# Robot Learning from Demonstration Using Elastic Maps

arXiv: https://arxiv.org/abs/2208.02207 · HTML: https://mlsanity.com/paper/2208.02207/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Placed in

- Offline RL and imitation learning from data / [Robot learning from demonstration](https://mlsanity.com/offlinerl/robot-learning-from-demonstration/)

## Builds on (most cited first, 5 of 5)

- [An Overview of Distance and Similarity Functions for Structured Data](https://mlsanity.com/paper/2002.07420/) (2020)
- [Benchmark for Skill Learning from Demonstration: Impact of User Experience, Task Complexity, and Start Configuration on Performance](https://mlsanity.com/paper/1911.02725/) (2019)
- [Skill Acquisition via Automated Multi-Coordinate Cost Balancing](https://mlsanity.com/paper/1903.11725/) (2019)
- [Learning from Successful and Failed Demonstrations via Optimization](https://mlsanity.com/paper/2107.11918/) (2021)
- [Similarity-Aware Skill Reproduction based on Multi-Representational Learning from Demonstration](https://mlsanity.com/paper/2110.14817/) (2021)

## Built on by (most cited first, 1 of 1)

- [One-Shot Multimodal Learning from Demonstration with Force-Constrained Elastic Maps](https://mlsanity.com/paper/2607.09515/) (2026)

## Abstract (arXiv)

Learning from Demonstration (LfD) is a popular method of reproducing and generalizing robot skills from human-provided demonstrations. In this paper, we propose a novel optimization-based LfD method that encodes demonstrations as elastic maps. An elastic map is a graph of nodes connected through a mesh of springs. We build a skill model by fitting an elastic map to the set of demonstrations. The formulated optimization problem in our approach includes three objectives with natural and physical interpretations. The main term rewards the mean squared error in the Cartesian coordinate. The second term penalizes the non-equidistant distribution of points resulting in the optimum total length of the trajectory. The third term rewards smoothness while penalizing nonlinearity. These quadratic objectives form a convex problem that can be solved efficiently with local optimizers. We examine nine methods for constructing and weighting the elastic maps and study their performance in robotic tasks. We also evaluate the proposed method in several simulated and real-world experiments using a UR5e manipulator arm, and compare it to other LfD approaches to demonstrate its benefits and flexibility across a variety of metrics.