KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning

Alice Kate Li, Thales C. Silva, Victoria Edwards, Vijay Kumar, M. Ani Hsieh

Keywords: motion planning;koopman operator theory, dynamical systems, learning from demonstrations

TL;DR: learning almost divergence free koopman dynamical systems for motion planning

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, and leverages the divergence properties of the learnt flow fields to obtain smooth motion fields that converge to a desired reference trajectory when the 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, 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.

Submission Number: 885