Stable and Accurate Robot Trajectory Tracking Using Variable-Stiffness Euclideanizing Flow

Area of Science:

• Robotics
• Machine Learning
• Control Theory

Background:

• Imitation learning using dynamical systems (DSs) offers real-time motion planning with stability.
• Existing DS methods struggle with trajectory deviations under perturbations, limiting precise path following.
• This necessitates improved methods for robust trajectory tracking in dynamic environments.

Purpose of the Study:

• To propose a novel imitation learning approach that overcomes trajectory deviation issues in dynamical systems.
• To enable robust tracking of specific reference trajectories and critical path points.
• To enhance the stability and accuracy of motion planning in uncertain environments.

Main Methods:

• Introduced variable stiffness Euclidean flow, utilizing diffeomorphic mapping to simplify complex trajectories.
• Transformed demonstrated trajectories into straight-line paths, bypassing traditional integration.
• Developed a gradient system for convergence to demonstrated trajectories, creating attractor-like behavior.

Main Results:

• The proposed method effectively transforms complex trajectories into simpler forms for imitation learning.
• The approach ensures convergence to demonstrated trajectories while preserving desired velocities.
• Experimental validation on datasets and real robots confirmed the method's effectiveness and robustness.

Conclusions:

• Variable stiffness Euclidean flow offers a significant advancement in imitation learning for robotics.
• The method enhances the ability of systems to track precise trajectories under perturbations.
• This technique improves the reliability of motion planning in complex and uncertain dynamic scenarios.