Dynamic path planning must remain reliable in the presence of sensing noise, uncertain localization, and incomplete semantic perception. We propose a practical, implementation-friendly planner that operates on occupancy grids and optionally incorporates occupancy-flow predictions to generate ego-centric, kinematically feasible paths that safely navigate through static and dynamic obstacles. The core is a nonlinear program in the spatial domain built on a modified bicycle model with explicit feasibility and collision-avoidance penalties. The formulation naturally handles unknown obstacle classes and heterogeneous agent motion by operating purely in occupancy space. The pipeline runs in real-time (faster than 10 Hz on average), requires minimal tuning, and interfaces cleanly with standard control stacks. We validate our approach in simulation with severe localization and perception noises, and on an F1TENTH platform, demonstrating smooth and safe maneuvering through narrow passages and rough routes. The approach provides a robust foundation for noise-resilient, prediction-aware planning, eliminating the need for handcrafted heuristics. The project website can be accessed at https://honda-research-institute.github.io/onrap/