Dynamic Movement Primitives in Robotics: A Tutorial Survey

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, Dynamic Movement Primitives (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.

Learning Pneumatic Non-Prehensile Manipulation with a Mobile Blower

“…There has also been extensive research in incorporating compositional temporal structure for multi-frequency robot control: from constructing a hierarchical abstraction of control primitives, to combining them with reinforcement learning. Early work in this area includes Dynamic Movement Primitives (DMPs) [21], [22], [23], [24], [25], [26], which use attractor dynamics to produce stable units of control that are sequenced or blended together to perform downstream tasks with imitation learning. DMPs have also since been extended and used within hierarchical reinforcement learning (RL) using the options framework [27], [28], [29], [30], where they are formulated as pretrained low-level skills that are composed hierarchically by having a high-level policy choose between primitive actions or pretrained skills [31].…”

Real-time temporal adaptation of dynamic movement primitives for moving targets

“…DMP framework provides an elegant way to encode any arbitrary spatial trajectory as a stable second-order nonlinear system, which is well suited and widely utilized controlling for robotic systems [21]. The standard DMP system consists of a point attractor formulated as a second-order ordinary differential equation (ODE) with a nonlinear forcing term.…”

“…Here xg is an estimate of the final goal position. A fair assumption is that the goal is moving slow enough such that v ≥ ẋg the convergence properties holds for the system in (21). The estimate of the final goal position at time t is updated with a simple weighted average of the current goal position and the position estimated using the goal velocity at time t,…”

“…The goal position is updated in realtime based on a simple estimate from equation (22). The DMP system is simulated with a velocity feedback from the moving goal based on the transformation system in (21). For all the scenarios, the real-time behaviour of DMP systems with both exponential and polynomial canonical systems described by ( 2) and ( 15) respectively are shown in figure 4.…”

Extended DMPs Framework for Position and Decoupled Quaternion Learning and Generalization

“…Thus, our framework can handle the Cartesian term q ∈ R and the Riemannian term v ∈ S 2 respectively. In brief, comparing with the state-of-theart researches [28], our framework can learn the multispace skills in cartesian space and 2D sphere manifold. The demonstrated human arm endpoint poses including positions and orientations can be transferred to robots simultaneously.…”