Imitating via manipulability: Geometry-aware combined DMP with via-point and speed adaptation

Manipulability ellipsoid on the Riemannian manifold provides an effective criterion for guiding the regulation of robot postures in an efficient and natural manner. While many manipulability-based learning by demonstration (LbD) methods achieve favorable performance in human-like manipulation, the adaptation of movement skills encapsulated in Symmetric Positive Definite (SPD) matrices and the implementation of manipulability-relevant skills related to velocity scaling are still largely open. In this paper, we develop a new framework based on Geometry-Aware Combined Dynamic Movement Primitives (GA-CDMP) for learning movement skills from demonstrations. The GA-CDMP model not only adapts learned trajectories to SPD-via-points but also establishes a correlation between SPD-based trajectories and position trajectories, enabling the adaptation of learned SPD-based trajectories across different non-linear motion velocity scales. The experimental evaluations show that our proposed method exhibits remarkable precision in passing through via-points positioned at a distance from the demonstration, while also substantially improving the invariant shape similarity in manipulability by approximately 65% compared to extended Kernelized Movement Primitives (KMPs). Moreover, our velocity adaptive approach achieves impressive success rates of up to 94% and demonstrates a notable reduction in execution time (11.72 ± 0.45 s), representing an almost 10% decrease in comparison to the state-of-the-art method employed in water-carrying tasks.