Incremental Learning of Full-Pose Via-Point Movement Primitives on Riemannian Manifolds

TL;DR

This paper proposes a set of seven fundamental operations to incrementally learn, improve, and re-organize MP libraries, and builds on Riemannian manifold theory to enable the incremental learning of all parameters of position and orientation VMPs within a library.

Abstract

Movement primitives (MPs) are compact representations of robot skills that can be learned from demonstrations and combined into complex behaviors. However, merely equipping robots with a fixed set of innate MPs is insufficient to deploy them in dynamic and unpredictable environments. Instead, the full potential of MPs remains to be attained via adaptable, large-scale MP libraries. In this paper, we propose a set of seven fundamental operations to incrementally learn, improve, and re-organize MP libraries. To showcase their applicability, we provide explicit formulations of the spatial operations for libraries composed of Via-Point Movement Primitives (VMPs). By building on Riemannian manifold theory, our approach enables the incremental learning of all parameters of position and orientation VMPs within a library. Moreover, our approach stores a fixed number of parameters, thus complying with the essential principles of incremental learning. We evaluate our approach to incrementally learn a VMP library from motion capture data provided sequentially.

Figures (6)

• Figure 1: Illustration of a Riemannian VMP on $\mathcal{S}^2$.
• Figure 2: Snapshots of the tasks from motion capture recordings from krebsMeixner2021manipulation that are incrementally learned in Section \ref{['subsec:experiments:learn_from_dataset']}.
• Figure 3: Added and incrementally improved VMP for an $\mathsf{approach}$ task. Left: Incrementally provided demonstrations. Middle: Incrementally learned full-pose VMP, with positions $\bm{p}$ ( $\blacksquare$$x$, $\blacksquare$$y$, $\blacksquare$$z$ ), and orientations $\bm{q}$ ( $\blacksquare$$q_x$, $\blacksquare$$q_y$, $\blacksquare$$q_z$, $\blacksquare$$q_w$ ). All executions are performed w.r.t. the start and end of the first demonstration. Colors go from transparent to opaque to show the incremental updates. Right: Weight means after $6$ demonstrations.
• Figure 4: Merge estimations of $\mathsf{lift}$ VMPs. The trajectories are normalized to the same start and end. Left: Demonstrations in the context of $\mathsf{cutting}$. Middle: Demonstrations in the context of $\mathsf{peeling}$. Right: Execution of the individual VMPs from the context of $\mathsf{cutting}$ (- -) and $\mathsf{peeling}$ ($\cdots$), and of the merged VMP (---).
• Figure 5: Splitting a $\mathsf{retreat}$ VMP into two modes. The trajectories are normalized to the same start and end. Left: Joint estimation (---) after 4 demonstrations. Demonstrations and estimated VMP are depicted by semitransparent and opaque lines, respectively. Middle: Mode 1 (---) and Mode 2 ($\cdots$) after splitting with a $5$th demonstration. Right: Mode 1 (---) and Mode 2 ($\cdots$) after further improvement from $4$ additional demonstrations.