co-simulation and embedded prototypes. Results indicate reduced end-to-end latency and energy consumption, improved success rates under distribution shift, and fewer safety violations, with ablations isolating the contributions of topological signals, software traceability, and hardware mapping. The implications are a portable blueprint for certifiable, adaptive autonomy that links mathematical guarantees to executable artifacts, supports rigorous verification and maintenance, and provides practical guidance for deploying learning-rich robotic systems under strict real-time and energy constraints. Keywords: topological robotics, persistent homology, topological data analysis, MATLAB–Simulink, model-based design, hardware-in-the-loop (HIL), system-on-chip (SoC), event-based cameras, neuromorphic computing, autonomous systems, runtime verification, edge computing