Abstract
In this work, we propose a novel flow field-based motion planning method that drives a robot from any initial state to a desired reference trajectory such that it converges to the trajectory's end point. Despite demonstrated efficacy in using Koopman operator theory for modeling dynamical systems, Koopman does not inherently enforce convergence to desired trajectories nor to specified goals -- a requirement when learning from demonstrations (LfD). We present KoopMotion which represents motion flow fields as dynamical systems, parameterized by Koopman Operators to mimic desired trajectories, and leverages the divergence properties of the learnt flow fields to obtain smooth motion fields that converge to a desired reference trajectory when a robot is placed away from the desired trajectory, and tracks the trajectory until the end point. To demonstrate the effectiveness of our approach, we show evaluations of KoopMotion on the LASA human handwriting dataset and a 3D manipulator end-effector trajectory dataset, including spectral analysis. We also perform experiments on a physical robot, verifying KoopMotion on a miniature autonomous surface vehicle operating in a non-static fluid flow environment. Our approach is highly sample efficient in both space and time, requiring only 3\% of the LASA dataset to generate dense motion plans. Additionally, KoopMotion provides a significant improvement over baselines when comparing metrics that measure spatial and temporal dynamics modeling efficacy.
Abstract (translated)
在这项工作中，我们提出了一种基于流场的运动规划方法，该方法能够引导机器人从任意初始状态到达期望参考轨迹，并确保最终收敛到该轨迹的终点。尽管Koopman算子理论在建模动力系统方面已经显示出良好的效果，但Koopman本身并不能自然地强制使系统向期望的轨迹或指定的目标收敛——这是从演示学习（LfD）时所需的关键特性。我们提出了名为KoopMotion的方法，它将运动流场表示为动态系统，并利用Koopman算子进行参数化以模仿所需的轨迹。此外，该方法通过利用所学流场的散度属性来获得平滑的运动场，在机器人远离期望轨迹时能够收敛到期望参考轨迹，并在到达终点之前始终跟踪此轨迹。 为了展示我们方法的有效性，我们在LASA人类手写数据集和一个3D机械臂末端执行器轨迹数据集上对KoopMotion进行了评估，包括频谱分析。此外，还在实际机器人上进行实验，在非静态流体环境中验证了KoopMotion在微型自主水面车辆上的应用。 我们的方法在空间和时间样本效率方面都非常高，仅需使用LASA数据集的3%就可以生成密集的运动计划。当比较用于衡量时空动力学建模效果的指标时，KoopMotion也显著优于基线模型。
URL
https://arxiv.org/abs/2509.09074
