# Teleoperator Imitation with Continuous-time Safety

## TL;DR

This paper introduces a novel control law learning method for teleoperation that guarantees safety and optimal imitation, enabling robots to adapt to dynamic environments and unseen scenarios with proven convergence.

## Contribution

It presents a contraction theory and sum-of-squares programming-based approach for learning polynomial control laws with continuous-time safety guarantees from demonstrations.

## Key findings

- Method achieves real-time adaptation to moving obstacles.
- Outperforms existing imitation learning methods on benchmarks.
- Provides provable safety and optimality guarantees.

## Abstract

Learning to effectively imitate human teleoperators, with generalization to unseen and dynamic environments, is a promising path to greater autonomy enabling robots to steadily acquire complex skills from supervision. We propose a new motion learning technique rooted in contraction theory and sum-of-squares programming for estimating a control law in the form of a polynomial vector field from a given set of demonstrations. Notably, this vector field is provably optimal for the problem of minimizing imitation loss while providing continuous-time guarantees on the induced imitation behavior. Our method generalizes to new initial and goal poses of the robot and can adapt in real-time to dynamic obstacles during execution, with convergence to teleoperator behavior within a well-defined safety tube. We present an application of our framework for pick-and-place tasks in the presence of moving obstacles on a 7-DOF KUKA IIWA arm. The method compares favorably to other learning-from-demonstration approaches on benchmark handwriting imitation tasks.