Composing Dynamical Systems to Realize Dynamic Robotic Dancing

This paper presents a methodology for the composition of complex dynamic behaviors in legged robots, and illustrates these concepts to experimentally achieve robotic dancing. Inspired by principles from dynamic locomotion, we begin by constructing controllers that drive a collection of virtual constraints to zero; this creates a low-dimensional representation of the bipedal robot. Given any two poses of the robot, we utilize this low-dimensional representation to connect these poses through a dynamic transition. The end result is a meta-dynamical system that describes a series of poses (indexed by the vertices of a graph) together with dynamic transitions (indexed by the edges) connecting these poses. These formalisms are illustrated in the case of dynamic dancing; a collection of ten poses are connected through dynamic transitions obtained via virtual constraints, and transitions through the graph are synchronized with music tempo. The resulting meta-dynamical system is realized experimentally on the bipedal robot AMBER 2 yielding dynamic robotic dancing.