用加速度建模让机器人运动更平滑，避免突变动作。

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.