Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors This paper introduces dynamical movement primitives (DMPs), a method for modeling attractor behaviors in autonomous nonlinear dynamical systems using statistical learning. The approach involves transforming a simple dynamical system, such as a set of linear differential equations, into a weakly nonlinear system with prescribed attractor dynamics using a learnable autonomous forcing term. Both point attractors and limit cycle attractors of arbitrary complexity can be generated. The design principle of the approach is to start with a simple system and transform it into a desired attractor system through a learnable forcing function. The system allows for the coordination of multiple degrees of freedom with arbitrary phase relationships, and guarantees the stability of the model equations. The approach also provides a metric to compare different dynamical systems in a scale-invariant and temporally invariant way. The paper discusses the theoretical properties of the approach, including its stability, invariance properties, and the ability to model both discrete and rhythmic movement patterns. The system is evaluated in the domain of motor control for robotics, where desired kinematic motor behaviors are coded in attractor landscapes and then converted into control commands with inverse dynamics controllers. Perceptual variables can be coupled back into the dynamic equations, enabling the creation of complex closed-loop motor behaviors from a relatively simple set of equations. The approach is inspired by the biological concept of motor primitives and is called dynamical movement primitives as they are seen as building blocks that can be used and modulated in real time for generating complex movements. The paper presents several example applications in motor control and robotics, including the imitation learning of discrete and rhythmic movements, online modulation with coupling terms, synchronization and entrainment phenomena, and movement recognition based on a motor generation framework. The approach is evaluated through simulations and robotic studies, demonstrating its effectiveness in modeling complex motor behaviors. The paper also discusses variations of the approach, including the use of second-order canonical systems, the use of second-order differential equations for the forcing term, and the use of two-dimensional input vectors for the forcing term. The paper concludes that the approach provides a flexible and effective method for modeling complex motor behaviors in a wide range of applications.Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors This paper introduces dynamical movement primitives (DMPs), a method for modeling attractor behaviors in autonomous nonlinear dynamical systems using statistical learning. The approach involves transforming a simple dynamical system, such as a set of linear differential equations, into a weakly nonlinear system with prescribed attractor dynamics using a learnable autonomous forcing term. Both point attractors and limit cycle attractors of arbitrary complexity can be generated. The design principle of the approach is to start with a simple system and transform it into a desired attractor system through a learnable forcing function. The system allows for the coordination of multiple degrees of freedom with arbitrary phase relationships, and guarantees the stability of the model equations. The approach also provides a metric to compare different dynamical systems in a scale-invariant and temporally invariant way. The paper discusses the theoretical properties of the approach, including its stability, invariance properties, and the ability to model both discrete and rhythmic movement patterns. The system is evaluated in the domain of motor control for robotics, where desired kinematic motor behaviors are coded in attractor landscapes and then converted into control commands with inverse dynamics controllers. Perceptual variables can be coupled back into the dynamic equations, enabling the creation of complex closed-loop motor behaviors from a relatively simple set of equations. The approach is inspired by the biological concept of motor primitives and is called dynamical movement primitives as they are seen as building blocks that can be used and modulated in real time for generating complex movements. The paper presents several example applications in motor control and robotics, including the imitation learning of discrete and rhythmic movements, online modulation with coupling terms, synchronization and entrainment phenomena, and movement recognition based on a motor generation framework. The approach is evaluated through simulations and robotic studies, demonstrating its effectiveness in modeling complex motor behaviors. The paper also discusses variations of the approach, including the use of second-order canonical systems, the use of second-order differential equations for the forcing term, and the use of two-dimensional input vectors for the forcing term. The paper concludes that the approach provides a flexible and effective method for modeling complex motor behaviors in a wide range of applications.