Coordinated motion design on Lie groups

2008/07/28 by Sarlette, Alain, Bonnabel, Silvère, Sepulchre, Rodolphe · 1 citation
#34H05 #93C10 #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.0807.4416

Abstract

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. This allows among others to retrieve control laws in the literature for particular examples. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3).

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