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Composing Dynamical Systems to Realize Dynamic Robotic Dancing

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Algorithmic Foundations of Robotics XI

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 107))

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Abstract

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.

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Notes

  1. 1.

    Note that the motivation for this coordinate is given by Partial Zero Dynamics as considered in [3].

  2. 2.

    Note: The construction of the PD controller defined in (7)–(10) is based on the notion that the desired angles and velocities: \((\theta ^d_\mathrm {SS},\dot{\theta }^d_\mathrm {SS}) \in \mathbb {Z}_\mathrm {SS}\).

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Correspondence to Shishir Kolathaya .

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Kolathaya, S., Ma, WL., Ames, A.D. (2015). Composing Dynamical Systems to Realize Dynamic Robotic Dancing. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_25

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_25

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