Abstract
This review synthesizes advances in supervisory control for walking robots, integrating perspectives on architectural frameworks and decision-making strategies, and analyzing their performance across diverse application contexts. We survey centralized, decentralized or distributed, hierarchical, and hybrid architectures, then examine rule-based, model-based, AI-driven, fuzzy, event-driven, and adaptive supervisory strategies. A multi-criteria lens encompassing stability, adaptability, energy efficiency, fault tolerance, and computational cost is adopted to enable principled comparison and context-aware selection. We delineate domain-specific requirements in rehabilitation and assistive systems, humanoid platforms, quadrupedal explorers, and industrial or military deployments, highlighting the interplay between safety, responsiveness, and endurance. The review identifies a fundamental trade-off: transparency and verifiability tend to favor rule-based or hierarchical schemes, whereas versatility and environment generalization increasingly rely on data-driven and adaptive methods with higher computational burdens. Promising directions include the fusion of model-based prediction with learning-based adaptation, energy-aware supervisory layers, and formal safety guarantees through reachability and barrier certificates. We also emphasize the role of digital twins for rapid in silico evaluation and policy transfer. Finally, we call for standardized benchmarks, open datasets, and reproducible protocols to accelerate translation from laboratory prototypes to reliable field systems and to enable fair, quantitative assessment of supervisory controllers.