Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

TitleFeedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions
Publication TypeConference Paper
Year of Publication2017
AuthorsMamakoukas, G., M. A. MacIver, and T. D. Murphey
Conference NameRobotics: Science and Systems
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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