This study provides a critical analysis of contemporary approaches to local navigation and motion control for logistics mobile robots operating in dynamically changing environments. Logistics mobile robots are increasingly deployed in manufacturing facilities, warehouse systems, service infrastructures, healthcare institutions, and other indoor technological domains to support automated material handling, object delivery, and service-oriented operations. However, the coexistence of mobile robots with humans, moving carts, other robotic platforms, and temporarily appearing obstacles substantially increases the complexity of ensuring safe, stable, and smooth motion. Under such conditions, conventional navigation and control strategies are often limited in maintaining reliable obstacle avoidance, motion continuity, and real-time adaptability to environmental uncertainties. Accordingly, the systematic investigation of SLAM-based localization and mapping, local navigation algorithms, and adaptive motion control methods is of considerable scientific and practical relevance for enhancing the autonomy, robustness, and operational reliability of logistics mobile robots.