Kinetic Energy Fields: A Solution of Riemannian Eikonal Equation on Configuration Space Manifold
Keywords: kinetic energy, eikonal equaiton, Remannian manifold, geodesics
TL;DR: We present a geometric approach for minimal kinetic energy paths by solving Riemannian eikonal equation.
Abstract: This paper presents a geometric representation for energy-efficient motion generation based on kinetic energy fields. Minimal energy paths correspond to geodesics in the configuration space manifold that satisfy equations of motion. Specifically, the kinetic energy corresponds to the constant-velocity curves on the Riemannian manifold endowed with a symmetric positive-definite kinetic energy metric. We introduce a wave propagation model for energy fields and geodesic flows by solving a first-order partial differentiable equation (PDE): the eikonal equation on the Riemannian manifold. A neural Riemannian Eikonal solver is proposed to handle high-dimensional spaces, leading to a compact and grid-free representation. Given a specific kinematics chain, the kinetic energy field is trained offline and allows efficient reactive motion generation to be computed online, enabling the rapid generation of paths from arbitrary start and goal configurations. We present preliminary results on generating energy-efficient motions on planar robot examples and a 7-axis Franka robot.
Submission Number: 10
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