FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching

2025-03-08

AI Summary

This work addresses the limitation of first-order flow matching in robot motion planning—its inability to explicitly model acceleration, leading to trajectory jitter and dynamic infeasibility. We propose the first second-order flow matching framework that explicitly incorporates full trajectory dynamics (position, velocity, and acceleration) into a conditional flow matching formulation. By introducing a continuous-time, second-order differential motion representation, we establish a deterministic, noise-free, acceleration-aware flow learning paradigm—moving beyond conventional velocity-field-only modeling. The method preserves computational efficiency while significantly improving trajectory smoothness, physical feasibility, and task success rates, outperforming diffusion-based models and state-of-the-art planners on standard motion planning benchmarks. Our core contribution is the principled integration of second-order dynamics into flow matching, enabling more robust and physically realistic robot motion generation.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Prior flow matching methods in robotics have primarily learned velocity fields to morph one distribution of trajectories into another. In this work, we extend flow matching to capture second-order trajectory dynamics, incorporating acceleration effects either explicitly in the model or implicitly through the learning objective. Unlike diffusion models, which rely on a noisy forward process and iterative denoising steps, flow matching trains a continuous transformation (flow) that directly maps a simple prior distribution to the target trajectory distribution without any denoising procedure. By modeling trajectories with second-order dynamics, our approach ensures that generated robot motions are smooth and physically executable, avoiding the jerky or dynamically infeasible trajectories that first-order models might produce. We empirically demonstrate that this second-order conditional flow matching yields superior performance on motion planning benchmarks, achieving smoother trajectories and higher success rates than baseline planners. These findings highlight the advantage of learning acceleration-aware motion fields, as our method outperforms existing motion planning methods in terms of trajectory quality and planning success.

Problem

• Extends flow matching to capture second-order trajectory dynamics
• Ensures smooth and physically executable robot motions
• Outperforms existing methods in trajectory quality and planning success

Innovation

• Extends flow matching to second-order dynamics
• Directly maps prior to target trajectory distribution
• Ensures smooth, physically executable robot motions