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.