Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

TLDR

Nonlinear dynamical systems are widely used to model complex behaviors, but creating goal‑directed behavior is challenging because of parameter sensitivity, phase transitions, and difficulty predicting long‑term dynamics. The paper introduces dynamical movement primitives, a statistical‑learning framework for modeling attractor behaviors in autonomous nonlinear systems, and evaluates its design principles in motor control and robotics examples. The method starts from a simple linear dynamical system and adds a learnable autonomous forcing term to produce a weakly nonlinear system with prescribed attractor dynamics. The approach can generate both point and limit‑cycle attractors of arbitrary complexity.

Abstract

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.