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Robot Learning Using Multi-Coordinate Elastic Maps (2505.06092v1)

Published 9 May 2025 in cs.RO

Abstract: To learn manipulation skills, robots need to understand the features of those skills. An easy way for robots to learn is through Learning from Demonstration (LfD), where the robot learns a skill from an expert demonstrator. While the main features of a skill might be captured in one differential coordinate (i.e., Cartesian), they could have meaning in other coordinates. For example, an important feature of a skill may be its shape or velocity profile, which are difficult to discover in Cartesian differential coordinate. In this work, we present a method which enables robots to learn skills from human demonstrations via encoding these skills into various differential coordinates, then determines the importance of each coordinate to reproduce the skill. We also introduce a modified form of Elastic Maps that includes multiple differential coordinates, combining statistical modeling of skills in these differential coordinate spaces. Elastic Maps, which are flexible and fast to compute, allow for the incorporation of several different types of constraints and the use of any number of demonstrations. Additionally, we propose methods for auto-tuning several parameters associated with the modified Elastic Map formulation. We validate our approach in several simulated experiments and a real-world writing task with a UR5e manipulator arm.

Summary

Robot Learning Using Multi-Coordinate Elastic Maps

The paper introduces a novel methodology for advancing robot learning through the use of a technique called Multi-Coordinate Elastic Maps (MC-Elmap). This approach aims to enhance the capabilities of robots in acquiring manipulation skills by learning from human demonstrations and encoding these skills in various differential coordinate frames. The methodology leverages the flexibility and computational efficiency of Elastic Maps, incorporating multiple differential coordinates to improve skill reproduction.

Methodological Innovations

Elastic Maps traditionally model trajectories as a series of nodes connected by springs, focusing primarily on position approximation, smoothness, and flexibility. The paper extends this concept by allowing it to encode information in multiple differential coordinate spaces, specifically Cartesian, Tangent, and Laplacian coordinates. The differential coordinate transform utilizes Graph Tangent and Laplacian matrices, facilitating a comprehensive capture of skill-relevant information beyond mere positional data. Thus, MC-Elmap enables the encoding of complex skill properties, such as shape-preserving and velocity profiles, which are crucial for tasks where such features outweigh basic Cartesian space considerations.

The paper outlines its methodology for hyperparameter tuning, employing an Expectation-Maximization (EM) algorithm to iteratively update the clustering of data points and solve for optimal reproduction. This meta-optimization helps fine-tune the approximation energies in different coordinate spaces, ensuring balanced importance is given to each differential coordinate based on the underlying skill characteristics demonstrated.

Experimental Validation

Several experiments are conducted across 2D and 3D datasets to validate the MC-Elmap approach's efficacy. The methodology was applied to the handwriting shapes of the LASA dataset, and various quantitative metrics, including Fréchet distance, Sum of Squared Errors (SSE), Angular Similarity, and jerk, were measured. MC-Elmap shows superior performance in maintaining spatial similarity, producing smooth trajectories with lower jerk values, and effectively capturing the geometric shape of the skills demonstrated.

Further experiments using 3D robot skills from the RAIL dataset highlight MC-Elmap's flexibility and ability to generalize across diverse starting positions. The reproduction of pressing, pushing, and reaching tasks demonstrates the approach's robustness, even capturing crucial task features like pressing actions without explicit constraint specifications. Additionally, a real-world writing task using a UR5e manipulator arm verified the ability of MC-Elmap to interpret and enhance demonstrations by smoothing jagged edges and upholding the intended shapes.

Implications and Future Directions

The paper presents a significant advancement in Learning from Demonstration (LfD) methodologies, offering an efficient framework for encoding skill demonstrations in multiple coordinate frames. This method provides practical benefits in application scenarios where capturing the geometric features of a skill is essential. The robust performance and flexibility of MC-Elmap suggest promising applications in industrial automation, complex task refinement, and dynamic environment adaptation.

Future research could explore expanding differential coordinate options beyond the currently employed Cartesian, Tangent, and Laplacian spaces. Additionally, incorporating variable weighing schemes within Elastic Maps or developing kernel-based approaches for automated coordinate selection could enhance the adaptability and precision of the methodology. Such expansions align with the increasing demand for more advanced robotic skills acquisition systems, presenting vast potential for further exploration and application in diverse robotic domains.