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An Alignment-Based Approach to Learning Motions from Demonstrations

Alex Cuellar, Christopher K Fourie, Julie A Shah

TL;DR

This work addresses the limitation of traditional LfD methods in learning from few demonstrations by introducing CALM, an alignment-based framework that uses a mean-trajectory representation to bridge time-independent and time-dependent approaches. CALM computes robot velocity through a gradient of a mixture-of-Gaussians alignment score, with alignment updated by an HMM-based forward model and demonstrated via TRACER clustering to enable multi-modal behavior. The key contributions include an alignment-dependent controller with stability guarantees, an HMM alignment mechanism robust to perturbations, and a cluster-selection scheme to follow the most appropriate mean trajectory, all validated on 2D datasets and three 7-DoF robot tasks. Empirically, CALM improves overlap handling, perturbation recovery, and multi-cluster switching, offering a practical, provably stable alternative for learning motions from demonstrations.

Abstract

Learning from Demonstration (LfD) has shown to provide robots with fundamental motion skills for a variety of domains. Various branches of LfD research (e.g., learned dynamical systems and movement primitives) can generally be classified into ''time-dependent'' or ''time-independent'' systems. Each provides fundamental benefits and drawbacks -- time-independent methods cannot learn overlapping trajectories, while time-dependence can result in undesirable behavior under perturbation. This paper introduces Cluster Alignment for Learned Motions (CALM), an LfD framework dependent upon an alignment with a representative ''mean" trajectory of demonstrated motions rather than pure time- or state-dependence. We discuss the convergence properties of CALM, introduce an alignment technique able to handle the shifts in alignment possible under perturbation, and utilize demonstration clustering to generate multi-modal behavior. We show how CALM mitigates the drawbacks of time-dependent and time-independent techniques on 2D datasets and implement our system on a 7-DoF robot learning tasks in three domains.

An Alignment-Based Approach to Learning Motions from Demonstrations

TL;DR

This work addresses the limitation of traditional LfD methods in learning from few demonstrations by introducing CALM, an alignment-based framework that uses a mean-trajectory representation to bridge time-independent and time-dependent approaches. CALM computes robot velocity through a gradient of a mixture-of-Gaussians alignment score, with alignment updated by an HMM-based forward model and demonstrated via TRACER clustering to enable multi-modal behavior. The key contributions include an alignment-dependent controller with stability guarantees, an HMM alignment mechanism robust to perturbations, and a cluster-selection scheme to follow the most appropriate mean trajectory, all validated on 2D datasets and three 7-DoF robot tasks. Empirically, CALM improves overlap handling, perturbation recovery, and multi-cluster switching, offering a practical, provably stable alternative for learning motions from demonstrations.

Abstract

Learning from Demonstration (LfD) has shown to provide robots with fundamental motion skills for a variety of domains. Various branches of LfD research (e.g., learned dynamical systems and movement primitives) can generally be classified into ''time-dependent'' or ''time-independent'' systems. Each provides fundamental benefits and drawbacks -- time-independent methods cannot learn overlapping trajectories, while time-dependence can result in undesirable behavior under perturbation. This paper introduces Cluster Alignment for Learned Motions (CALM), an LfD framework dependent upon an alignment with a representative ''mean" trajectory of demonstrated motions rather than pure time- or state-dependence. We discuss the convergence properties of CALM, introduce an alignment technique able to handle the shifts in alignment possible under perturbation, and utilize demonstration clustering to generate multi-modal behavior. We show how CALM mitigates the drawbacks of time-dependent and time-independent techniques on 2D datasets and implement our system on a 7-DoF robot learning tasks in three domains.

Paper Structure

This paper contains 27 sections, 4 theorems, 27 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Time-Independent LfD
  4. Time-Dependent LfD
  5. CALM Framework
  6. Problem Setting
  7. CALM Controller
  8. Stability Guarantees
  9. Velocity Matching
  10. Alignment Technique for CALM
  11. Alignment Via HMM
  12. Choice of HMM Transition Function
  13. Accounting for Multiple Demonstrated Clusters
  14. Experiments
  15. Replication on 2D Datasets
  16. ...and 12 more sections

Key Result

Theorem 1

The CALM system defined in Eq eq:DS_Def is globally asymptotically stable. (See proof in Appendix proof:thm1)

Figures (8)

  • Figure 1: Example of CALM's learned behavior. There are two demonstration clusters. One cluster (blue) passes the blue box and marker, while the other (red) passes the red box and marker. The robot starts with blue, but is perturbed and aligns to red. CALM maintains alignment despite cluster overlap.
  • Figure 2: Behavior of each tested method on three datasets: Messy Snake (top), Overlap (middle), and Multi-Motion (bottom).
  • Figure 3: Two 2D motion datasets created for this paper: Multi-Motion (left) and Overlap (right). The Multi-Motion dataset includes six demonstrations following two clusters (shown in purple and green); Overlap includes four demonstrations which include a section of overlap (see numbered labels).
  • Figure 4: Behavior under perturbation: Messy Snake with "uninformative" perturbation (top), Messy Snake with "informative" perturbation to another region of demonstrations (middle), Multi-Motion with "informative" perturbation (bottom).
  • Figure 5: Each method with an out-of-distribution initial state.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4