Dynamic movement primitives in robotics: A tutorial survey

Abstract

Biological systems, including human beings, have the innate ability to perform complex tasks in a versatile and agile manner. Researchers in sensorimotor control have aimed to comprehend and formally define this innate characteristic. The idea, supported by several experimental findings, that biological systems are able to combine and adapt basic units of motion into complex tasks finally leads 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 in a considerable amount of published papers. The goal of this tutorial survey is two-fold. On one side, we present the existing DMP formulations in rigorous mathematical terms and discuss the 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.

A robot motion skills method with explicit environmental constraints

“…Through investigating previous works (Ijspeert et al , 2013; Lu et al , 2021; Saveriano et al , 2021), we found that the real-time status of the robot and the relative position relationship of the workspace can be used to design additional terms and achieve the desired functionality through these additional terms. They can be summarized in the following abstract form: here, ϕ ( s , τ ) represents “canonical system” similar to equation (4), f 2 ( g , x , v , τ ) represents K ( g − x ) − Dv in (1), u ( g , x 0 , s , τ ) represents a forcing term similar to equation (3), Δ u and Δ v , respectively, represent additional acceleration terms and additional velocity terms for achieving the desired functionality.…”

“…In this section, we introduce the process of motion skill learning and generalization based on EC-DMPs. Similar to the general skill learning process based on DMPs (Saveriano et al , 2021), the entire process can be divided into two stages: skill learning and skill generalization. In the learning stage, a reference task is first given, and a parameterized primitive sequence is obtained through task decomposition (Da Silva et al , 2012).…”

Motion optimization for safe robot–environment interaction with force constraints

“…Here, we provide a short demonstration about the convergence and stability of the proposed frame, with respect to reference [21]. Theorem With the consideration of the manipulator system, integrated with the force tracking error constraints framework and adaptive DMPs, the proposed scheme guarantee the stability of DMPs and convergency to target point .…”

“…Previous researches illustrate that a safe interaction can also be achieved by developing an online adaptive motion generation scheme. The conventional dynamic movement primitive (DMP) framework is developed by introducing a coupling term to improve the limitation while tackling the problems of assembly, trajectory planning, obstacle avoidance, etc [21, 22]. Afterwards, various researches attempted to take the force and stiffness information into account while designing a modified DMPs [23–25].…”

Safe and Human‐Like Trajectory Planning of Self‐Driving Cars: A Constraint Imitative Method

“…Within the field of robotics, dynamic movement primitives (DMP) refers to a commonly applied imitative motion planning method. [ 17,18 ] Similar to APF, DMP encodes obstacles as PFs to generate repulsive effects, while it differs from traditional APF in that the attractive effect is encoded using local targets and human demonstrations. DMP encodes the target and demonstration with a succession or concurrent execution of primitive movement.…”