A Linearly Constrained Nonparametric Framework for Imitation Learning

TL;DR

This paper introduces a non-parametric imitation learning framework that incorporates linear constraints, enabling robots to learn constrained skills effectively by leveraging probabilistic demonstration data and connecting with model predictive control.

Contribution

The paper presents a novel linearly constrained non-parametric imitation learning approach that addresses constrained motor skills, bridging the gap between demonstration-based learning and control constraints.

Findings

Effective in simulated writing tasks

Applicable to locomotion tasks

Connects with model predictive control

Abstract

In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample applications (e.g., grasping tasks and human-robot collaborations) further show the applicability of imitation learning in a wide range of domains. While numerous literature is dedicated to the learning of human skills in unconstrained environment, the problem of learning constrained motor skills, however, has not received equal attention yet. In fact, constrained skills exist widely in robotic systems. For instance, when a robot is demanded to write letters on a board, its end-effector trajectory must comply with the plane constraint from the board. In this paper, we aim to tackle the problem of imitation learning with linear constraints. Specifically, we propose to exploit the probabilistic properties of multiple demonstrations, and subsequently incorporate them into a linearly constrained optimization problem, which finally leads to a non-parametric solution. In addition, a connection between our framework and the classical model predictive control is provided. Several examples including simulated writing and locomotion tasks are presented to show the effectiveness of our framework.