Scalable Learning of High-Dimensional Demonstrations with Composition of Linear Parameter Varying Dynamical Systems

TL;DR

This paper introduces a scalable compositional method for learning stable high-dimensional dynamical systems from demonstrations, overcoming computational challenges of traditional BMI-based approaches.

Contribution

A novel compositional approach that improves the scalability and applicability of learning stable dynamical systems with BMI constraints.

Findings

Enhanced scalability in high-dimensional settings

Reduced computational resources required

Maintained stability and robustness of learned systems

Abstract

Learning from Demonstration (LfD) techniques enable robots to learn and generalize tasks from user demonstrations, eliminating the need for coding expertise among end-users. One established technique to implement LfD in robots is to encode demonstrations in a stable Dynamical System (DS). However, finding a stable dynamical system entails solving an optimization problem with bilinear matrix inequality (BMI) constraints, a non-convex problem which, depending on the number of scalar constraints and variables, demands significant computational resources and is susceptible to numerical issues such as floating-point errors. To address these challenges, we propose a novel compositional approach that enhances the applicability and scalability of learning stable DSs with BMIs.