# Dynamic Movement Primitives in Robotics: A Tutorial Survey

arXiv: https://arxiv.org/abs/2102.03861 · HTML: https://mlsanity.com/paper/2102.03861/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2021.

## Built on by (most cited first, 30 of 47)

- [ProDMPs: A Unified Perspective on Dynamic and Probabilistic Movement Primitives](https://mlsanity.com/paper/2210.01531/) (2022)
- [Interactive Imitation Learning of Bimanual Movement Primitives](https://mlsanity.com/paper/2210.16220/) (2022)
- [SAIL: Faster-than-Demonstration Execution of Imitation Learning Policies](https://mlsanity.com/paper/2506.11948/) (2025)
- [SAR: Generalization of Physiological Agility and Dexterity via Synergistic Action Representation](https://mlsanity.com/paper/2307.03716/) (2023)
- [A Survey on Imitation Learning for Contact-Rich Tasks in Robotics](https://mlsanity.com/paper/2506.13498/) (2025)
- [Continual Learning from Demonstration of Robotics Skills](https://mlsanity.com/paper/2202.06843/) (2022)
- [Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrations](https://mlsanity.com/paper/2206.04632/) (2022)
- [ROS-PyBullet Interface: A Framework for Reliable Contact Simulation and Human-Robot Interaction](https://mlsanity.com/paper/2210.06887/) (2022)
- [Scalable and Efficient Continual Learning from Demonstration via a Hypernetwork-generated Stable Dynamics Model](https://mlsanity.com/paper/2311.03600/) (2023)
- [MMP++: Motion Manifold Primitives with Parametric Curve Models](https://mlsanity.com/paper/2310.17072/) (2023)
- [Fast Ergodic Search with Kernel Functions](https://mlsanity.com/paper/2403.01536/) (2024)
- [Multiscale Sensor Fusion and Continuous Control with Neural CDEs](https://mlsanity.com/paper/2203.08715/) (2022)
- [Autonomous Catheterization with Open-source Simulator and Expert Trajectory](https://mlsanity.com/paper/2401.09059/) (2024)
- [Bridging the gap between Learning-to-plan, Motion Primitives and Safe Reinforcement Learning](https://mlsanity.com/paper/2408.14063/) (2024)
- [Interactive Imitation Learning for Dexterous Robotic Manipulation: Challenges and Perspectives -- A Survey](https://mlsanity.com/paper/2506.00098/) (2025)
- [Style-transfer based Speech and Audio-visual Scene Understanding for Robot Action Sequence Acquisition from Videos](https://mlsanity.com/paper/2306.15644/) (2023)
- [Using Implicit Behavior Cloning and Dynamic Movement Primitive to Facilitate Reinforcement Learning for Robot Motion Planning](https://mlsanity.com/paper/2307.16062/) (2023)
- [Conditional Neural Expert Processes for Learning Movement Primitives from Demonstration](https://mlsanity.com/paper/2402.08424/) (2024)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Periodic DMP formulation for Quaternion Trajectories](https://mlsanity.com/paper/2110.10510/) (2021)
- [Learning Pneumatic Non-Prehensile Manipulation with a Mobile Blower](https://mlsanity.com/paper/2204.02390/) (2022)
- [Constrained Dynamic Movement Primitives for Safe Learning of Motor Skills](https://mlsanity.com/paper/2209.14461/) (2022)
- [Guided Learning from Demonstration for Robust Transferability](https://mlsanity.com/paper/2302.03901/) (2023)
- [Motion Manifold Flow Primitives for Task-Conditioned Trajectory Generation under Complex Task-Motion Dependencies](https://mlsanity.com/paper/2407.19681/) (2024)
- [Variable-Frequency Imitation Learning for Variable-Speed Motion](https://mlsanity.com/paper/2411.12310/) (2024)
- [A Comprehensive Survey on Physical Risk Control in the Era of Foundation Model-enabled Robotics](https://mlsanity.com/paper/2505.12583/) (2025)
- [Multifunctional physical reservoir computing in soft tensegrity robots](https://mlsanity.com/paper/2507.21496/) (2025)
- [Conditional Variational Auto Encoder Based Dynamic Motion for Multi-task Imitation Learning](https://mlsanity.com/paper/2405.15266/) (2024)
- [Enabling robots to follow abstract instructions and complete complex dynamic tasks](https://mlsanity.com/paper/2406.11231/) (2024)
- [Mastering Contact-rich Tasks by Combining Soft and Rigid Robotics with Imitation Learning](https://mlsanity.com/paper/2410.07787/) (2024)

## Abstract (arXiv)

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.