Geometry-aware Dynamic Movement Primitives
This work addresses a domain-specific limitation in robotics for enabling learned skill models to handle geometric data, representing an incremental advancement by extending existing DMP methods to non-Euclidean spaces.
The paper tackles the problem of applying dynamic movement primitives (DMPs) to robot control with symmetric positive definite (SPD) matrices, which represent factors like stiffness and manipulability, by proposing a Riemannian metric-based framework that reformulates DMPs to operate on SPD manifolds, demonstrating that key DMP properties such as goal change during operation are preserved.
In many robot control problems, factors such as stiffness and damping matrices and manipulability ellipsoids are naturally represented as symmetric positive definite (SPD) matrices, which capture the specific geometric characteristics of those factors. Typical learned skill models such as dynamic movement primitives (DMPs) can not, however, be directly employed with quantities expressed as SPD matrices as they are limited to data in Euclidean space. In this paper, we propose a novel and mathematically principled framework that uses Riemannian metrics to reformulate DMPs such that the resulting formulation can operate with SPD data in the SPD manifold. Evaluation of the approach demonstrates that beneficial properties of DMPs such as change of the goal during operation apply also to the proposed formulation.