Robotics: Science and Systems XIII

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

Giorgos Mamakoukas, Malcolm MacIver, Todd Murphey

Abstract:

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.

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Bibtex:

  
@INPROCEEDINGS{Mamakoukas-RSS-17, 
    AUTHOR    = {Giorgos Mamakoukas AND Malcolm MacIver AND Todd Murphey}, 
    TITLE     = {Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2017}, 
    ADDRESS   = {Cambridge, Massachusetts}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2017.XIII.066} 
}