Integrating Flow Matching and Model Predictive Control for Safe Robot Navigation

Learning-based path planners based on diffusion and flow matching can generate diverse trajectories from demonstrations but typically lack mechanisms for constraint satisfaction and collision avoidance during deployment. This work proposes a framework that combines flow-matching-based path planning with model predictive path-following control to integrate data-driven path generation with real-time, constraint-aware execution. The flow-matching model captures multimodal path distributions, while the predictive controller adapts motion online to satisfy state and input constraints and avoid obstacles using updated local sensor information. An event-triggered re-planning scheme incorporates predictive control solutions into subsequent path generation, promoting collision-free navigation in environments with previously unseen obstacles. Simulation results for mobile robot navigation demonstrate robust performance across cluttered environments. The framework provides a systematic approach to combining flow matching with predictive control for adaptive, data-driven navigation.