Sparse Control for Dynamic Movement Primitives

Abstract

Abstract:This paper describes the use of spatially-sparse inputs to influence global changes in the behavior of Dynamic Movement Primitives (DMPs). The dynamics of DMPs are analyzed through the framework of contraction theory as networked hierarchies of contracting or transversely contracting systems. Within this framework, sparsely-inhibited rhythmic DMPs (SI-RDMPs) are introduced to both inhibit or enable rhythmic primitives through spatially-sparse modification of the DMP dynamics. SI-RDMPs are demonstrated in experiments to manage start-stop transitions for walking experiments with the MIT Cheetah. New analytical results on the coupling of oscillators with diverse natural frequencies are also discussed.

Convergence of Dynamical Movement Primitives with Temporal Coupling

“…is contracting. This follows directly from Proposition 2 in [13], by applying it to autonomous systems.…”

“…Stability for the original DMP framework was shown in [12], [13] by utilizing that f (x) converged to 0, which followed from the fact that x decayed exponentially, regardless of any deviation from the intended movement. However, this is true only if temporal coupling is not used, and the convergence of f (x) is less obvious for the DMP version studied in this paper.…”

“…Stability for the original DMP framework, i.e., not including temporal coupling, was concluded in [12], [13]. The aim of this paper is to provide a stability analysis for temporally coupled DMPs, as formulated in [11].…”

Dynamic Movement Primitives for moving goals with temporal scaling adaptation

“…Contraction Analysis was introduced in [20] and used in conjunction with DMP in [21] with the objective to provide a simpler method for the stability analysis of non linear dynamical systems. Instead of trying to verify point equilibrium stability, this framework tries to prove that if neighbouring state trajectories converge to each other, then all trajectories should exponentially converge to a single trajectory.…”

A Control Scheme With a Novel DMP-Robot Coupling Achieving Compliance and Tracking Accuracy Under Unknown Task Dynamics and Model Uncertainties

“…Contraction analysis provides a simple and efficient way for analyzing the stability of non-linear dynamics [14], [15]. The basic convergence principle of contracting systems states that if all neighboring trajectories converge to each other (contraction behavior) global exponential convergence to a single trajectory can then be concluded [14].…”