BMP: Bridging the Gap between B-Spline and Movement Primitives

TL;DR

This paper introduces B-spline Movement Primitives (BMPs), which combine B-spline properties with movement primitive capabilities, enabling better modeling of trajectory distributions in robot learning tasks.

Contribution

The paper reformulates B-splines as Movement Primitives, integrating higher-order statistics modeling with boundary condition satisfaction for improved robot learning.

Findings

BMPs outperform existing MPs in imitation learning tasks.

BMPs effectively model complex trajectory distributions.

Empirical results show enhanced learning performance in RL.

Abstract

This work introduces B-spline Movement Primitives (BMPs), a new Movement Primitive (MP) variant that leverages B-splines for motion representation. B-splines are a well-known concept in motion planning due to their ability to generate complex, smooth trajectories with only a few control points while satisfying boundary conditions, i.e., passing through a specified desired position with desired velocity. However, current usages of B-splines tend to ignore the higher-order statistics in trajectory distributions, which limits their usage in imitation learning (IL) and reinforcement learning (RL), where modeling trajectory distribution is essential. In contrast, MPs are commonly used in IL and RL for their capacity to capture trajectory likelihoods and correlations. However, MPs are constrained by their abilities to satisfy boundary conditions and usually need extra terms in learning objectives to satisfy velocity constraints. By reformulating B-splines as MPs, represented through basis functions and weight parameters, BMPs combine the strengths of both approaches, allowing B-splines to capture higher-order statistics while retaining their ability to satisfy boundary conditions. Empirical results in IL and RL demonstrate that BMPs broaden the applicability of B-splines in robot learning and offer greater expressiveness compared to existing MP variants.