A Non-parametric Skill Representation with Soft Null Space Projectors for Fast Generalization

TL;DR

This paper introduces a non-parametric movement primitive method with a null space projector that enables fast, efficient, and adaptable skill generalization in robotics, outperforming traditional parametric approaches in computational speed and flexibility.

Contribution

The authors develop a non-parametric skill representation using null space projectors that allows for rapid motion generation and on-the-fly adaptation without matrix inversions.

Findings

Achieves O(n^2) computational complexity, faster than O(n^3 for matrix inversions.

Performs favorably against state-of-the-art parametric methods in 2D examples.

Enables real-time adaptation for high-dimensional robotic skills.

Abstract

Over the last two decades, the robotics community witnessed the emergence of various motion representations that have been used extensively, particularly in behavorial cloning, to compactly encode and generalize skills. Among these, probabilistic approaches have earned a relevant place, owing to their encoding of variations, correlations and adaptability to new task conditions. Modulating such primitives, however, is often cumbersome due to the need for parameter re-optimization which frequently entails computationally costly operations. In this paper we derive a non-parametric movement primitive formulation that contains a null space projector. We show that such formulation allows for fast and efficient motion generation with computational complexity O(n2) without involving matrix inversions, whose complexity is O(n3). This is achieved by using the null space to track secondary targets, with a precision determined by the training dataset. Using a 2D example associated with time input we show that our non-parametric solution compares favourably with a state-of-the-art parametric approach. For demonstrated skills with high-dimensional inputs we show that it permits on-the-fly adaptation as well.