English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Mechanical systems naturally evolve on principal bundles describing theirinherent symmetries. The ensuing factorization of the configuration manifoldinto a symmetry group and an internal shape space has provided deep insightsinto the locomotion of many robotic and biological systems. On the other hand,the property of differential flatness has enabled efficient, effective planningand control algorithms for various robotic systems. Yet, a practical means offinding a flat output for an arbitrary robotic system remains an open question.In this work, we demonstrate surprising new connections between these twodomains, for the first time employing symmetry directly to construct a flatoutput. We provide sufficient conditions for the existence of a trivializationof the bundle in which the group variables themselves are a flat output. Wecall this a geometric flat output, since it is equivariant (i.e. maintains thesymmetry) and is often global or almost-global, properties not typicallyenjoyed by other flat outputs. In such a trivialization, the motion planningproblem is easily solved, since a given trajectory for the group variables willfully determine the trajectory for the shape variables that exactly achievesthis motion. We provide a partial catalog of robotic systems with geometricflat outputs and worked examples for the planar rocket, planar aerialmanipulator, and quadrotor.

The Role of Symmetry in Constructing Geometric Flat Outputs for Free-Flying Robotic Systems