[Paper Review] Dynamic Movement Primitives in Robotics: A Tutorial Survey

Matteo Saveriano, Fares J. Abu‐Dakka+2 more|arXiv (Cornell University)|Feb 7, 2021

Muscle activation and electromyography studiesEngineering318 references46 citations

TL;DR

A comprehensive tutorial survey that unifies, analyzes, and reviews Dynamic Movement Primitives (DMPs) in robotics, covering classical formulations, extensions, implementations, and open issues.

ABSTRACT

Biological systems, including human beings, have the innate ability to perform complex tasks in versatile and agile manner. Researchers in sensorimotor control have tried to understand and formally define this innate property. The idea, supported by several experimental findings, that biological systems are able to combine and adapt basic units of motion into complex tasks finally lead to the formulation of the motor primitives theory. In this respect, Dynamic Movement Primitives (DMPs) represent an elegant mathematical formulation of the motor primitives as stable dynamical systems, and are well suited to generate motor commands for artificial systems like robots. In the last decades, DMPs have inspired researchers in different robotic fields including imitation and reinforcement learning, optimal control,physical interaction, and human-robot co-working, resulting a considerable amount of published papers. The goal of this tutorial survey is two-fold. On one side, we present the existing DMPs formulations in rigorous mathematical terms,and discuss advantages and limitations of each approach as well as practical implementation details. In the tutorial vein, we also search for existing implementations of presented approaches and release several others. On the other side, we provide a systematic and comprehensive review of existing literature and categorize state of the art work on DMP. The paper concludes with a discussion on the limitations of DMPs and an outline of possible research directions.

Motivation & Objective

• Explain the motor primitives theory and how DMPs formalize stable dynamical systems for robot motion generation.
• Provide a unified mathematical treatment of classical DMPs and their extensions.
• Review integration of DMPs into control frameworks and learning paradigms.
• Survey available implementations and discuss practical considerations and limitations.
• Identify open issues and outline potential future research directions.

Proposed method

• Present classical and extended DMP formulations for discrete and rhythmic motions with rigorous mathematical terms.
• Discuss learning of the forcing term via methods like Locally Weighted Regression (LWR) and alternatives (GMM, GMR, GP, NN).
• Describe phase variables and alternatives (exponential, sigmoidal, piecewise, linear, and others) for timing and stopping.
• Extend DMPs to orientation representations (quaternions and rotation matrices) and SPD manifolds.
• Survey integration of DMPs into manipulation, learning, and interaction frameworks and provide open-source implementations.

Experimental results

Research questions

• RQ1 What are the classical and extended DMP formulations for discrete and rhythmic motions?
• RQ2 How can DMPs be learned from demonstrations and generalized across tasks and spaces?
• RQ3 How can DMPs be extended to handle orientation, SPD matrices, and interaction tasks?
• RQ4 What are the practical considerations, implementations, and limitations of DMPs across applications?
• RQ5 What open issues and future directions emerge from a comprehensive DMP survey?

Key findings

• DMPs provide stable, flexible motion generation capable of learning from data and responding to perturbations in real-time.
• The tutorial unifies multiple DMP formulations and extensions, including orientation and SPD manifold representations.
• Learning the forcing term can be performed with LWR, GMM/GMR, GP, or neural networks, with multiple demonstrations enhancing generalization.
• Phase variable choices and phase stopping/goal switching enable flexible timing and online adaptation.
• A wide range of implementations and open-source resources are catalogued to facilitate adoption.
• The survey delineates limitations and outlines future research directions in DMPs.