PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation

• URL: http://arxiv.org/abs/2607.10288v1
• Date: Sat, 11 Jul 2026 12:34:28 GMT
• Title: PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation
• Abstract summary: PIER-Flow is a lightweight navigation policy for mobile robots.<n>It achieves a 98.85% success rate and zero collisions, with an average inference of $sim$1.29 ms.
• Score: 10.164953732323463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and low-latency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85\% success rate and zero collisions, with an average inference of $\sim$1.29 ms, which accelerates planning by 37.2$\times$ compared to MPC and over 800$\times$ against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of $\sim$5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines.

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