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.

Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot’s workspace. This work presents a novel approach to learn workspace constraints from human demonstrations and to generate motion trajectories for the robot that lie in the constrained workspace. Training data are incrementally clustered into different linear subspaces and used to fit a low dimensional representation of each subspace. By considering the learned constraint subspaces as zeroing barrier functions, we are able to design a control input that keeps the system trajectory within the learned bounds. This control input is effectively combined with the original system dynamics preserving eventual asymptotic properties of the unconstrained system. Simulations and experiments on a real robot show the effectiveness of the proposed approach.

In this work, we propose a model-based and data efficient approach for reinforcement learning. The main idea of our algorithm is to combine simulated and real rollouts to efficiently find an optimal control policy. While performing rollouts on the robot, we exploit sensory data to learn a probabilistic model of the residual difference between the measured state and the state predicted by a simplified model. The simplified model can be any dynamical system, from a very accurate system to a simple, linear one. The residual difference is learned with Gaussian processes. Hence, we assume that the difference between real and simplified model is Gaussian distributed, which is less strict than assuming that the real system is Gaussian distributed. The combination of the partial model and the learned residuals is exploited to predict the real system behavior and to search for an optimal policy. Simulations and experiments show that our approach significantly reduces the number of rollouts needed to find an optimal control policy for the real system.