Graph Conditioned Flow Matching for Uncertain Motion Modeling in Human-Robot Collaboration

Abstract

Human motion in human-robot collaboration (HRC) is intrinsically stochastic, with repeated task executions often resulting in varied motion trajectories. Predicting such motion thus requires modeling a probability distribution over future states, rather than estimating a single deterministic path. Although diffusion-based methods have recently advanced probabilistic motion generation, they remain constrained by two critical shortcomings in HRC settings: first, they frequently emphasize sample diversity at the expense of kinematic plausibility, and second, they lack explicit mechanisms to capture the structured, multi-scale interdependencies between human and robot movements. To address these limitations, this paper introduces GCFM-a graph-conditioned flow matching model for interactive motion forecasting. By adopting a flow matching objective, GCFM learns a time-continuous vector field that deterministically transports a simple noise distribution toward the data manifold of human-robot collaboration sequences. This formulation offers greater training stability and sampling efficiency compared to iterative denoising paradigms. The model further incorporates a dual-graph prior, combining a fixed topological graph that enforces skeletal and mechanical constraints with a learnable collaboration graph that captures task-driven collaboration patterns. These relational structures are embedded into a flow prediction network, which performs multi-scale feature aggregation through graph convolutions and temporal filtering. To preserve coherence with observed motion history, a mask-based conditioning mechanism anchors known frames throughout the flow integration process. Experimental results demonstrate that GCFM achieves great prediction accuracy while maintaining competitive inference speed.