# Extended Diffeomorphism for Real-Time Motion Replication in Workspaces with Different Spatial Arrangements

## TL;DR

This paper introduces extended diffeomorphism techniques to enable real-time, smooth motion replication across robots in different spatial arrangements, enhancing teleoperation efficiency.

## Contribution

It proposes novel extended diffeomorphism designs for compensating spatial workspace differences, improving motion accuracy and smoothness in robot teleoperation.

## Key findings

- Reduced mapping errors in target keypoints
- Achieved smooth and precise motion replication
- Demonstrated effectiveness with dual-arm UR5 robot

## Abstract

This paper presents two types of extended diffeomorphism designs to compensate for spatial placement differences between robot workspaces. Teleoperation of multiple robots is attracting attention to expand the utilization of the robot embodiment. Real-time reproduction of robot motion would facilitate the efficient execution of similar tasks by multiple robots. A challenge in the motion reproduction is compensating for the spatial arrangement errors of target keypoints in robot workspaces. This paper proposes a methodology for smooth mappings that transform primary robot poses into follower robot poses based on the predefined key points in each workspace. Through a picking task experiment using a dual-arm UR5 robot, this study demonstrates that the proposed mapping generation method can balance lower mapping errors for precise operation and lower mapping gradients for smooth replicated movement.